Reliable linear-quadratic optimal control for discrete-time singular linear systems

The paper is concerned with the problem of designing reliable linear-quadratic state-feedback control for a class of discrete-time singular linear systems. A reliable state-feedback control is designed for the case of possible actuator faults, and the proposed state-feedback controller guarantees that the closed-loop system is admissible and its quadratic performance index is bounded by a constant. An example is given to illustrate effectiveness of the proposed method.

1 Introduction

Reliable control designs which guarantee stability and allow the actuator (sensor) failure have been studied by many scholars [1]–[15]. In these literature, three main design approaches are concerned. One approach is redundant control in which the reliability of the control structures is guaranteed by using multiple controllers [7], [12]. The other approach is reliable control [1]–[5],[8]–[11],[13],[14] where the design will tolerate outages within a selected subset of susceptible actuators. Control laws design guaranteeing the closed-loop system is stable and its norm is bounded in [8]–[10],[14], and controllers which ensure the closed-loop system is stable and its LQ norm is bounded are proposed. Another approach is adaptive control which deals with unknown actuator (sensor) failure of the system (see [15] and its references).