Efficient model predictive control via convex optimization

This dissertation aims to develop a systematic approach to synthesize efficient stabilizing model predictive control (MPC) algorithms for both constrained linear time varying (LTV) systems and nonlinear systems.; For constrained LTV systems, we developed four computationally efficient algorithms. (1) We formulated an efficient robust constrained state feedback MPC that gives a sequence of explicit control laws corresponding to a sequence of invariant ellipsoids constructed one inside another in state space. (2) We extended the above algorithm to output feedback systems, and formulated an efficient robust constrained output feedback MPC which enjoys both on-line determination of control moves and off-line analysis of robust stability of closed-loop systems. (3) We developed an efficient robust constrained MPC with a time varying terminal con straint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. More over, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. (4) We developed a two-level hierarchical structure. For the low level control objective—stabilization, no optimization is involved, making it computationally efficient. For the higher level control objective of achieving an economic target, on-line optimization is performed with any desired objective function and control horizon without affecting the stability of the closed-loop system, and does not have to be solved within one sampling period.; For constrained nonlinear systems, we developed both state feedback and output feed-back scheduled MPC algorithms. In the algorithms, a set of predictive controllers are designed with their estimated regions of stability overlapping each other, and supervisory scheduling of the local controllers can move the state through the intersections of the regions of stability of different controllers to the desired operating point with guaranteed stability.; All of the algorithms developed in this dissertation have been formulated as linear objective minimizations subject to linear matrix inequality (LMI) constraints. This optimization is convex, and linear combination of the off-line solutions provides a feasible solution for the on-line optimization.