Time-Sequence Based Modeling of Finite Automata in Model Predictive Control of Hybrid Systems

In the model predictive control (MPC) of hybrid systems, the problem of reducing the online computational complexity for generating a control input is one of the main issues. Thus focussing on how concisely a model of discrete dynamics is expressed, the authors have recently proposed a minimal representation of a finite automaton, which is given as a linear state equation with the smallest number of free binary variables (called here binary input variables). This representation enables us to reduce the computational time for solving the MPC problem of hybrid systems. This paper proposes a more effective modeling method for the MPC problem. The main idea is to derive an initial-mode- dependent model by using the above minimal representation, which expresses only mode trajectories for a given initial mode to save the number of binary input variables. The effectiveness of the proposed method is shown by numerical examples.