This paper investigates the problem of eventtriggered pinning control for the synchronization of networks of nonlinear dynamical agents onto a desired reference trajectory. The pinned agents are those that have access to the reference trajectory. We consider both static and switching topologies. We prove that the system is well posed and identify conditions under which the network achieves exponential convergence. A lower bound for the rate of convergence is also derived. Numerical examples demonstrating the effectiveness of the results are provided.
This paper investigates event-triggered pinning control for the synchronization of complex networks of nonlinear dynamical systems. We consider networks described by time-varying weighted graphs and featuring generic linear interaction protocols. Sufficient conditions for the absence of Zeno behavior are derived and exponential convergence of a global normed error function is proven. Static networks are considered as a special case, wherein the existence of a lower bound for interevent times is also proven. Numerical examples demonstrate the effectiveness of the proposed control strategy.
In this paper, we present a distributed algorithm for cloud-supported effective coverage of 3D structures with a network of sensing agents. The structure to inspect is abstracted into a set of landmarks, where each landmark represents a point or small area of interest, and incorporates information about position and orientation. The agents navigate the environment following the proposed control algorithm until all landmarks have reached a satisfactory level of coverage. The agents do not communicate with each other directly, but exchange data through a shared cloud repository which is accessed asynchronously and intermittently. We show formally that, under the proposed control architecture, the networked agents complete the coverage mission in finite time. The results are corroborated by simulations in ROS, and experimental evaluation is in progress.
In this paper, we present an algorithm for pose control of a team of mobile sensors for coverage and inspection applications. The region to cover is abstracted into a finite set of landmarks, and each sensor is responsible to cover some of the landmarks. The sensors progressively improve their coverage by adjusting their poses and by transferring the ownership of some landmarks to each other. Inter-sensor communication is pairwise and intermittent. The sensor team is formally modeled as a multi-agent hybrid system, and an invariance argument formally shows that the team reaches an equilibrium configuration, while a global coverage measure is improving monotonically. A numerical simulation corroborates the theoretical results.
A cloud-supported multi-agent system is composed of autonomous agents required to achieve a common coordination objective by exchanging data over a shared cloud repository. The repository is accessed asychronously by different agents, and direct inter-agent commuication is not possible. This model is motivated by the problem of coordinating a fleet of autonomous underwater vehicles, with the aim to avoid the use of expensive and power-hungry modems for underwater communication. For the case of agents with integrator dynamics, a control law and a rule for scheduling the cloud access are formally defined and proven to achieve the desired coordination. A numerical simulation corroborate the theoretical results.
This paper addresses a formation problem for a network of autonomous agents with second-order dynamics and bounded disturbances. Coordination is achieved by having the agents asynchronously upload (download) data to (from) a shared repository, rather than directly exchanging data with other agents. Well-posedness of the closed-loop system is demonstrated by showing that there exists a lower bound for the time interval between two consecutive agent accesses to the repository. Numerical simulations corroborate the theoretical results.
This paper presents a cloud-supported control algorithm for coordinated trajectory tracking of networked autonomous agents. The motivating application is the coordinated control of Autonomous Underwater Vehicles. The control objective is to have the vehicles track a reference trajectory while keeping an assigned formation. Rather than relying on inter-agent communication, which is interdicted underwater, coordination is achieved by letting the agents intermittently access a shared information repository hosted on a cloud. An event-based law is proposed to schedule the accesses of each agent to the cloud. We show that, with the proposed scheduling of the cloud accesses, the agents achieve the required coordination objective. Numerical simulations corroborate the theoretical results.
This paper investigates a multi-agent formation control problem with event-triggered control updates and additive disturbances. The agents communicate only by exchanging information in a cloud repository. The communication with the cloud is considered a shared and limited resource, and therefore it is used intermittently and asynchronously by the agents. The proposed approach takes advantage of having a shared asynchronous cloud support while guaranteeing a reduced number of communication. More in detail, each agent schedules its own sequence of cloud accesses in order to achieve a coordinated network goal. A control law is given with a criterion for scheduling the control updates recursively. The closed loop scheme is proven to be effective in achieving the control objective and a numerical simulation corroborates the theoretical results.
