Optimal dynamic output feedback control of Lipschitz nonlinear systems under input saturation

Abstract

In this study, the problem of optimal guaranteed cost control (OGCC) for nonlinear systems under input saturation is investigated. The purpose is to design a dynamic output feedback controller such that the closed-loop system is asymptotically stable and the upper bound of the cost function is minimized. Moreover, the designed controller ensures that the control signals do not exceed their permissible values. This leads to an optimization problem with bilinear matrix inequality (BMI) constraints. The BMI conditions are converted into the linear matrix inequality conditions by using some technical lemmas for straightforward computation of the controller matrices. The simulation results show the effectiveness and advantages of the proposed theoretical results.

A linear matrix inequality approach to optimal reset control design for a class of nonlinear systems

“…Proof of Theorem The base controller design is borrowed from Reference 30. Let us consider the following Lyapunov function candidate $$$$ V\left(\overline{x}\right)={\overline{x}}^{\mathrm{T}}(t)P\overline{x}(t), $$$$ where $$$ P $$$ is a symmetric positive definite matrix.…”