Design of reliable control system guaranteeing H∞-norm performance bound for uncertain linear plants

Abstract

In this dissertation, design of a reliable control systems is investigated for a class of uncertain linear plants in which disturbances and noises are taken into account as exogenous inputs. The goal of a reliable control system is to retain the stability and hold performance degradation within some allowable prescribed bound despite failures on sensors and/or actuators in the closed-loop system. A decentralized control scheme with two observer-based feedback controllers is developed for such a class of uncertain linear plants to achieve the design objectives. The design problem is to determine the controller parameters so that $H_∞$-norm of the closed-loop system transfer function matrix from exogenous input to regulated variable remains within the pre-specified value. Hence, the resulting closed-loop system is reliable in the sense that the control scheme provides guaranteed stability and $H_∞$-norm bounded performance in the sensor and/or actuator failures as well as in the presence of parameter uncertainties. For this, the controllers are first designed for the uncertain linear plant without consideration of failures in the system, and then, based on the observations that the sensor and/or actuator failures can be another sources of exogenous inputs(unknown inputs) to the closed-loop system, the methodology developed for the normal case when only the parameter uncertainties are considered is extended to the case when the sensor and/or actuator failures are taken into account in the design. Designing the controllers involves solving two Riccati-like algebraic equations. In this step, some tuning capability is provided in solving the two Riccati-like algebraic equations, which enables us to arbitrarily determine the controller dynamics within the $H_∞$-norm performance bound. Several simulation results illustrate the effectiveness of the reliable designs proposed in the dissertation.