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Real-time MPC - Stability through robust MPC design


M.N. Zeilinger

University of California, Berkeley, CA

Recent results suggest that online Model Predictive Control (MPC) may be adapted to be suitable for fast sampled systems. By exploiting the structure and sparsity inherent in MPC problems the computational complexity can be significantly reduced making an online solution a reasonable alternative for the control of high-speed systems. The application of MPC to high-speed systems imposes a hard real-time constraint on the solution of the MPC problem and generally makes the computation of the optimal control action infeasible in the given time. Most available methods for fast online MPC do not provide guarantees on feasibility or stability of the suboptimal control action in such a real-time setting or, if they do, the conditions cannot be practically tested. In this work we develop a real-time MPC scheme based on robust MPC design that recovers these guarantees while allowing for extremely fast computation. We show that a simple warm-start optimization procedure providing an enhanced feasible solution guarantees feasibility and stability for arbitrary time constraints. Additional computation time can then be used to improve the performance. The focus of this work is to provide a real-time robust MPC method than can be practically implemented and efficiently solved for systems of significant size. The computational details for implementation of the proposed method using a custom interior-point solver that ensures only stabilizing step directions are presented. The developed custom solver achieves computation times equal to those reported for methods without guarantees which is highlighted using some numerical examples. A 12-dimensional problem with 3 control inputs and a prediction horizon of 10 time steps is solved in 2msec with a performance deterioration less than 1% and thereby allows for sampling rates of 500Hz.


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