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  • 1.
    Axehill, Daniel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindqvist, Kristian
    Scania.
    Adaptive Cruise Control for Heavy Vehicles2004In: Proceedings of Reglermöte 2004, 2004Conference paper (Other academic)
    Abstract [en]

    An Adaptive Cruise Controller (ACC) is an extension of an ordinary cruise controller. In addition to maintaining a desired set speed, an ACC can also maintain a desired time gap to the vehicle ahead. For this end, both the engine and the brakes are controlled. The interest in the MPC-controller as a solution to the problem was to achieve automatic actuator switching, thus with no explicitly defined switch points. The MPC-controller is based on a model of the system including bounds on the control signals and on linear combinations of the states. Using this knowledge, the MPC-controller will choose the correct actuator for the current driving situation. Among the drawbacks, it can be mentioned that the variant of MPC, used in this paper, is too complex to implement in the control system currently used in trucks.

  • 2.
    Gerdin, Markus
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering2006In: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, p. 6630-6635Conference paper (Refereed)
    Abstract [en]

    Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.

  • 3.
    Gerdin, Markus
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Nonlinear Stochastic Differential-Algebraic Equations with Application to Particle Filtering2007Report (Other academic)
    Abstract [en]

    Differential-algebraic equation (DAE) models naturally arise when modeling physical systems from first principles. To be able to use such models for state estimation procedures such as particle filtering, it is desirable to include a noise model. This paper discusses well-posedness of differential-algebraic equations with noise models, here denoted stochastic differential-algebraic equations. Since the exact conditions are rather involved, approximate implementation methods are also discussed. It is also discussed how a particle filter can be implemented for DAE models, and how the approximate implementation methods can be used for particle filtering. Finally, the particle filtering methods are exemplified by implementation of a particle filter for a DAE model.

  • 4.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hamilton-Jacobi Equations for Nonlinear Descriptor Systems2006In: Proceedings of the 2006 American Control Conference, 2006, p. 1027-1031Conference paper (Refereed)
    Abstract [en]

    Optimal control problems for nonlinear descriptor systems are considered. Anapproach where the descriptor system is conceptually reduced to a state spaceform is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approches.

  • 5.
    Glad, Torkel
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hamilton-Jacobi Equations for Nonlinear Descriptor Systems2005Report (Other academic)
    Abstract [en]

    Optimal control problems for nonlinear descriptor systems are considered. Anapproach where the descriptor system is conceptually reduced to a state spaceform is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approches.

  • 6.
    Isaksson, Alf
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Corp Research, Sweden.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering. Volvo Construct Equipment, Sweden.
    Tornqvist, David
    SenionLab AB, S-58330 Linkoping, Sweden.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Kok, Manon
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
    Using horizon estimation and nonlinear optimization for grey-box identification2015In: Journal of Process Control, ISSN 0959-1524, E-ISSN 1873-2771, Vol. 30, p. 69-79Article in journal (Refereed)
    Abstract [en]

    An established method for grey-box identification is to use maximum-likelihood estimation for the nonlinear case implemented via extended Kalman filtering. In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that, in the linear case, horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. For the nonlinear case two special cases are presented where the bias correction can be determined without approximation. A procedure how to approximate the bias correction for general nonlinear systems is also outlined. (C) 2015 Elsevier Ltd. All rights reserved.

  • 7.
    Isaksson, Alf
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology. ABB AB, Sweden.
    Törnqvist, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Grey-Box Identification Based on Horizon Estimation and Nonlinear Optimization2009In: Proceedings of the 41st ISCIE International Symposium on Stochastic Systems, Institute of Systems, Control and Information Engineers , 2009, p. 1-6Conference paper (Refereed)
    Abstract [en]

    In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. A procedure how to approximate the bias correction for nonlinear systems is outlined.

  • 8.
    Isaksson, Alf
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Törnqvist, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Ljung, Lennart
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Grey-Box Identification Based on Horizon Estimation and Nonlinear Optimization2010Report (Other academic)
    Abstract [en]

    In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. A procedure how to approximate the bias correction for nonlinear systems is outlined.

