A new reaching law for sliding mode control of continuous time systems with constraints

Abstract

In this paper, we propose a new reaching law for variable structure control of continuous time dynamic systems. The proposed reaching law is a refined version of the classical Gao and Hung’s constant plus a proportional one. Contrary to the original formulation, our reaching law ensures that the sliding variable rate of change is bounded and its upper and lower bounds do not depend on the system initial conditions. This approach ensures that the control signal and all state variables of the system are limited by design parameters which do not depend on the initial state. Therefore, our approach leads to faster error convergence subject to input signal and output signal rate of change constraints. These desirable properties are obtained by replacing the proportional term in Gao and Hung’s reaching law with a more sophisticated nonlinear expression which is limited by a known constant and does not grow when the sliding variable becomes bigger, but still remains significant when this variable decreases.