Measures and LMIs for optimal control of piecewise-affine dynamical systems: Systematic feedback synthesis in continuous-time
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
The project considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector fields and polynomial data. The OCP is relaxed as an infinite-dimensional linear program (LP) over space of occupation measures. The LP is then written as a particular instance of the generalized moment problem which is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP gives a polynomial approximation of the value function along optimal trajectories. Based on this polynomial approximation, a novel suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.
Place, publisher, year, edition, pages
2012. , 42 p.
Technology, optimal control, piecewise-affine, measures, moments, discontinuous feedback, SDP, LMIs, polynomials
IdentifiersURN: urn:nbn:se:ltu:diva-56887Local ID: da0b6b1e-8fa3-464b-97e3-ea5b3c0c52c5OAI: oai:DiVA.org:ltu-56887DiVA: diva2:1030274
Subject / course
Student thesis, at least 30 credits
Space Engineering, master's level
Validerat; 20120629 (anonymous)2016-10-042016-10-04Bibliographically approved