scholarly journals Off-line robustification of Generalized Predictive Control for uncertain systems

2014 ◽  
Vol 24 (4) ◽  
pp. 499-513 ◽  
Author(s):  
Khelifa Khelifi Otmane ◽  
Nordine Bali ◽  
Lazhari Nezli
Keyword(s):  
Predictive Control ◽  
Uncertain Systems ◽  
Optimization Problem ◽  
Main Idea ◽  
Optimal Solution ◽  
Generalized Predictive Control ◽  
Quadratic Constraints ◽  
Stability Robustness ◽  
Convex Quadratic Constraints ◽  
Polytopic Uncertainties

Abstract An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and structured polytopic uncertainties. The main idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given

scholarly journals Improved Robustness of Generalized Predictive Control for Uncertain Systems

2015 ◽  
Vol 65 (6) ◽  
pp. 349-355 ◽  
Author(s):  
Khelifi Otmane Khelifa ◽  
Bali Noureddine ◽  
Nezli Lazhari
Keyword(s):  
Convex Optimization ◽  
Quadratic Programming ◽  
Predictive Control ◽  
Stability Condition ◽  
Uncertain Systems ◽  
Optimization Problem ◽  
Generalized Predictive Control ◽  
Stability Robustness ◽  
Polytopic Uncertainties ◽  
Quadratically Constrained

Abstract An off-line methodology has been developed to improve the robustness of an initial generalized predictive control (GPC) through convex optimization of the Youla parameter. However, this method is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and polytopic uncertainties. The basic idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a non convex quadratically constrained quadratic programming (QCQP) problem. Based on semidefinite programming (SDP), this problem is relaxed and solved. Therefore, the robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, we present a numerical example to demonstrate the proposed method.

scholarly journals An Approach to Distributed Min-Max Model Predictive Control of Linear Systems with Parametric Uncertainty

2015 ◽  
Vol 13 (1-2) ◽  
pp. 2-9
Author(s):  
Alexandra Grancharova ◽  
Sorin Olaru
Keyword(s):  
Predictive Control ◽  
Uncertain Systems ◽  
Optimization Problem ◽  
Closed Loop ◽  
Parametric Uncertainty ◽  
Uncertain System ◽  
Input Constraints ◽  
Dual Decomposition ◽  
Suggested Approach ◽  
Control Of Linear Systems

Abstract In this paper, a suboptimal approach to distributed closed-loop min-max MPC for uncertain systems consisting of polytopic subsystems with coupled dynamics subject to both state and input constraints is proposed. The approach applies the dynamic dual decomposition method and reformulates the original centralized min-max MPC problem into a distributed optimization problem. The suggested approach is illustrated on a simulation example of an uncertain system consisting of two interconnected polytopic subsystems.

Adaptive Weighting Decoupling Design for Constrained Generalized Predictive Control Using Improved Genetic Algorithm

2013 ◽  
Vol 441 ◽  
pp. 829-832
Author(s):  
Yong Bin Dai
Keyword(s):  
Genetic Algorithm ◽  
Predictive Control ◽  
Shape Control ◽  
Control Method ◽  
Dynamic Performance ◽  
Main Idea ◽  
Generalized Predictive Control ◽  
Multivariable System ◽  
Improved Genetic Algorithm ◽  
Error Weight

The paper proposes a new method for decoupling multivariable system based on generalized predictive control (GPC) with constrains. It is the main idea of proposed control method that the error weight can change with output deviation caused by reference changes in order to reduce interactions in the system and improve dynamic performance of coupling loops. With improved genetic algorithm to optimize the performance index of GPC, the algorithm is applied to auto shape control and auto gauge control (ASC-AGC). The simulation results demonstrate the efficiency and correctness of approach proposed.

Robust model predictive control of heterogeneous time-delay multi-agent systems with polytopic uncertainties and input amplitude constraints

2020 ◽  
pp. 107754632093722
Author(s):  
Nahid Rahimi ◽  
Tahereh Binazadeh
Keyword(s):  
Time Delay ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Optimization Problem ◽  
Multi Agent Systems ◽  
Robust Model Predictive Control ◽  
Agent Systems ◽  
Robust Model ◽  
Multi Agent ◽  
Polytopic Uncertainties

This article studies the robust model predictive control of heterogeneous multi-agent systems with polytopic uncertainties and time delay. Moreover, some constraints on the amplitude of the control inputs are considered for each agent. The proposed distributed controllers are designed as state feedback. The goal is to design the feedback gains such that the multiagent system achieves consensus in the presence of time-delay and model uncertainties. For this purpose, an optimization problem is proposed, and by using the constrained robust model predictive control and the appropriate Lyapunov–Krasovskii functional, sufficient conditions are obtained to solve the optimization problem through solving the linear matrix inequalities. In this regard, a theorem is presented, and it is proved that the consensus errors converge to zero. Finally, the effectiveness of the proposed method is illustrated using numerical simulations.

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