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Occupation Measures and LMI Relaxations for Deterministic In nite Horizon Discounted Optimal Control Problems


A. Kamoutsi

Master Thesis, FS16 (10543)

We consider the deterministic, continuous time, discounted infinite horizon optimal control problem (OCP) subject to state constraints, for which the dynamics and cost function are polynomials and the state constraint and control spaces are compact basic semi-algebraic sets. We first relax the OCP to an infinite dimensional linear program over a space of measures and we derive an hierarchy of moment LMI (linear matrix inequality) relaxations whose values, under some mild assumptions, approximate pointwise the OCPs value function. Moreover, using duality theory, we introduce the dual linear program which is to find the supremum of all smooth subsolutions to the associated Hamilton-Jacobi-Bellman equation. Finally, we use the optimal solutions of the dual sum-of-squares semidefinite relaxations to approximate the value function on a set and compute an approximate control feedback.

Supervisors: Peyman Mohajerin Esfahani, Tobias Sutter, John Lygeros, Halil Mete Soner (D-MATH)


Type of Publication:

(12)Diploma/Master Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2016:IFA_5448
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