On nonlinear H ∞ sliding mode control for a class of nonlinear cascade systems

Abstract

In this work two main robust control strategies, the sliding mode control (SMC) and nonlinear H 8 control, are integrated to function in a complementary manner for tracking control tasks. The SMC handles matched L 8 [0,8) type system uncertainties with known bounding functions. H 8 control deals with unmatched disturbances of L 2 [0,8) type where the upper-bound knowledge is not available. The new control method is designed for a class of nonlinear uncertain systems with two cascade subsystems. Nonlinear H 8 control is applied to the first subsystem in the presence of unmatched disturbances. Through solving a Hamilton-Jacoby inequality, the nonlinear H 8 control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H 8 control, the resulting sliding manifold in the sliding phase possesses the desired L 2 gain property and to a certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L 2 gain robustness in the reaching phase. Two illustrative examples are given to show the effectiveness of the proposed robust control scheme.