Switching and impulsive control algorithms for nonlinear hybrid dynamical systems. (English) Zbl 1378.93057
Summary: Control algorithms are developed for physical processes modeled as Hybrid Dynamical Systems (HDSs). In this framework, a HDS is a nonlinear switched system of Ordinary Differential Equations (ODEs) coupled with impulsive equations. Switching and impulsive control is applied with two performance goals in mind: First, a high-frequency switching control method is provided to drive a HDS state to the origin while only requiring the HDS state intermittently. Attractivity of the origin is proved under a shell bisection algorithm; a high-frequency switching control rule is designed for this purpose. Second, a state-dependent switching control strategy is derived for when the transient behavior of the HDS is of interest. Finite-time stabilization is guaranteed under a so-called minimum rule algorithm; for each HDS mode, the state space is divided into different control regions and a switching control rule is constructed to switch between controllers whenever a boundary is reached. The theoretical tools used in this article include the Campbell-Baker-Hausdorff formula, multiple Lyapunov functions, and average dwell-time conditions.
MSC:
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C10 | Nonlinear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34A37 | Ordinary differential equations with impulses |
| 93D99 | Stability of control systems |
Keywords:
hybrid systems; switched systems; high-frequency switching; state-dependent switching; multiple Lyapunov functions; finite-time stabilizationReferences:
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