UC San Diego

In this thesis, two subjects are considered: new techniques to improve stabilizing performance and feasibility in model predictive control and disturbance rejection control in coordinated systems. Model predictive control is powerful when a system has constraints. However, by nature, feasibility and stabilizing property of model predictive control can be lost without proper treatments. A new idea is studied for the case that a system is not well stabilized by classical model predictive control since the origin is not reachable from initial states in a limited horizon. We handle this matter by using a time- varying contractive terminal state equality constraint in model predictive control. The core condition to execute our idea is a structural property of the system such as contractibility or a known control lyapunov function. In addition, algorithmic approaches to guarantee feasible model predictive control are developed with several state constraint structures. Assuming that the model predictive control problem at current time is feasible, we want to know the set of terminal states or new references such that the problem at the next time instant is still feasible. Solutions are given for the linear system case using reachability analysis. The rest of the talk considers disturbance rejection control in coordinated systems. We employ a fixed vehicle formation problem as a working problem. The aim is to design a controller to maintain the formation and avoid collisions in the presence of disturbance, measurement, and communication noises. Each vehicle has its own local controller that uses the state and input information from neighbors via communication. We formulate local model predictive control and estimators for one vehicle to estimate the states of the neighboring vehicles. Since coordinated systems interact via the exchange of information through communication, as the network of coordinated systems increases in the number of subsystems, natural limits on the available bandwidth of communication need to be imposed. With the gaussian assumptions on the noises and disturbance, the estimators are designed by linear matrix inequality methods, which link control objective, estimation performance, and communication limits. Even when bounds on the uncertainties are known instead of the gaussian assumptions, controllers and estimators can be formulated. Case studies are provided to demonstrate the main ideas and discuss interesting design issues