Abstract
Many real world systems are inherently nonlinear. Therefore, the linear quadratic regulator theory is rarely efficient for these systems. In this paper, we propose the design of an optimal feedback control for polynomial systems in the indeterminate state variables. To deal with the case of a nonlinear infinite-horizon-cost-functional, we investigate the control based on the Lyapunov functions (LF) and by using the Kronecker product (KP) algebra. Then, we analyze the stability of the feedback and its domain of attraction (DA) in form of convex problems based on the linear matrix inequality (LMI) formalism. The practical sub-optimal control is evaluated through simulation results and comparative schemes.
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