Nonlinear model predictive control using multiple shooting combined with collocation on finite elements

Abstract

A new approach to nonlinear model predictive control (NMPC) is proposed in this paper. The multiple shooting method is used for discretizing the dynamic system, through which the optimal control problem is transformed to a nonlinear program (NLP). To solve this NLP problem state variables and their gradients at the end of each shooting need to be computed. Here we employ the method of collocation on finite elements to carry out this task. Due to its high numerical accuracy, the computation efficiency for the integration of model equations can be enhanced, in comparison to the existing multiple shooting method where an ODE solver is applied for the integration and the chain-rule for the gradient computation. The numerical solution framework is implemented in C++. Two examples are taken to demonstrate the effectiveness of the proposed NMPC algorithm.