Switching boundary estimation and adaptive sliding mode control for the dynamical systems with discontinuity due to the actuators

Abstract

Due to the discontinuous physical property of the control actuators, the state space of such a dynamical system is divided into many subdomains. For each subdomain, the flow of such a system is governed by the corresponding subsystem. The state boundary between the adjacent subdomains is called the physical switching boundary. The controller is designed to switch when the subsystem of such a discontinuous dynamical system is switched in order to have the optimum control performance. Since the ambiguity and uncertainty of modeling, the mathematical expressions for describing the discontinuous physical properties of the control actuators may not be accurate. Since the nominal switching boundary where the controller really switches is not exactly the corresponding physical switching boundary, the mismatch between the subsystem and the corresponding controller will occur and it may seriously affect the control performance. Therefore, a boundary estimation algorithm is proposed to estimate the physical switching boundaries based on the model reference control and error backpropagation. The simulation results show that the adaptive sliding mode control with the boundary estimation algorithm has superior control performance and strong robustness to deal with the internal uncertainty, the external interference, and the boundary ambiguity.

Nonlinear dynamics of two electromechanical arms acting discontinuously on a balloon under the action of a sinusoidal excitation

“…They showed that the system undergoes a transition from periodic to chaotic motion. It has also been found that discontinuity in the physical property of a control actuator led to many subdomains in the state space of the dynamical system [ 25 ]. A study of a microbeam with geometric discontinuity under electrostatic load was conducted.…”