A moving switching sequence approach for nonlinear model predictive control of switched systems with state-dependent switches and state jumps

Abstract

In this paper, we propose an approach for real-time implementation of nonlinear model predictive control (NMPC) for switched systems with state-dependent switches called the moving switching sequence approach. In this approach, the switching sequence on the horizon moves to the present time at each time as well as the optimal state trajectory and the optimal control input on the horizon. We assume that the switching sequence is basically invariant until the first predicted switching time reaches the current time or a new switch enters the horizon. This assumption is reasonable in NMPC for systems with state-dependent switches and reduces computational cost significantly compared with the direct optimization of the switching sequence all over the horizon. We update the switching sequence by checking whether an additional switch occurs or not at the last interval of the present switching sequence and whether the actual switch occurs or not between the current time and the next sampling time. We propose an algorithm consisting of two parts: (1) the local optimization of the control input and switching instants by solving the two-point boundary-value problem for the whole horizon under a given switching sequence and (2) the detection of an additional switch and the reconstruction of the solution taking into account the additional switch. We demonstrate the effectiveness of the proposed method through numerical simulations of a compass-like biped walking robot, which contains state-dependent switches and state jumps.