Construction of nonlinear optimal control theory based on fusion of quantization methods for HJB equations and stochastic processes

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To stabilize nonlinear control systems such as nonholonomic systems, discontinuous state-feedback control laws should be designed 。 Furthermore, energy conservation measures are recently required for controlling mechanical and electrical dynamical systems。 To solve the problems at one time, this research has proposed a new numerical approximation method for nonlinear optimal regulator problems by combining two quantization methods of Hamilton-Jacobi-Bellman equations and stochastic processes。 The industrial value of the proposed method has been confirmed by the experimental researches of controlling ultrasonic motors。