Optimality based structured control of distributed parameter systems

Abstract

This thesis proposes a complete procedure to obtain static output feedback (SOF) controllers for large scale discrete time linear time invariant (LTI) systems by considering two criteria: (1) use a small number of actuators and sensors, (2) calculate a SOF gain that minimizes a quadratic cost of the states and the input. If the considered system is observable and stabilizable, the proposed procedure leads to a SOF gain which has a performance comparable to the linear quadratic regulator (LQR) problem in terms of the H2 norm of the closed loop system. When the system is not observable but detectable, only the observable part is considered. Since the structure of input and output matrices for the LTI system have a significant importance for the success of the proposed algorithm, an optimal actuator/sensor placement problem is considered first. This problem is handled by taking the final goal of SOF stabilization into account. In order to formulate the actuator/sensor placement as an optimization problem, a method to calculate the generalized Gramians of unstable discrete time LTI systems is developed. The results are demonstrated on a large scale flexible system and a biological network model.