Controle preditivo iterativo não linear multivariável sob restrições com complexidade temporal reduzida

Abstract

This thesis deals with the numerical resolution of optimal control problems using an iterative Model Predictive Control (MPC) method for non-linear multivariable systems under constraints. This iterative method was recently presented in the literature and avoids the need to solve a nonconvex optimization problem using a time-variant linearization of the nonlinear model of the system, which is iteratively adjusted by solving at each sampling time an iterative optimization problem using quadratic programming. The main advantage is the faster resolution of the optimal control problem using quadratic programming rather than non-convex programming, while maintaining an appropriate description of the nonlinear dynamics of the process being controlled. The approach presented is an evolution of the original iterative algorithm, based on the convergence analysis of the method, and a tightening strategy of the domain of admissible states for constraint observance, which is based on reachable sets obtained using the interval arithmetic. Firstly, MPC as an optimal control technique is presented. Next, we analyze some MPC approaches available in the literature that deal with the reduction of the time complexity of the method, and then the proposed approach is introduced, being systematically discussed the convergence of the method and its uncertainty, a new and concise mathematical description of the algorithm, the technique for observing the constraints, as well as the aspects related to its implementation. In sequence, applications of the proposed algorithm are presented to demonstrate the feasibility of the approach used and to emphasize the form of its application.