Generalized predictive control robustification under frequency and time-domain constraints

Rodriguez, Pedro; Dumur, Didier

doi:10.1109/tcst.2005.847330

Cited by 34 publications

(42 citation statements)

References 12 publications

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“…As given in [1], the Youla parameterization of the previous initial generalized predictive controller (R 0 , S 0 , T 0 ) leads to the following stabilizing polynomials…”

Section: Youla Parametrizationmentioning

confidence: 99%

“…So, the specifications defined by equation (9) are convex in Q 1 . This convex optimization problem leads to a Q 1 parameter varying in an infinite dimensional space [1].…”

Section: Fig 3 Unstructured Additive Direct Uncertaintymentioning

confidence: 99%

“…As given in [1], these inequalities lead to the cost minimization under inequality constraints. Hence, the stability robustness problem towards additive unstructured uncertainties can be written as follows…”

Section: Fig 3 Unstructured Additive Direct Uncertaintymentioning

confidence: 99%

“…Another sophisticated methodology has been developed recently in [1] to enhance the robustness of the GPC controller towards unstructured uncertainties while respecting time-domain constraints. This methodology starts with the design of an initial stabilizing GPC controller; this controller is then robustified via the Youla parametrization which permits to access all the stabilising controllers.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents an extension of this methodology to the systems subjected to both unstructured and polytopic structured uncertainties, while preserving the same formalism by Youla parametrization adopted in [1].…”

Section: Introductionmentioning

confidence: 99%

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Improved Robustness of Generalized Predictive Control for Uncertain Systems

Khelifa

Bali

Nezli

2015

Journal of Electrical Engineering

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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.K e y w o r d s: generalized predictive control, quadratically constrained quadratic programming, polytopic uncertainties, relaxation, robust control, semidefinite programming, Youla parameterization

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“…As given in [1], the Youla parameterization of the previous initial generalized predictive controller (R 0 , S 0 , T 0 ) leads to the following stabilizing polynomials…”

Section: Youla Parametrizationmentioning

confidence: 99%

“…So, the specifications defined by equation (9) are convex in Q 1 . This convex optimization problem leads to a Q 1 parameter varying in an infinite dimensional space [1].…”

Section: Fig 3 Unstructured Additive Direct Uncertaintymentioning

confidence: 99%

Section: Fig 3 Unstructured Additive Direct Uncertaintymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved Robustness of Generalized Predictive Control for Uncertain Systems

Khelifa

Bali

Nezli

2015

Journal of Electrical Engineering

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A robustification approach in unconstrained quadratic optimization

Bernauer

Griesse

2009

Math. Program.

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Abstract. Unconstrained convex quadratic optimization problems subject to parameter perturbations are considered. A robustification approach is proposed and analyzed which reduces the sensitivity of the optimal function value with respect to the parameter. Since reducing the sensitivity and maintaining a small objective value are competing goals, strategies for balancing these two objectives are discussed. Numerical examples illustrate the approach.

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Transient response improvement of predictive control under time domain constraints

Khelifi Otmane,

Bessaad

2024

Heliyon

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Generalized predictive control robustification under frequency and time-domain constraints

Cited by 34 publications

References 12 publications

Improved Robustness of Generalized Predictive Control for Uncertain Systems

Improved Robustness of Generalized Predictive Control for Uncertain Systems

A robustification approach in unconstrained quadratic optimization

Transient response improvement of predictive control under time domain constraints

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