A Non-Smooth Optimization Framework For Fault-Tolerant Control of Power Electronic Systems

Abstract

Power electronic converters used for renewable energy integration are usually based on the algorithm that may fail to work in case of open-circuit or short-circuit faults of the semiconductor devices. The traditional approaches to control, such as linear quadratic control, and model predictive control, assume that dynamics are smooth. However, that cease to be valid in the presence of faults that lead to discontinuities in the topological sense. This article presents a unified approach to non-smooth optimization where the process of deciding the switching mode and analyzing the fault is viewed as a part of the variational problem. The dynamics of the switched system are described by using differential inclusions, while optimization is necessary to minimize tracking errors, power, and thermal stress by means of Clarke generalized gradient. The optimality conditions are derived by using parameters of finite dimensional variational problem using the approach based on Fritz-John condition, while a Lyapunov function is constructed to demonstrate the convergence of the state trajectory to the closed invariant set in the presence of faults. A proximal bundle algorithm that is designed specifically for the chosen inclusion is applied in this paper, while the convergence is guaranteed due to the property of semi-smoothness. The numerical experiments show performance of the algorithms in terms of the reduction of tracking error values and sliding mode accuracy in course of many iterations making evidence of high validity of the proposed approach for different cases of switches failures.