In this article, we propose a planning algorithm for coverage of complex structures with a network of robotic sensing agents, with multi-robot surveillance missions as our main motivating application. The sensors are deployed to monitor the external surface of a 3D structure. The algorithm controls the motion of each sensor so that a measure of the collective coverage attained by the network is nondecreasing, while the sensors converge to an equilibrium configuration. A modified version of the algorithm is also provided to introduce collision avoidance properties. The effectiveness of the algorithm is demonstrated in a simulation and validated experimentally by executing the planned paths on an aerial robot.
We describe a recurrent neural network (RNN) based architecture to learn the flow function of a causal, time-invariant and continuous-time control system from trajectory data. By restricting the class of control inputs to piecewise constant functions, we show that learning the flow function is equivalent to learning the input-to-state map of a discrete-time dynamical system. This motivates the use of an RNN together with encoder and decoder networks which map the state of the system to the hidden state of the RNN and back. We show that the proposed architecture is able to approximate the flow function by exploiting the system's causality and time-invariance. The output of the learned flow function model can be queried at any time instant. We experimentally validate the proposed method using models of the Van der Pol and FitzHugh-Nagumo oscillators. In both cases, the results demonstrate that the architecture is able to closely reproduce the trajectories of these two systems. For the Van der Pol oscillator, we further show that the trained model generalises to the system's response with a prolonged prediction time horizon as well as control inputs outside the training distribution. For the FitzHugh-Nagumo oscillator, we show that the model accurately captures the input-dependent phenomena of excitability.
We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we prove that an architecture based on discrete-time recurrent neural networks universally approximates flows of continuous-time dynamical systems with inputs. The required assumptions are shown to hold for systems whose dynamics are well-behaved ordinary differential equations and with practically relevant classes of input signals. This enables the use of off-the-shelf solutions for learning such flow functions in continuous-time from sampled trajectory data.
Wireless sensors and networks are used only occasionally in current control loops in the process industry. With rapid developments in embedded and highperformance computing, wireless communication, and cloud technology, drastic changes in the architecture and operation of industrial automation systems seem more likely than ever. These changes are driven by ever-growing demands on production quality and flexibility. However, as discussed in "Summary," there are several research obstacles to overcome. The radio communication environment in the process industry is often troublesome, as the environment is frequently cluttered with large metal objects, moving machines and vehicles, and processes emitting radio disturbances [1], [2]. The successful deployment of a wireless control system in such an environment requires careful design of communication links and network protocols as well as robust and reconfigurable control algorithms.
As a first step towards developing efficient building energy management techniques, in this paper, we first study the energy consumption patterns of heating, ventilation and cooling (HVAC) systems across the KTH Royal Institute of Technology campus and we identify some possible areas where energy consumption can be made less wasteful. Later, we describe a test-bed where wireless sensor networks are used to collect data and eventually control the HVAC system in a distributed way. We present some of the data, temperature, humidity, and CO2 measurements, that are collected by the aforementioned network and compare them with the measurements collected by the legacy sensors already in place. In the end we present a preliminary result on modelling the dynamics of the temperature, humidity, and CO2 using the data gather by the sensor network. We check the validity of the model via comparing the out put of the system with measured data. As a future work we identify the possibility of using the models obtained here for model based control, and fault detection and isolation techniques.
Vehicle platooning has become important for the vehicle industry. Yet conclusive results with respect to the fuel reduction possibilities of platooning remain unclear. The focus in this study is the fuel reduction that heavy duty vehicle platooning enables and the analysis with respect to the influence of a commercial adaptive cruise control on the fuel consumption. Experimental results show that by using preview information of the road ahead from the lead vehicle, the adaptive cruise controller can reduce the fuel consumption. A study is undertaken for various masses of the lead vehicle. The results show that the best choice with respect to a heavier or lighter lead vehicle depends on the desired time gap. A maximum fuel reduction of 4.7-7.7% depending on the time gap, at a set speed of 70 km/h, can be obtained with two identical trucks. If the lead vehicle is 10 t lighter a corresponding 3.8-7.4% fuel reduction can be obtained depending on the time gap. Similarly if the lead vehicle is 10 t heavier a 4.3-6.9% fuel reduction can be obtained. All results indicate that a maximum fuel reduction can be achieved at a short relative distance, due to both air drag reduction and suitable control.
