Adaptive AEM Controller for a Wide Class of Nonlinear Discrete-Time Stochastic Systems Using On-Line State Estimation

Resumen: This paper describes the Attractive Ellipsoid Method (AEM) application, which uses the state estimates obtained by a sliding mode observer (SMO) for a wide class of quasi-Lipschitz nonlinear stochastic discrete-time systems. For the extended vector, containing state estimation and tracking errors as its components, we prove the mean square convergence to an attractive ellipsoid, which “size" is done as small as possible by the corresponding optimal selection of the gain matrices in both the SMO and in the linear feedback, using obtained current state estimates. It is shown that the procedure of the gain matrices optimization consists of the numerical solution of a corresponding matrix optimization problem subject to a set of bilinear matrix inequalities (BMIs), which by a special transformation procedure can be converted to a set of linear matrix inequalities (LMIs). An illustrative example shows the effectiveness of the suggested approach.

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D. Velázquez & A. Poznyak. Adaptive AEM Controller for a Wide Class of Nonlinear Discrete-Time Stochastic Systems Using On-Line State Estimation. Memorias del Congreso Nacional de Control Automático, pp. 249-254, 2021.

Palabras clave

Control de Sistemas No Lineales, Sistemas Discretos, Sistemas Estoc´asticos

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