Mode-Prefix-Based Control of Switched Linear Systems with Applications to Fault Tolerance

TL;DR

This paper introduces a prefix-based optimal control framework for switched linear systems, enhancing fault tolerance by ensuring consistent control despite abrupt system changes, and formulates the problem as a convex optimization.

Contribution

It develops a convex optimization approach for mode-prefix-based control of switched systems, enabling fault-tolerant control with guaranteed performance.

Findings

Convex formulation for prefix-based control problems.

Controller synthesis for fault-tolerant switched systems.

Application to fighter jet model demonstrating fault tolerance.

Abstract

In this paper, we consider the problem of designing prefix-based optimal controllers for switched linear systems over finite horizons. This problem arises in fault-tolerant control, when system faults result in abrupt changes in dynamics. We consider a class of mode-prefix-based linear controllers that depend only on the history of the switching signal. The proposed optimal control problems seek to minimize both expected performance and worst-case performance over switching signals. We show that this problem can be reduced to a convex optimization problem. To this end, we synthesize one controller for each switching signal under a prefix constraint that ensures consistency between controllers. Then, system level synthesis is used to obtain a convex program in terms of the system-level parameters. In particular, it is shown that the prefix constraints are linear in terms of the system-level parameters. Finally, we apply this framework for optimal control of a fighter jet model suffering from system faults, illustrating how fault tolerance is ensured.