This research monograph develops a systematic approach to synthesize efficient robust MPC for constrained LTV systems and nonlinear systems. Specifically, (a) by using the concept of invariant sets, robustness is achieved without online computation; (b) by using a two-level control structure, optimization is separated from stabilization; (c) by constructing a continuum of terminal sets, both large operating regions and local optimality can be achieved without large number of control decision variables; (d) by decomposing a nonlinear control problem into a sequence of linear control problems, a nonlinear non-convex optimization problem is reduced to a convex optimization problem. Algorithms developed in this monograph have been formulated into linear objective minimisations subject to linear matrix inequality constraints. This optimization is convex and can be solved efficiently using interior point methods. Since state and decision variables appear linearly in the objective function and the matrix inequality constraints, linear combination of off-line MPC solutions provides a feasible solution, which can potentially replace online optimization in MPC.

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