It is fuel efficient to minimize the relative distance between vehicles to achievea maximum reduction in air drag. However, the relative distance can only be reduced to acertain extent without endangering a collision. Factors such as the vehicle velocity, the relativevelocity, and the characteristics of the vehicle ahead has a strong impact on what minimumrelative distance can be obtained. In this paper, we utilize optimal control and game theory toestablish safety criteria for heavy duty vehicle platooning applications. The derived results showthat a minimum relative distance of 1.2m can be obtained for two identical vehicles withoutendangering a collision, assuming that there is no delay present in the feedback system. If aworst case delay is present in the system, a minimum relative distance is deduced based uponthe vehicle’s maximum deceleration ability. The relative distance can be reduced if the followervehicle has a greater overall braking capability, which suggests that vehicle heterogeneity andorder has substantial impact. The findings are verified by simulations and the main conclusion isthat the relative distance utilized in commercial applications today can be reduced significantlywith a suitable advanced cruise control system.
The current system of global trade is largely based on transportation and communication technology from the 20th century. Advances in technology have led to an increasingly interconnected global market and reduced the costs of moving goods, people, and technology around the world [1]. Transportation is crucial to society, and the demand for transportation is strongly linked to economic development. Specifically, road transportation is essential since about 60% of all surface freight transportation (which includes road and rail transport) is done on roads [2]. Despite the important role of road freight transportation in the economy, it is facing serious challenges, such as those posed by increasing fuel prices and the need to reduce greenhouse gas emissions. On the other hand, the integration of information and communication technologies to transportation systems-leading to intelligent transportation systems-enables the development of cooperative methods to enhance the safety and energy efficiency of transportation networks. This article focuses on one such cooperative approach, which is known as platooning. The formation of a group of heavy-duty vehicles (HDVs) at close intervehicular distances, known as a platoon (see Figure 1) increases the fuel efficiency of the group by reducing the overall air drag. The safe operation of such platoons requires the automatic control of the velocity of the platoon vehicles as well as their intervehicular distance. Existing work on platooning has focused on the design of controllers for these longitudinal dynamics, in which simple vehicle models are typically exploited and perfect environmental conditions, such as flat roads, are generally assumed. The broader perspective of how platooning can be effectively exploited in a freight transportation system has received less attention. Moreover, experimental validations of the fuel-saving potential offered by platooning have typically been performed by reproducing the perfect conditions as assumed in the design of the automatic controllers. This article focuses on these two aspects by addressing the following two objectives.
In this paper, we consider the problem of finding a safety criteria between neighboring heavy duty vehicles traveling in a platoon. We present a possible framework for analyzing safety aspects of heavy duty vehicle platooning. A nonlinear underlying dynamical model is utilized, where the states of two neighboring vehicles are conveyed through radar information and wireless communication. Numerical safe sets are derived through the framework, under a worst-case scenario, and the minimum safe spacing is studied for heterogenous platoons. Real life experimental results are presented in an attempt to validate the theoretical results in practice. The findings show that a minimum relative distance of 1.2 m at maximum legal velocity on Swedish highways can be maintained for two identical vehicles without endangering a collision. The main conclusion is that the relative distance utilized in commercial applications today can be reduced significantly with a suitable automatic control system.
We consider suboptimal decentralized controllerdesign for subsystems with interconnected dynamics and costfunctions. A systematic design methodology is presented overthe class of linear quadratic regulators (LQR) for chain graphs.The methodology is evaluated on heavy duty vehicle platooningwith physical constraints. A simulation and frequency analysisis performed. The results show that the decentralized controllergives good tracking performance and a robust system. We alsoshow that the design methodology produces a string stablesystem for an arbitrary number of vehicles in the platoon, ifthe vehicle configurations and the LQR weighting parametersare identical for the considered subsystems.
In this paper, we consider the problem of finding decentralized controllers for heavy-duty vehicle (HDV) platooning by establishing empiric results for a qualitative verification of a control design methodology. We present a linear quadratic control framework for the design of a high-level cooperative platooning controller suitable for modern HDVs. A nonlinear low-level dynamical model is utilized, where realistic response delays in certain modes of operation are considered. The controller performance is evaluated through numerical and experimental studies. It is concluded that the proposed controller behaves well in the sense that experiments show that it allows for short time headways to achieve fuel efficiency, without compromising safety. Simulation results indicate that the model mimics real life behavior. Experiment results show that the dynamic behavior of the platooning vehicles depends strongly on the gear switching logic, which is confirmed by the simulation model. Both simulation and experiment results show that the third vehicle never displays a bigger undershoot than its preceding vehicle. The spacing errors stay bounded within 6.8. m in the simulation results and 7.2. m in the experiment results for varying transient responses. Furthermore, a minimum spacing of -0.6. m and -1.9. m during braking is observed in simulations and experiments, respectively. The results indicate that HDV platooning can be conducted at close spacings with standardized sensors and control units that are already present on commercial HDVs today.
