Robust model predictive control of uncertain fractional systems: a thermal application

Rhouma, Aymen; Bouani, Faouzi

doi:10.1049/iet-cta.2014.0703

Cited by 24 publications

(10 citation statements)

References 35 publications

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“…Its application to arrhythmic medicine with fractional-order pharmacokinetics was described in [15]. In [16] a robust model predictive control of uncertain fractional thermal system was designed.…”

Section: Figure 1 Basic Structure Of the Fompcmentioning

confidence: 99%

Novel Fractional-Order Model Predictive Control: State-Space Approach

Petráš

2021

IEEE Access

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This paper deals with a novel approach to the fractional-order model predictive control in state space. Except well known fractional-order models of processes (plants) with arbitrary (real) order of the derivatives in fractional differential equations a new fractional performance index (cost function) and fractional control action are considered. Such combined approach to the model predictive control provides more degrees of freedom and incorporates fractional-order dynamics into the control in the form of memory due to the property of the fractional-order operator. An illustrative example of this approach is presented.INDEX TERMS model predictive control (MPC), fractional calculus, fractional-order model, fractional derivative, fractional-order cost function, fractional integral, constrains, linear quadratic regulator (LQR)

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Section: Figure 1 Basic Structure Of the Fompcmentioning

confidence: 99%

Novel Fractional-Order Model Predictive Control: State-Space Approach

Petráš

2021

IEEE Access

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“…In practice people have used other approximations to design MPC controllers (than the Grünwald-Letnikov discrete-time derivative) [20,40,22], however, without any guarantees of constraint satisfaction which is particularly important in failsensitive applications (e.g., medical).…”

Section: Problem Statement: Objectives and Constraintsmentioning

confidence: 99%

“…A common limitation of all aforementioned works is that although they recognize the importance of MPC in handling input and output/state constraints, they do not take explicitly into account those constraints in the proposed MPC formulations. In [22] input constraints were considered in the formulation of the MPC optimization problem, however, without constraints on the state variables and without theoretical stability guarantees.…”

Section: Introductionmentioning

confidence: 99%

Model predictive control for offset-free reference tracking of fractional order systems

Ntouskas

Sarimveis

Sopasakis

2018

Control Engineering Practice

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In this paper an offset-free model predictive control scheme is presented for fractionalorder systems using the Grünwald-Letnikov derivative. The infinite-history fractionalorder system is approximated by a finite-dimensional state-space system and the modeling error is cast as a bounded disturbance term. Using a state observer, it is shown that the unknown disturbance at steady state can be reconstructed and modeling errors and other persistent disturbances can be attenuated. The effectiveness of the proposed controller-observer ensemble is demonstrated in the optimal administration of an anti-arrhythmic medicine with fractional-order pharmacokinetics.

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“…In 1999, Podlubny has also developed the non-integer PID regulator [1]. The evolution of fractional control continues to draw the attention of several researchers as well as industrialists [8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller

2022

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In this paper, we suggest an improvement to our previously undertaken approach. Briefly, this approach consisted of applying the robust fractional predictive control (RFPC) for a class of constrained fractional systems implementing the min–max optimization technique. The RFPC controller requires resolution of a non-convex min–max optimization problem. The resolution of this problem, however, can only conduce to local solutions. The reason is simple: the objective function to be optimized is non-convex due to the presence of uncertainties. In the present work, we propose a global optimization-based RFPC controller for an uncertain fractional order system. A determinist global optimization method, namely, generalized geometric programming (GGP), is proposed to solve this problem for the uncertain fractional order system. The GGP method consists of converting a non-convex problem into a convex one via the application of variable changes. The technique of the convexification of this method is applied in line with the objective function to be optimized. Consequently, we obtained a new convex criterion and a convex problem. From an experimental point of view, we applied the proposed RFPC to a real thermal system using an STM32 microcontroller in order to control our thermal system.

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Robust model predictive control of uncertain fractional systems: a thermal application

Cited by 24 publications

References 35 publications

Novel Fractional-Order Model Predictive Control: State-Space Approach

Novel Fractional-Order Model Predictive Control: State-Space Approach

Model predictive control for offset-free reference tracking of fractional order systems

Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller

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