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Optimal Control for Polynomial Systems Using Matrix Sum of Squares Relaxations

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1 Author(s)
Ichihara, H. ; Dept. of Syst. Design & Inf., Kyushu Inst. of Technol., Fukuoka

This note deals with a computational approach to an optimal control problem for input-affine polynomial systems based on a state-dependent linear matrix inequality (SDLMI) from the Hamilton-Jacobi inequality. The design follows a two-step procedure to obtain an upper bound on the optimal value and a state feedback law. In the first step, a direct usage of the matrix sum of squares relaxations and semidefinite programming gives a feasible solution to the SDLMI. In the second step, two kinds of polynomial annihilators decrease the conservativeness of the first design. The note also deals with a control-oriented structural reduction method to reduce the computational effort. Numerical examples illustrate the resulting design method.

Published in:

Automatic Control, IEEE Transactions on  (Volume:54 ,  Issue: 5 )