Choosing the number of time intervals for solving a model predictive control problem of nonlinear systems

Model predictive control (MPC) is a control strategy that can handle state and control multi-variables at same time. To use the MPC using direct methods for solving the a dynamic optimization problem, one needs, for example, to transform the optimization problem into a nonlinear programming (NLP) problem by dividing the prediction horizon into equal time intervals. In this work, we suggest a tool and procedures for helping to choose a 'compromise' number of time intervals with a needed accuracy, objective cost, number of turned NLP iterations and computational time. On the other hand, we offer a simplified nonlinear program to ensure the convergence of a class of finite optimal control problem by modifying the state box constraints. In particular, a special type of box constraints were used to the constrained optimal control problem to enforce the state trajectories to reach the desired stationary point. These box constraints are characterized by some parameters that are easily optimized by our proposed nonlinear program. Our proposed tools are tested using two case studies; nonlinear continuous stirred tank reactor (CSTR) and nonlinear batch reactor.