Model Predictive Control for discrete fuzzy systems via iterative quadratic programming

Abstract

Takagi-Sugeno fuzzy models are exact representations of nonlinear systems in a compact region. Guaranteed-cost linear matrix inequalities produce controllers which minimize a shape-independent bound on a quadratic cost; however, the controller has a fixed structure (possibly suboptimal), say a Parallel Distributed Compensator (PDC), and does not allow input saturation. By posing the problem as a Model Predictive Control one, the ideas of terminal set, terminal controller and feasible set can be used in order to improve the performance of usual guaranteed-cost controllers for Takagi-Sugeno systems via Quadratic Programming. A Polya-based approach has been introduced in order to (conservatively) transform the invariant set problem into a polytopic one, as well as computing the controller feasibility region. The optimal controller is computed iteratively.Index Terms-Discrete Takagi-Sugeno Fuzzy Models, Invariant sets, Contractive sets and Robust Stability.

Nonlinear model predictive control for models in quasi‐linear parameter varying form

“…A fast approximate NMPC using a moving linearization, resulting in a linear time‐varying (LTV) model, is presented in Kunz et al This method bears similarity with the one presented in this article; however, the use of the quasi‐linear parameter varying (LPV) framework here allows for exact nonlinear system representation and no time‐consuming linearization takes place. Similarly, an iterative procedure using Takagi‐Sugeno Fuzzy modeling is presented in Ariño et al, and this approach can be considered as a special case of the presented one if one restricts the quasi‐LPV model to be polytopic.…”

Metodología de programación dinámica aproximada para control óptimo basada en datos

“…En el caso no-lineal, en general no existen soluciones con una expresión analítica explícita del controlóptimo. Una alternativa sería hacer control predictivo (Camacho and Bordons, 2010) no lineal, resolviendo problemas de optimización en línea (Allgöwer and Zheng, 2012;Ziogou et al, 2013) o iterativa (Ariño et al, 2014;Armesto et al, 2015); no obstante, las técnicas de control predictivo se dejan, intencionalmente, fuera de los objetivos de este manuscrito porque se quieren plantear soluciones que impliquen el ajuste de controladores aproximadamenteóptimos a horizonte infinito, basados en datos, en vez de en simulaciones a horizonte finito propias del control predictivo no lineal.…”

Método de error de Bellman con ponderación de volumen para mallado adaptativo en programación dinámica aproximada

“…En el caso no-lineal, en general no existen soluciones con una expresión analítica explícita del control óptimo. Una alternativa sería ha-cer control predictivo (Camacho and Bordons, 2010) no lineal, resolviendo problemas de optimización en línea (Allgower and Zheng, 2012;Ziogou et al, 2013) o iterativa (Ariño et al, 2014;Armesto et al, 2015;Li and Todorov, 2007), si bien el principal problema que plantean es que el tiempo de resolución en línea.…”