Sliding mode control for non-linear systems with adaptive sliding surfaces

Abstract

This study covers the sliding mode control design with adaptive sliding surfaces for a class of affine non-linear systems, which can be described by ẋ = A(x)x + B(x)u + f(x) + d(x, t). The main streamline of the study is the sliding surface design for such systems. The sliding surfaces are designed to be moving with varying slopes and offsets. The varying sliding surface parameters are determined by solving the state-dependent Riccati equations online during the control process. Thus, the sliding surfaces are updated in an adaptive manner to cope with the non-linearities of the system. The adaptive sliding mode control method developed in this study is used to design a longitudinal controller based on the mathematical model of a generic hypersonic aircraft. Then, the successful performance of this controller is demonstrated by means of a simulated manoeuvre of the aircraft.