  • 9.
    Karlsson, Rickard
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Törnqvist, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hol, Jeroen
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Positioning and Control of an Unmanned Aerial Vehicle2006In: Proceedings of the 2nd International CDIO Conference and Collaborators' Meeting, 2006Conference paper (Refereed)
    Abstract [en]

    In the CDIO-project course in Automatic Control, an Autonomous Unmanned Aerial vehicle (UAV) is constructed, utilizing an existing radio controlled model aircraft. By adding an inertial sensor measuring acceleration and rotation, together with a Global Positioning System (GPS) sensor, the aim is to construct an accurate positioning system. This is used by an on board computer to calculate rudder control signals to a set of DC-servos in order to follow a predefined way-point trajectory. The project involves 17 students, which is roughly three times as big as previous projects, and it comprises both positioning, control, and hardware design. Since the project is still ongoing some preliminary results and conclusions are presented.

  • 10.
    Karlsson, Rickard
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Törnqvist, David
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hol, Jeroen
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Hansson, Anders
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Positioning and Control of an Unmanned Aerial Vehicle2006Report (Other academic)
    Abstract [en]

    In the CDIO-project course in Automatic Control, an Autonomous Unmanned Aerial vehicle (UAV) is constructed, utilizing an existing radio controlled model aircraft. By adding an inertial sensor measuring acceleration and rotation, together with a Global Positioning System (GPS) sensor, the aim is to construct an accurate positioning system. This is used by an on board computer to calculate rudder control signals to a set of DC-servos in order to follow a predefined way-point trajectory. The project involves 17 students, which is roughly three times as big as previous projects, and it comprises both positioning, control, and hardware design. Since the project is still ongoing some preliminary results and conclusions are presented.

  • 11.
    Linder, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Enqvist, Martin
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Gustafsson, Fredrik
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Identifiability of physical parameters in systems with limited sensors2014In: Proceedings of the 19th IFAC World Congress, 2014, p. 6454-6459Conference paper (Refereed)
    Abstract [en]

    In this paper, a method for estimating physical parameters using limited sensors is investigated. As a case study, measurements from an IMU are used for estimating the change in mass and the change in center of mass of a ship. The roll motion is studied and an instrumental variable method estimating the parameters of a transfer function from the tangential acceleration to the angular velocity is presented. It is shown that only a subset of the unknown parameters are identifiable simultaneously. A multi-stage identification approach is presented as a remedy for this. A limited simulation study is also presented to show the properties of the estimator. This shows that the method is indeed promising but that more work is needed to reduce the variance of the estimator.

  • 12.
    Linder, Jonas
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindkvist, Simon
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Two-Step Framework for Interactive Multi-Objective Optimization2012Report (Other academic)
    Abstract [en]

    In many real-world optimization applications there are often a number of conflicting objective functions that are all important to optimize. The purpose of multiobjective optimization (MOO) is to give the decision maker(DM) an understanding of how these functions are conflicting and the possibility to choose an appropriate trade-off between them. There are multiple methods for solving MOO problems but the focus in this paper is on interactive methods. When the size and complexity of the MOO problem grows the time needed to find a solution is too long to yield a pleasant experience for the DM. In this paper, a method to replace the original MOO problem with an approximation is suggested to speed up the process. The approximation is created and used in a two-step framework which makes it possible to investigate the Pareto frontier in real-time and that can handle nonlinear and non-convex MOO problems with m objective functions. The first step generates a number of samples of the complete Pareto frontier which is sparse but dense enough for the approximation. The second stepis an interactive tool for the DM to use to continuously and in real-time navigate on the approximated Pareto set in both objective- and decision space. The tool is used to investigate the Pareto frontier and to find a preferred solution. A method of decomposing the approximated set into simplices has been developed using Delaunay triangulation. This methodis able to make a good approximation for sets that are non-convex. The method is also able to handle disconnected sets and holes. This makes it possible to change the feasible region in both decision- and objective space. The framework is demonstrated on three example problems that show the functionality and performance of the implemented framework.

