Nonlinear optimal control synthesis via occupation measures

We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given OCP, using a hierarchy of linear matrix inequality (LMI) relax...

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Bibliographic Details
Main Authors: Henrion, D., Lasserre, J.B., Savorgnan, C.
Format: Conference Proceeding
Language:English
Subjects:
Cost function
Differential equations
Helium
Linear matrix inequalities
Mathematics
Optimal control
Polynomials
System testing
Online Access:Request full text
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Summary:We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given OCP, using a hierarchy of linear matrix inequality (LMI) relaxations. In the second part, we extend the methodology to approximate the optimal value function on a given set and we use such a function to constructively and computationally derive an almost optimal control law. Numerical examples show the effectiveness of the approach.
ISSN:0191-2216
DOI:10.1109/CDC.2008.4739136