An efficient reliability method for probabilistic H-infinity robust control of uncertain linear dynamic systems

Achieving balance between robustness and performance is always a fundamental challenge we are faced with in control design of systems in the presence of uncertainties. H∞ robust control theory has been extensively used to deal with the problems of robust stabilization and disturbance attenuation of uncertain systems. However, in traditional H∞ robust control, the most frequently used method for dealing with uncertainties is adopting the assumption of norm-bounded perturbations of arbitrary structure about a nominal plant and the design techniques are based on the deterministic worst-case scenarios that may never occur in a particular control system and thus often led to over-conservative results. In this paper we focus on developing a reliability method for probabilistic H∞ robust control of linear uncertain systems by describing the uncertain parameters as random variables. A new efficient reliability method for robust control of dynamic systems with probabilistic parametric uncertainties is presented systematically. Robust control design is carried out by solving a reliability-based optimization problem where the disturbance attenuation and control cost are minimized under the condition that reliability requirement is satisfied. One of the advantages of the presented reliability method is that it can be used directly for robust control design of parametric uncertain systems. Another advantage of the presented method is that it makes it possible to consider the factors such as system performance, control cost, and reliability simultaneously in an integrated framework and provides an essential basis for the coordination and tradeoffs between these important factors in control design of uncertain systems. Compared to traditional H∞ robust control, the presented method is less-conservative and more reasonable for dealing with probabilistic uncertainties. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. Two numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.