  • 13.
    Liu, Bin
    et al.
    ABB Corp Research Centre, Sweden.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
    Laiho, Antti
    ABB, Finland.
    Optimization-based radial active magnetic bearing controller design and verification for flexible rotors2016In: Proceedings of the Institution of mechanical engineers. Part I, journal of systems and control engineering, ISSN 0959-6518, E-ISSN 2041-3041, Vol. 230, no 4, p. 339-351Article in journal (Refereed)
    Abstract [en]

    Engineering costs, especially cost for controller design, are substantial and obstruct active magnetic bearings for broader industrial applications. An optimization-based active magnetic bearing controller design method is developed to solve this problem. Optimization criteria are selected to describe active magnetic bearing practical performance. Controller components are chosen considering that the parameters can be manually interpreted and modified on-site for commissioning. A multi-objective optimization toolbox can be used to tune the controller parameters automatically by minimizing the optimization criteria. The method has been verified within a controller design process for an active magnetic bearing levitated machine. With this method, engineering effort for controller design can be reduced significantly.

  • 14.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Computation of Upper Bound on the L2-gain for Polynomial Differential-Algebraic Systems, using Sum of Squares Decomposition2007Report (Other academic)
  • 15.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Descriptor Systems and Control Theory2005Report (Other academic)
    Abstract [en]

    This report is a brief survey over different concepts and methods concerning singular systems. Singular system is also called differential algebraic equations (DAE) since a DAE model may involve both differential and algebraic equations. There is an growing interest in DAE systems much depending on the increased usage of object oriented modeling languages, like Modelica, in the modeling of dynamical systems. These programs often give DAE models as result. Another advantage of DAE models is that they sometimes can keep the natural structure of the dynamical model.

  • 16.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Optimal Control and Model Reduction of Nonlinear DAE Models2008Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, different topics for models that consist of both differential and algebraic equations are studied. The interest in such models, denoted DAE models, have increased substantially during the last years. One of the major reasons is that several modern object-oriented modeling tools used to model large physical systems yield models in this form. The DAE models will, at least locally, be assumed to be described by a decoupled set of ordinary differential equations and purely algebraic equations. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general DAE models to satisfy this assumption.

    One of the topics considered in this thesis is optimal feedback control. For state-space models, it is well-known that the Hamilton-Jacobi-Bellman equation (HJB) can be used to calculate the optimal solution. For DAE models, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation has an extra term in order to incorporate the algebraic equations, and it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations.

    A problem when using the HJB to find the optimal feedback law is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. For analytic nonlinear time-invariant state-space models, this problem was solved in the 1960's, and in the 1970's the time-varying case was solved as well. In both cases, the optimal solution is described by convergent power series. In this thesis, both of these results are extended to analytic DAE models.

    Usually, the power series solution of the optimal feedback control problem consists of an infinite number of terms. In practice, an approximation with a finite number of terms is used. A problem is that for certain problems, the region in which the approximate solution is accurate may be small. Therefore, another parametrization of the optimal solution, namely rational functions, is studied. It is shown that for some problems, this parametrization gives a substantially better result than the power series approximation in terms of approximating the optimal cost over a larger region.

    A problem with the power series method is that the computational complexity grows rapidly both in the number of states and in the order of approximation. However, for DAE models where the underlying state-space model is control-affine, the computations can be simplified. Therefore, conditions under which this property holds are derived.

    Another major topic considered is how to include stochastic processes in nonlinear DAE models. Stochastic processes are used to model uncertainties and noise in physical processes, and are often an important part in for example state estimation. Therefore, conditions are presented under which noise can be introduced in a DAE model such that it becomes well-posed. For well-posed models, it is then discussed how particle filters can be implemented for estimating the time-varying variables in the model.

    The final topic in the thesis is model reduction of nonlinear DAE models. The objective with model reduction is to reduce the number of states, while not affecting the input-output behavior too much. Three different approaches are studied, namely balanced truncation, balanced truncation using minimization of the co-observability function and balanced residualization. To compute the reduced model for the different approaches, a method originally derived for nonlinear state-space models is extended to DAE models.

  • 17.
    Sjöberg, Johan
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Some Results On Optimal Control for Nonlinear Descriptor Systems2006Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, optimal feedback control for nonlinear descriptor systems is studied. A descriptor system is a mathematical description that can include both differential and algebraic equations. One of the reasons for the interest in this class of systems is that several modern object-oriented modeling tools yield system descriptions in this form. Here, it is assumed that it is possible to rewrite the descriptor system as a state-space system, at least locally. In theory, this assumption is not very restrictive because index reduction techniques can be used to rewrite rather general descriptor systems to satisfy this assumption.