Vehicle platooning has become important for thevehicle industry. Yet conclusive results with respect to thefuel reduction possibilities of platooning remain unclear, inparticular when considering constraints imposed by the topography.The focus of this study is to establish whether itis more fuel-efficient to maintain or to split a platoon that isfacing steep uphill and downhill segments. Two commercialcontrollers, an adaptive cruise controller and a look-aheadcruise controller, are evaluated and alternative novel controlstrategies are proposed. The results show that an improvedfuel-efficiency can be obtained by maintaining the platoonthroughout a hill. Hence, a cooperative control strategy basedon preview information is presented, which initiates the changein velocity at a specific point in the road for all vehiclesrather than simultaneously changing the velocity to maintainthe spacing. A fuel reduction of up to 14% can be obtainedover a steep downhill segment and a more subtle benefit of0.7% improvement over an uphill segment with the proposedcontroller, compared to the combination of the commerciallyavailable cruise controller and adaptive cruise controller thatcould be used for platooning. The findings show that it isboth fuel-efficient and desirable in practice to consider previewinformation of the topography in the control strategy.
We propose a method to perform set-based state estimation of an unknown dynamical linear system using a data-driven set propagation function. Our method comes with set-containment guarantees, making it applicable to safety-critical systems. The method consists of two phases: (1) an offline learning phase where we collect noisy input-output data to determine a function to propagate the state-set ahead in time; and (2) an online estimation phase consisting of a time update and a measurement update. It is assumed that known finite sets bound measurement noise and disturbances, but we assume no knowledge of their statistical properties. These sets are described using zonotopes, allowing efficient propagation and intersection operations. We propose a new approach to compute a set of models consistent with the data and noise-bound, given input-output data in the offline phase. The set of models is utilized in replacing the unknown dynamics in the data-driven set propagation function in the online phase. Then, we propose two approaches to perform the measurement update. Simulations show that the proposed estimator yields state sets comparable in volume to the 3 sigma confidence bounds obtained by a Kalman filter approach, but with the addition of state set-containment guarantees. We observe that using constrained zonotopes yields smaller sets but with higher computational costs than unconstrained ones.
The set-based estimation has gained a lot of attention due to its ability to guarantee state enclosures for safety-critical systems. However, collecting measurements from distributed sensors often requires out-sourcing the set-based operations to an aggregator node, raising many privacy concerns. To address this problem, we present set-based estimation protocols using partially homomorphic encryption that pre-serve the privacy of the measurements and sets bounding the estimates. We consider a linear discrete-time dynamical system with bounded modeling and measurement uncertainties. Sets are represented by zonotopes and constrained zonotopes as they can compactly represent high-dimensional sets and are closed under linear maps and Minkowski addition. By selectively encrypting parameters of the set repre-sentations, we establish the notion of encrypted sets and intersect sets in the encrypted domain, which enables guaranteed state estimation while ensuring privacy. In particular, we show that our protocols achieve computational privacy using the cryptographic notion of computational indistinguishability. We demonstrate the efficiency of our approach by localizing a real mobile quadcopter using ultra-wideband wireless devices.
A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XORing a binary vector with a combination of other binary vectors called generators. Such a zonotope can represent up to 2γ binary vectors using only γ generators. It is shown that logical operations over sets of binary vectors can be performed on the zonotopes' generators and, thus, significantly reduce the computational complexity of various logical operations (e.g., XOR, NAND, AND, OR, and semi-tensor products). Similar to traditional zonotopes' role in the formal verification of dynamical systems over real vector spaces, logical zonotopes can efficiently analyze discrete dynamical systems defined over binary vector spaces. We illustrate the approach and its ability to reduce the computational complexity in two use cases: (1) encryption key discovery of a linear feedback shift register and (2) safety verification of a road traffic intersection protocol.
