An observer-based control of linear systems with uncertain parameters

Rachik, Mostafa; Lhous, Mustapha

doi:10.1515/acsc-2016-0031

Cited by 4 publications

(2 citation statements)

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“…The maximal output sets (MOS) are of interest for the analysis of controlled constrained systems. Recently, maximal output set has been characterized for observability and asymptotically stable systems in the case of linear discrete-time systems (see [17][18][19][20][21]), this concept allows the comprehension of the analysis of constrained control systems. In addition, it is applied in control system design techniques [22].…”

Section: Introductionmentioning

confidence: 99%

On the maximal output set of fractional-order discrete-time linear systems

Bhih¹,

Benfatah²,

Ghazaoui³

et al. 2022

Math. Model. Comput.

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In this paper, we consider a linear discrete-time fractional-order system defined by \[\Delta ^{\alpha }x_ {k+1}=Ax_k+B u_k, \quad k \geq 0, \quad x_{0} \in \mathbb{R}^{n};\] \[y_{k}=Cx_k, \quad k \geq 0,\] where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $\alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control. By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, $\Gamma(\Omega)=\lbrace x_{0} \in \mathbb{R}^{n}/y_{i} \in \Omega,\forall i \geq 0 \rbrace$, where $\Omega\subset\mathbb{R}^{p}$ is a constraint set; and, by using some hypotheses of stability and observability, we prove that $\Gamma(\Omega)$ can be derived from a finite number of inequations. A powerful algorithm approach is included to identify the maximal output set; also, some appropriate algorithms and numerical simulations are given to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

On the maximal output set of fractional-order discrete-time linear systems

Bhih¹,

Benfatah²,

Ghazaoui³

et al. 2022

Math. Model. Comput.

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“…Studies of disturbed systems have continued to grow in importance in recent years. Unknown disturbances are detected by observation and several works have been devoted to their detection and reconstruction from the corresponding observation (see [6,9,12,13,17,21,22,24,26]).…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Magri,

Amissi,

Afifi

et al. 2022

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We consider in this work a class of finite dimensional time-varying linear disturbed systems. The main objective of this work is to studied the optimal control which ensures the remediability of a disturbance of time-varying disturbed systems. The remediability concept consist to find a convenient control which bringing back the corresponding observation of disturbed system to the normal one at the final time. We give firstly some characterisations of compensation and in second party we find a control which annul the output of the system and we show also that the Hilbert Uniqueness Method can be used to solve the optimal control which ensure the remediability. A general approach was given to minimize the linear quadratic problem. Examples and numerical simulations are given.

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