    The Hamilton-Jacobi-Bellman equation can be used to calculate the optimal feedback control for systems in state-space form. For descriptor systems, a similar result exists where a Hamilton-Jacobi-Bellman-like equation is solved. This equation includes an extra term in order to incorporate the algebraic equations. Since the assumptions made here make it possible to rewrite the descriptor system in state-space form, it is investigated how the extra term must be chosen in order to obtain the same solution from the different equations.

    A problem when computing the optimal feedback law using the Hamilton-Jacobi-Bellman equation is that it involves solving a nonlinear partial differential equation. Often, this equation cannot be solved explicitly. An easier problem is to compute a locally optimal feedback law. This problem was solved in the 1960's for analytical systems in state-space form and the optimal solution is described using power series. In this thesis, this result is extended to also incorporate descriptor systems and it is applied to a phase-locked loop circuit.

    In many situations, it is interesting to know if a certain region is reachable using some control signal. For linear time-invariant state-space systems, this information is given by the controllability gramian. For nonlinear state-space systems, the controllabilty function is used instead. Three methods for calculating the controllability function for descriptor systems are derived in this thesis. These methods are also applied to some examples in order to illustrate the computational steps.

    Furthermore, the observability function is studied. This function reflects the amount of output energy a certain initial state corresponds to. Two methods for calculating the observability function for descriptor systems are derived. To describe one of the methods, a small example consisting of an electrical circuit is studied.

  • 18.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Findeisen, Rolf
    Otto von Guericke University Magdeburg, Germany.
    Allgower, Frank
    University of Stuttgart, Germany.
    Model Predictive Control of Continuous Time Nonlinear Differential Algebraic Systems2007In: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, 2007, p. 48-53Conference paper (Refereed)
    Abstract [en]

    This work presents a sampled-data nonlinear model predictive control scheme with guaranteed stability for differential-algebraic systems. The main challenge is the avoidance of impulsive solutions due to discontinuities in the input or its derivatives. This is guaranteed by requiring the applied input to be sufficiently smooth. Stability is guaranteed by a terminal penalty term, together with a terminal region constraint. The control scheme is illustrated considering the control of an electrical circuit.

  • 19.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Computing the Controllability Function for Nonlinear Descriptor Systems2006In: Proceedings of the 2006 American Control Conference, 2006, p. 1027-1031Conference paper (Refereed)
    Abstract [en]

    The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution.

  • 20.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Computing the Controllability Function for Nonlinear Descriptor Systems2005Report (Other academic)
    Abstract [en]

    The computation of the controllability function for nonlinear descriptor systems is considered. Three different methods are derived. The first method is based on the necessary conditions for optimality from the Hamilton-Jacobi-Bellman theory for descriptor systems. The second method uses completion of squares to find the solution. The third method gives a series expansion solution, which with a finite number of terms can serve as an approximate solution.

  • 21.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for DAE Models with a Discounted Cost2008Report (Other academic)
    Abstract [en]

    This paper considers infinite horizon optimal feedback control of nonlinear models with discounted cost. The paper includes two extensions of existing results about optimal feedback control. First, it is proven that for real analytic statespace models, a time-invariant real analytic feedback solution exists, even when the cost function includes a discount factor, provided certain regularity conditions. Second, the result is generalized to nonlinear DAE models. The feedback solution is valid in a neighborhood of the origin. In both cases, explicit formulas for the series expansions of the cost function and control law are given.

  • 22.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for DAE Models with a Discounted Cost2008In: Proceedings of the 47th IEEE Conference on Decision and Control, 2008, p. 4761-4766Conference paper (Refereed)
    Abstract [en]

    This paper considers infinite horizon optimal feedback control of nonlinear models with discounted cost. The paper includes two extensions of existing results about optimal feedback control. First, it is proven that for real analytic statespace models, a time-invariant real analytic feedback solution exists, even when the cost function includes a discount factor, provided certain regularity conditions. Second, the result is generalized to nonlinear DAE models. The feedback solution is valid in a neighborhood of the origin. In both cases, explicit formulas for the series expansions of the cost function and control law are given.