This paper presents algorithms for performingdata-driven reachability analysis under temporal logic sideinformation. In certain scenarios, the data-driven reachablesets of a robot can be prohibitively conservative due to theinherent noise in the robot’s historical measurement data. Inthe same scenarios, we often have side information about therobot’s expected motion (e.g., limits on how much a robotcan move in a one-time step) that could be useful for furtherspecifying the reachability analysis. In this work, we showthat if we can model this side information using a signaltemporal logic (STL) fragment, we can constrain the datadriven reachability analysis and safely limit the conservatismof the computed reachable sets. Moreover, we provide formalguarantees that, even after incorporating side information, thecomputed reachable sets still properly over-approximate therobot’s future states. Lastly, we empirically validate the practicality of the over-approximation by computing constrained,data-driven reachable sets for the Small-Vehicles-for-Autonomy(SVEA) hardware platform in two driving scenarios.
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and, under the assumption of Lipschitz continuity, to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and comparisons are made between algorithms.
In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a data-driven reachability analysis approach from noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for Lipschitz nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.
This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the system's state in real-time. Although the system is assumed to be a polynomial type, the exact polynomial functions, and their coefficients are assumed to be unknown. To this end, the estimator relies on offline and online phases. The offline phase utilizes past input-output data to estimate a set of possible coefficients of the polynomial system. Then, using this estimated set of coefficients and the side information about the system, the online phase provides a set estimate of the state. Finally, the proposed methodology is evaluated through its application on SIR (Susceptible, Infected, Recovered) epidemic model.
We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion step, which decreases the estimation errors and the size of estimated sets, and can be seen as a lightweight approach to achieve partial consensus between the distributed estimated sets. Every node shares its measurement with its neighbor in the measurement update step. In the diffusion step, the neighbors intersect their estimated sets using our novel lightweight zonotope intersection technique. A localization example demonstrates the applicability of our algorithms.
We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive con-trol, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.
This paper deals with the consensus problem under network induced communication delays. It is well-known that introducing a delay generally leads to a reduce of the performance or to instability. Thus, investigating the impact of time-delays in the consensus problem is an important issue. Another important issue is to obtain an estimate of the convergence rate, which is not straightforward when delays appear in the network. In this paper, the agents are modelled as double integrator systems. It is assumed that each agent receives instantaneously its own output information but receives the information from its neighbors after a constant delay. A stability criterion is provided based on Lyapunov-Krasovskii techniques and is expressed in terms of LMI. An expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval is derived. The results are supported through several simulations for different network symmetric communication schemes.
This paper studies the design and real-time implementation of an event-triggered controller for a nonlinear 3D tower crane where the communication between the controller and the actuators is performed over a low-power wireless network. A flexible Event-Generation Circuit (EGC) is proposed in order to implement event-driven controllers for Networked Control Systems. Furthermore, a detailed experimental analysis on the performance of the event-triggered controller and the influence of packet losses on the transmitted actuation messages are presented. The results show that the event-triggered controllers in networked control systems are able to maintain the same level of performance as compared to periodic controllers, while increasing the sensors/actuators lifetime by reducing network bandwidth utilization.
A hybrid control scheme is proposed for the stabilization of backward driving along simple paths for a miniature vehicle composed of a truck and a two-axle trailer. When reversing, the truck and trailer can be modelled as an unstable nonlinear system with state and input saturations. Due to these constraints the system is impossible to globally stabilize with standard smooth control techniques, since some initial states necessarily lead to that the so called jack-knife locks between the truck and the trailer. The proposed hybrid control method, which combines backward and forward motions, provide a global attractor to the desired reference trajectory. The scheme has been implemented and successfully evaluated on a radio-controlled vehicle. Results from experimental trials are reported.
We propose a mathematical framework, inspired by the WirelessHART specification, for modeling and analysing multi-hop communication networks. The framework is designed for systems consisting of multiple control loops closed over a multi-hop communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system. The main technical contribution of the paper is an explicit translation of multi-hop control networks to switched systems. We describe a Mathematica notebook that automates the translation of multihop control networks to switched systems, and use this tool to show how techniques for analysis of switched systems can be used to address control and networking co-design challenges.
