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In this paper we investigate the optimal controller synthesis problem, so
that the system under the controller can reach a specified target set while
satisfying given constraints. Existing model predictive control (MPC) methods
learn from a set of discrete states visited by previous (sub-)optimized
trajectories and thus result in computationally expensive mixed-integer
nonlinear optimization. In this paper a novel MPC method is proposed based on
reach-avoid analysis to solve the controller synthesis problem iteratively. The
reach-avoid analysis is concerned with computing a reach-avoid set which is a
set of initial states such that the system can reach the target set
successfully. It not only provides terminal constraints, which ensure
feasibility of MPC, but also expands discrete states in existing methods into a
continuous set (i.e., reach-avoid sets) and thus leads to nonlinear
optimization which is more computationally tractable online due to the absence
of integer variables. Finally, we evaluate the proposed method and make
comparisons with state-of-the-art ones based on several examples.