  • 23.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems2005In: Proceedings of the 44th IEEE Conference on Decision and Control, 2005, p. 6869-6874Conference paper (Refereed)
    Abstract [en]

    Optimal control problems for a class of nonlinear descriptor systems are considered. It is shown that they possess a well-defined analytical feedback solution in a neighborhood of the origin, provided stabilizability and some other regularity conditions are satisfied. Explicit formulas for the series expansions of the cost function and control law are given.

  • 24.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Descriptor Systems2005Report (Other academic)
    Abstract [en]

    Optimal control problems for a class of nonlinear descriptor systems are considered. It is shown that they possess a well-defined analytical feedback solution in a neighborhood of the origin, provided stabilizability and some other regularity conditions are satisfied. Explicit formulas for the series expansions of the cost function and control law are given.

  • 25.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations2006In: Proceedings of the 45th IEEE Conference on Decision and Control, 2006, p. 870-875Conference paper (Refereed)
    Abstract [en]

    Optimal control problems for a class of nonlinear time-varying differentialalgebraic equations are considered. It is shown that they possess a welldefined feedback solution in a neighborhood of the origin. Explicit formulasfor the series expansions of the cost function and control law are given.

  • 26.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations2006In: Proceedings of Reglermöte 2006, 2006Conference paper (Refereed)
    Abstract [en]

    Optimal control problems for a class of nonlinear time-varying differentialal gebraic equations are considered. It is shown that they possess a well defined feedback solution in a neighborhood of the origin. Explicit formulas for the series expansions of the cost function and control law are given.

  • 27.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-Varying Differential-Algebraic Equations2007Report (Other academic)
    Abstract [en]

    Optimal control problems for a class of nonlinear time-varying differential-algebraic equations are considered. It is shown that they possess a well-defined feedback solution in a neighborhood of the origin. Explicit formulas for the series expansions of the cost function and control law are given.

  • 28.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Rational Approximation of Nonlinear Optimal Control Problems2008In: Proceedings of the 17th IFAC World Congress, 2008, p. 11340-11345Conference paper (Refereed)
    Abstract [en]

    In this paper rational approximation of solutions to nonlinear optimal control problems is considered. A computational procedure is presented that makes it possible to compute a rational function that approximates the true optimal cost function. It is shown that the rational function has the same series expansion around the origin as the true solution. Finally, two examples are given that compares the new method with the power series approximation, which is a rather well-known method to find approximative solutions.

  • 29.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Glad, Torkel
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Fujimoto, Kenji
    Nagoya University, Japan.
    Model Reduction of Nonlinear Differential-Algebraic Equations2007In: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, 2007, p. 176-181Conference paper (Refereed)
    Abstract [en]

    In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for nonlinear control-affine systems, and is based on analysis of the controllability and observability functions.

  • 30.
    Sjöberg, Johan
    et al.
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Lindkvist, Simon
    ABB, Sweden.
    Linder, Jonas
    Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
    Daneryd, Anders
    ABB, Sweden.
    Interactive Multiobjective Optimization for the Hot Rolling Process2012In: Proceedings of 51st IEEE Conference on Decision and Control, 2012, p. 7030-7036Conference paper (Refereed)
    Abstract [en]

    In this paper, multi-objective optimization is applied to the hot rolling process. It is modeled mostly using first principle models considering, for instance, the mass balance (or mass flow rate), the tensions in the material, the power requirements, the thermal field, and the microstructure of the material.

    Two optimization formulations are considered. In the first case, both the grain size and the power consumption in the rolling process are minimized. It is shown that the result from a single-objective optimization formulation, i.e., where only one of the two objectives are considered, yields control schedules with poor performance for the other objective. Furthermore, the differences between optimal control schedules for different objectives are compared and analyzed. The second case is a design optimization problem where the optimal positioning of cooling pipes is considered. This study shows how the MOO framework can be used to systematically choose a good cooling pipe setup. 

    The two studies shows that MOO can be a helpful tool when designing and running hot rolling processes. Furthermore, navigation among the Pareto optimal solutions is very useful when the user wants to learn how the control variables interact with the process.

1 - 30 of 30
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