A new trust region–sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control

Abstract

In this article, a superlinearly convergent trust region–sequential quadratic programming approach is first proposed, developed and investigated for nonlinear systems based on nonlinear model predictive control. The method incorporates a combination algorithm that allows both the trust region technique and the sequential quadratic programming method to be used. If the attempted search of the trust region method is not accepted, the line search rule will be adopted for the next iteration. Also, having to resolve the quadratic programming subproblem for nonlinear constrained optimization problems is avoided. This gives the potential for fast convergence in the neighbourhood of an optimal solution. Moreover, additional characteristics of the algorithm are that each quadratic programming subproblem is regularized and the quadratic programming subproblem always has a consistent point. The main result is illustrated on a nonlinear system with a variable parameter and a bipedal walking robot system through simulations and is utilized to achieve rapidly stability. Numerical results show that the trust region–sequential quadratic programming algorithm is feasible and effective for a nonlinear system with a variable parameter and a bipedal walking robot system. Therefore, the simulation results demonstrate the usefulness of the trust region–sequential quadratic programming approach with nonlinear model predictive control for real-time control systems.