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Nonlinear Model Predictive Control for Systems with State-Dependent Switches and State Jumps Using a Penalty Function Method

In this work, we propose a real-time algorithm of nonlinear model predictive control (NMPC) for a class of switched systems with state-dependent switches and state jumps based on the continuation/GMRES (C/GMRES) method. This approach utilizes the characteristic of NMPC that the optimal solution changes continuously with respect to time and optimizes control input and switching instants simultaneously by updating them at each sampling time. To avoid difficulty in updating the solution based on the C/GMRES method and to construct a simple algorithm, we treat the switching condition by using a penalty function method. We demonstrate the effectiveness of the proposed method using a numerical simulation of a compass-like biped walking robot, which contains state-dependent discrete events.