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Measures and LMIs for optimal control of piecewise-affine systems
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0001-5474-7060
2013 (English)In: 2013 European Control Conference, ECC 2013, 2013, 3173-3178 p.Conference paper (Refereed)
Abstract [en]

This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an infinite-dimensional linear program (LP) over a space of occupation measures. This LP is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP returns a polynomial approximation of the value function that solves the Hamilton-Jacobi-Bellman (HJB) equation of the OCP. Based on this polynomial approximation, a 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 suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

Place, publisher, year, edition, pages
2013. 3173-3178 p.
Keyword [en]
Hamilton-Jacobi-Bellman equations, Input and state constraints, Linear matrix inequality (LMI) relaxation, Occupation measure, Optimal control problem, Optimal controls, Optimal trajectories, Piecewise affine systems
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-143131ISI: 000332509703095ScopusID: 2-s2.0-84893292748ISBN: 978-303303962-9OAI: diva2:705874
2013 12th European Control Conference, ECC 2013; Zurich; Switzerland; 17 July 2013 through 19 July 2013

QC 20140318

Available from: 2014-03-18 Created: 2014-03-17 Last updated: 2014-04-24Bibliographically approved

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Abdalmoaty, Mohamed R.
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ReferencesLink to record
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