A hybrid model-based optimal control method for nonlinear systems using simultaneous dynamic optimization strategies

Abstract

To improve the overall control performance of nonlinear systems, an optimal control method, based on the framework of hybrid systems, is proposed. Firstly, the nonlinear systems are approximated by a number of piecewise affine models which are produced by the nonlinear systems at the specified operating points, then the piecewise affine models are synthesized under the framework of hybrid systems, and an associated optimal control problem, in which decision variables involve not only admissible continuous control but also the scheduling of subsystem modes, is established. Secondly, the optimal control problem is transformed into a MIQP problem by discretization over the whole state space and admissible control space to obtain the numerical optimal solution. For speeding up the algorithm, the simultaneous method on finite elements is used to lower the dimensions of the MIQP problem. Consequently, a hybrid model-based MPC for nonlinear systems is designed, and the adverse effects of model mismatch resulted from simultaneous method is weakened by MPC strategy. Simulations and comparisons with soft-switching method, hard-switching method and MLD method, confirm that a satisfactory performance can be obtained using the presented approach.