We propose a mathematical framework for modeling and analyzing multi-hop control networks designed for systems consisting of multiple control loops closed over a multi-hop (wireless) communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system, providing an explicit translation of multi-hop control networks to switched systems. We propose formal models for analyzing robustness of multi-hop control networks, where data is exchanged through a multi-hop communication network subject to disruptions. When communication disruptions are long, compared to the speed of the control system, we propose to model them as permanent link failures. We show that the complexity of analyzing such failures is NP-hard, and discuss a way to overcome this limitation for practical cases using compositional analysis. For typical packet transmission errors, we propose a transient error model where links fail for one time slot independently of the past and of other links. We provide sufficient conditions for almost sure stability in presence of transient link failures, and give efficient decision procedures. We deal with errors that have random time span and show that, under some conditions, the permanent failure model can be used as a reliable abstraction. Our approach is compositional, namely it addresses the problem of designing scalable scheduling and routing policies for multiple control loops closed on the same multi-hop control network. We describe how the translation of multi-hop control networks to switched systems can be automated, and use it to solve control and networking co-design challenges in some representative examples, and to propose a scheduling solution in a mineral floatation control problem that can be implemented on a time triggered communication protocols for wireless networks.
The increasing demand for wireless cyber-physical systems requires correct design, implementation and validation of computation, communication and control methods. Traditional simulation tools, which focus on either computation, communication or control, are insufficient when the three aspects interact. Efforts to extend the traditional tools to cover multiple domains, e.g., from simulating only control aspects to simulating both control and communication, often rely on simplistic models of a small subset of possible communication solutions. We introduce GISOO, a virtual testbed for simulation of wireless cyber-physical systems that integrates two state-of-the art simulators, Simulink and COOJA. GISOO enables users to evaluate actual embedded code for the wireless nodes in realistic cyber-physical experiments, observing the effects of both the control and communication components. In this way, a wide range of communication solutions can be evaluated without developing abstract models of their control-relevant aspects, and changes made to the networking code in simulations is guaranteed to be translated into production code without errors. A double-tank laboratory experimental setup controlled over a multi-hop relay wireless network is used to validate GISOO and demonstrate its features.
After a general introduction of the VIKING EU FP7 project two specific cyber-attack mechanisms, which have been analyzed in the VIKING project, will be discussed in more detail. Firstly an attack and its consequences on the Automatic Generation Control (AGC) in a power system are investigated, and secondly the cyber security of State Estimators in SCADA systems is scrutinized.
In this work we have analyzed the effectsof correlated failures of power lines on the total systemload shed. The total system load shed is determined bysolving the optimal load shedding problem, which is thesystem operator’s best response to a system failure.We haveintroduced a Monte Carlo based simulation framework forestimating the statistics of the system load shed as a functionof stochastic network parameters, and provide explicitguarantees on the sampling accuracy. This framework hasbeen applied to a 470 bus model of the Nordic power systemand a correlated Bernoulli failure model. It has been foundthat increased correlations between Bernoulli failures ofpower lines can dramatically increase the expected valueas well as the variance of the system load shed.
This paper analyzes a class of nonlinear consensus algorithms where the input of an agent can be decoupled into a product of a gain function of the agents own state, and a sum of interaction functions of the relative states of its neighbors. We prove the stability of the protocol for both single and double integrator dynamics using novel Lyapunov functions, and provide explicit formulas for the consensus points. The results are demonstrated through simulations of a realistic example within the framework of our proposed consensus algorithm.
This paper considers a distributed control algorithm for frequency control of electrical power systems. We propose a distributed controller which retains the reference frequency of the buses under unknown load changes, while asymptotically minimizing a quadratic cost of power generation. For comparison, we also propose a centralized controller which also retains the reference frequency while minimizing the same cost of power generation. We derive sufficient stability criteria for the parameters of both controllers. The controllers are evaluated by simulation on the IEEE 30 bus test network, where their performance is compared.
High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper a distributed controller for multi-terminal high-voltage direct current (MTDC) transmission systems is considered. Sufficient conditions for when the proposed controller renders the closed-loop system asymptotically stable are provided. Provided that the closed loop system is asymptotically stable, it is shown that in steady-state a weighted average of the deviations from the nominal voltages is zero. Furthermore, a quadratic cost of the current injections is minimized asymptotically.
