Adaptive Stabilizing Control Design For Several Classes Of Systems With Unknown Parameters

The present paper focus on the investigation of the adaptive stabilizing control for several classes of uncertain systems with uncertainty parameters. The main contents of this paper are composed of the following two parts:(I). Adaptive Stabilizing Control Design for Deterministic SystemsIn this part, we study the problem of the output-feedback adaptive stabilizing control design for two classes of linear systems with uncertainty parameters. Different from [1], where 2-order systems were studied, the adaptive stabilizing control design applicable to n-order systems with relative degree n is investigated firstly in this paper. By introducing a 3n-order dynamic compensator, the explicit expression of the output-feedback adaptive stabilizing controller is constructively provided. The controller designed guarantees that the states x of the closed-loop systems are asymptotic stable, while all the other signals are uniformly bounded. Then based on the aforementioned results, we study the problem of the output-feedback adaptive stabilizing control design for a class of n-order minimum-phase linear systems with uncertainty parameters and relative degree n — m (n is a natural number, m ≤ n is a nonnegative integer). By introducing a novel (3n + 2m)-order dynamic compensator, the explicit expression of the output-feedback adaptive stabilizing controller is constructively provided. The controller designed guarantees that the states x of the closed-loop systems are asymptotic stable, while all the other signals are uniformly bounded. Simulation results is addressed to illustrate the correctness of the proposed theory and approach.(II). Adaptive Stabilizing Control Design for Stochastic Nonlinear SystemsIn this part, we consider the problem of the adaptive control for two classes of stochastic nonlinear systems with uncertainty parameters. Firstly, eliminating the key assumption that the coefficient functions of system stochastic noise vanish at the desired trajectory, we study the adaptive tracking control design for the stochastic nonlinear strict-feedback system with unknown parametric nonlin-...