Interval-Based Implementation of Robust Variable-Structure and Backstepping Controllers of Single-Input Single-Output Systems

Abstract For dynamic systems with uncertain but bounded parameters, it is desired to design feedback control strategies that are capable of stabilizing the system dynamics with certainty with a minimum amount of conservatism. This conservatism usually results from overapproximating the influence of uncertain parameters during offline design stages in terms of worst-case (norm) bounds. Using such bounds, classical sliding mode techniques can be designed. However, this offline overapproximation of the influence of uncertainties typically leads to unnecessarily large control amplitudes as well as to the effect of chattering which may cause undesired actuator wear. Therefore, interval-based variable-structure control procedures were developed in previous work for a guaranteed stabilizing online adaptation of the control strategy. These approaches have already been applied successfully to various real-life systems and have been extended by approaches that allow for handling both one-sided and two-sided hard state constraints. This paper presents further methodological extensions of interval-based real-time capable control laws which can be interpreted as a generalization of backstepping controllers for single-input single-output systems that are given in strict feedback form.