High-voltage direct current (HVDC) is a commonly used technology for long-distance electric power transmission, mainly due to its low resistive losses. In this paper the voltagedroop method (VDM) is reviewed, and three novel distributed controllers for multi-terminal HVDC (MTDC) transmission systems are proposed. Sufficient conditions for when the proposed controllers render the closed-loop system asymptotically stable are provided. These conditions give insight into suitable controller architecture, e.g., that the communication graph should be identical with the graph of the MTDC system, including edge weights. Provided that the closed-loop systems are asymptotically stable, it is shown that the voltages asymptotically converge to within predefined bounds. Furthermore, a quadratic cost of the injected currents is asymptotically minimized. The proposed controllers are evaluated on a four-bus MTDC system.
This paper considers a distributed PI-controller for networked dynamical systems. Sufficient conditions for when the controller is able to stabilize a general linear system and eliminate static control errors are presented. The proposed controller is applied to frequency control of power transmission systems. Sufficient stability criteria are derived, and it is shown that the controller parameters can always be chosen so that the frequencies in the closed loop converge to nominal operational frequency. We show that the load sharing property of the generators is maintained, i.e., the input power of the generators is proportional to a controller parameter. The controller is evaluated by simulation on the IEEE 30 bus test network, where its effectiveness is demonstrated.
This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.
High-voltage direct current (HVDC) is a commonly used technology for long-distance power transmission, due to its low resistive losses and low costs. In this paper, a novel distributed controller for multi-terminal HVDC (MTDC) systems is proposed. Under certain conditions on the controller gains, it is shown to stabilize the MTDC system. The controller is shown to always keep the voltages close to the nominal voltage, while assuring that the injected power is shared fairly among the converters. The theoretical results are validated by simulations, where the affect of communication time-delays is also studied.
This paper analyzes distributed proportional-integral controllers. We prove that integral action can be successfully applied to consensus algorithms, where attenuation of static disturbances is achieved. These control algorithms are applied to decentralized frequency control of electrical power systems. We show that the proposed algorithm can attenuate step disturbances of power loads. We provide simulations of the proposed control algorithm on the IEEE 30 bus test system that demonstrate its efficiency.
We consider frequency control of synchronous generator networks and study transient performance under both primary and secondary frequency control. We model random step changes in power loads and evaluate performance in terms of expected deviations from a synchronous frequency over the synchronization transient; what can be thought of as lack of frequency coherence. We compare a standard droop control strategy to two secondary proportional integral (PI) controllers: centralized averaging PI control (CAPI) and distributed averaging PI control (DAPI). We show that the performance of a power system with DAPI control is always superior to that of a CAPI controlled system, which in turn has the same transient performance as standard droop control. Furthermore, for a large class of network graphs, performance scales unfavorably with network size with CAPI and droop control, which is not the case with DAPI control. We discuss optimal tuning of the DAPI controller and describe how internodal alignment of the integral states affects performance. Our results are demonstrated through simulations of the Nordic power grid.
In this paper, we compare the transient performance of a multi-terminal high-voltage DC (MTDC) grid equipped with a slack bus for voltage control to that of two distributed control schemes: A standard droop controller and a distributed averaging proportional-integral (DAPI) controller. We evaluate performance in terms of an ℋ2 metric that quantifies expected deviations from nominal voltages, and show that the transient performance of a droop or DAPI controlled MTDC grid is always superior to that of an MTDC grid with a slack bus. In particular, by studying systems built up over lattice networks, we show that the ℋ2 norm of a slack bus controlled system may scale unboundedly with network size, while the norm remains uniformly bounded with droop or DAPI control. We simulate the control strategies on radial MTDC networks to demonstrate that the transient performance for the slack bus controlled system deteriorates significantly as the network grows, which is not the case with the distributed control strategies.
In this paper we propose a distributed dynamic controller for sharing frequency control reserves of asynchronous AC systems connected through a multi-terminal HVDC (MTDC) grid. We derive sufficient stability conditions, which guarantee that the frequencies of the AC systems converge to the nominal frequency. Simultaneously, the global quadratic cost of power generation is minimized, resulting in an optimal distribution of generation control reserves. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal voltages. The proposed controller is tested on a high-order dynamic model of a power system consisting of asynchronous AC grids, modelled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation.