A robust multi-model predictive controller for distributed parameter systems

García, Míriam R.; Vilas, Carlos; Santos, Lino O.; Alonso, Antonio A.

doi:10.1016/j.jprocont.2011.10.008

Cited by 52 publications

(22 citation statements)

References 68 publications

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“…Thereupon, SOS tools are also able to obtain numerical global or local solutions for fuzzypolynomial systems [26], [27]. There are, of course, other model-based control strategies which explicitly consider input and/or state constraints [28], but they require the execution of online optimization routines, so they have been intentionally left out of the paper's scope.…”

Section: Introductionmentioning

confidence: 99%

Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

Pitarch

Rakhshan

Mardani

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-This paper presents a systematic approach to deal with the saturated control of a class of distributed parameter systems which can be modeled by first-order hyperbolic partial differential equations (PDE). The approach extends (also improves over) the existing fuzzy Takagi-Sugeno (TS) state feedback designs for such systems by applying the concepts of the polynomial sum-of-squares (SOS) techniques. Firstly, a fuzzy-polynomial model via Taylor series is used to model the semilinear hyperbolic PDE system. Secondly, the closed-loop exponential stability of the fuzzy-PDE system is studied through the Lyapunov theory. This allows to derive a design methodology in which a more complex fuzzy state-feedback control is designed in terms of a set of SOS constraints, able to be numerically computed via semidefinite programming. Finally, the proposed approach is tested in simulation with the standard example of a nonisothermal plug-flow reactor (PFR).

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Section: Introductionmentioning

confidence: 99%

Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

Pitarch

Rakhshan

Mardani

et al. 2018

IEEE Trans. Fuzzy Syst.

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“…In order to tackle these problems and improve the performances, a model-free design was proposed [4]. Moreover, an other advantage of this method against the classics, as model predictive control [11], is the easier implementation [2].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis for unknown delayed systems controlled by model-free control

Doublet

Join

Hamelin

2017

2017 21st International Conference on System Theory, Control and Computing (ICSTCC)

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To cite this version:Maxime Doublet, Cédric Join, Frédéric Hamelin. Stability analysis for unknown delayed systems controlled by model-free control. Abstract-Unknown delayed systems are present in many domains and control this kind of systems remains a difficult problem. Indeed, we can find theses systems in physics, chemistry, aeronautics, etc. The main problem is that the delay is unknown, and so the model is not exactly well-known. By the way, the use of model-free control (MFC) remains a suitable solution to tackle this problem. This paper deals with a stability analysis to show the influence of a parameter on the stability of the systems regarding to the delay.

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“…In the past decade, numerous research studies have concentrated on the general framework of model predictive control synthesis for parabolic PDE systems and other PDE systems describing distributed parameter systems, such as MPC with internal model control structure on the PDE system [2] and characteristic-based MPC on the hyperbolic PDE system [3]. Besides the above MPC frameworks, which are derived with traditional order reduction techniques, notable research studies have been carried out on the development of MPC syntheses which are constructed on the basis of reducedorder models derived by the combination of the concept of inertial manifolds [4] and the spectrum method, including MPC on the parabolic PDE system with constraints [5], MPC with boundary control actuation on the parabolic PDE system [6], multivariable predictive control of PDE [7], and robust nonlinear MPC for the convection-diffusion-reaction system [8]. In addition, the receding horizon control strategy with terminal penalty is analyzed for the infinite dimensional system in [9], while the minimal stabilizing optimization horizon for MPC without terminal constraints is explored for the linear heat equation in [10].…”

Section: Introductionmentioning

confidence: 99%

Explicit/multi-parametric model predictive control of dissipative distributed parameter systems

Liu

Huang

Dubljević

2015

2015 American Control Conference (ACC)

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This work focuses on the development of an explicit/multi-parametric model predictive control algorithm to stabilize the discrete infinite-dimensional system arising from the discrete state space modeling of certain class of dissipative distributed parameter systems, specifically, parabolic partial differential equation (PDE) systems. In particular, the class of parabolic PDEs that captures a large number of transportreaction systems yields a discrete modal representation which captures the dominant dynamics of the parabolic PDE system. The proposed explicit/multi-parametric model predictive control algorithm is constructed in a way that the objective function is concerned with only the low-order modes, while the state constraints involve both the low-order and higher-order modes. The explicit model predictive control problem is solved offline by dynamic programming and multi-parametric quadratic programming techniques, and the solution is expressed as a piecewise affine function with its corresponding critical regions.

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A robust multi-model predictive controller for distributed parameter systems

Abstract: In this work a robust nonlinear model predictive controller for nonlinear convection-diffusion-reaction systems is presented. The controller makes use of a collection of reduced order approximations of the plant (models) re-

Cited by 52 publications

References 68 publications

Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

Stability analysis for unknown delayed systems controlled by model-free control

Explicit/multi-parametric model predictive control of dissipative distributed parameter systems

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