Nonlinear optimal control via occupation measures and LMI-relaxations. (English) Zbl 1188.90193

The authors consider the particular class of nonlinear optimal control problems (OCP) where the differential equation, the state and the control constraints are described by polynomials. Since polynomials are dense in the class of functions under consideration the results in this paper can be extended to problems with smooth data and compact sets. In this polynomial framework, OCP can be written as an infinite-dimensional linear program. The paper presents an approximation of the optimal value of the original problem by solving a sequence of linear matrix inequality relaxations providing a nondecreasing sequences of lower bounds. Under some additional assumptions, even convergence to the solution of the original OCP can be shown.


90C22 Semidefinite programming
93C10 Nonlinear systems in control theory
28A99 Classical measure theory
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