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 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 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.

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.

scholarly journals Explicit GPC Control Applied to an Approximated Linearized Crane System

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Daniel Guerra Vale da Fonseca ◽  
André Felipe O. de A. Dantas ◽  
Carlos Eduardo Trabuco Dórea ◽  
André Laurindo Maitelli
Keyword(s):  
Quadratic Programming ◽  
Predictive Control ◽  
Gantry Crane ◽  
Generalized Predictive Control ◽  
Control Law ◽  
Time Step ◽  
Constraint Violation ◽  
Piecewise Affine ◽  
Output Constraints ◽  
Overall Performance

This paper proposes a MIMO Explicit Generalized Predictive Control (EGPC) for minimizing payload oscillation of a Gantry Crane System subject to input and output constraints. In order to control the crane system efficiently, the traditional GPC formulation, based on online Quadratic Programming (QP), is rewritten as a multiparametric quadratic programming problem (mp-QP). An explicit Piecewise Affine (PWA) control law is obtained and holds the same performance as online QP. To test effectiveness, the proposed method is compared with two GPC formulations: one that handle constraints (CGPC) and another that does not handle constraints (UGPC). Results show that both EGPC and CGPC have better performance, reducing the payload swing when compared to UGPC. Also both EGPC and CGPC are able to control the system without constraint violation. When comparing EGPC to CGPC, the first is able to calculate (during time step) the control action faster than the second. The simulations prove that the overall performance of EGPC is superior to the other used formulations.

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