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A numerical approach to hybrid nonlinear optimal control. (English) Zbl 1478.93301

Summary: This paper proposes a novel optimal control design framework for hybrid nonlinear dynamical systems involving an interacting combination of continuous-time and discrete-time dynamics. Two numerical algorithms are proposed to approximate the continuous-time and discrete-time portions of the hybrid Hamilton-Jacobi-Bellman (HJB) equation. Galerkin’s spectral method is utilised to approximate the value function involved in the continuous-time HJB equation, thereby computing the optimal control gains between impulsive events. Employing the spectral collocation method, the discrete-time HJB equation is then approximated to find the optimal control gain vector at impulsive instants. These two algorithms are ultimately combined to obtain the desired hybrid nonlinear optimal control law. Describing practical considerations for implementing the algorithms, some illustrative examples are presented to evaluate the functionality of the proposed hybrid nonlinear optimal controller.

MSC:

93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B52 Feedback control
93C10 Nonlinear systems in control theory
49J15 Existence theories for optimal control problems involving ordinary differential equations
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