New Approach for Accuracy Enhancement of Terminal Constraints Satisfaction in Model Predictive Control Problem

In this paper, a new algorithm in order to increase the satisfaction of terminal constraints in the predictive control problem is presented. In this algorithm, by extracting mathematical relations, the terminal constraints are transferred from the final moment to the current moments. In each iteration, this transformation takes place in the optimization problem. At each moment of optimization, a new expression is obtained in terms of control inputs in each of the finite prediction control horizons. The equation of this transfer constraint is derived based on the variable discrete equations with the time of the controlled process and its execution at any moment fulfills the final constraints of the problem. This new algorithm, after extracting its mathematical relationships, is used to track the path of a robot with terminal constraints, and its performance is demonstrated using robot dynamics simulations. Also, the stability analysis of the proposed controller is performed by writing an appropriate cost function and applying Lyapunov theorem.