Robust optimal guaranteed cost control for 2D discrete systems

Guan, Xinping; Long, Chengnian; Duan, Guang‐Ren

doi:10.1049/ip-cta:20010596

Cited by 70 publications

(46 citation statements)

References 13 publications

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“…The matrices , , , , , and define the nominal model and , , , , , and represent admissible uncertainties which are assumed to be of the form (3) In this last equation, , , , , and are known constant matrices of compatible dimensions, and is an unknown matrix with constant entries which satisfies (4) To complete the process description, it is necessary to specify the boundary conditions, i.e., the state initial vector on each pass and the initial pass profile (i.e., on pass 0). The simplest possible choice for these is (5) where the vector has known constant entries and is the vector whose entries are known functions of over .…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

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Guaranteed Cost Control of Uncertain Differential Linear Repetitive Processes

Paszke

Gałkowski

Rogers

et al. 2004

IEEE Trans. Circuits Syst. II

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Abstract-This paper deals with the problem of designing a control law for differential linear repetitive processes based on minimizing a cost function in the presence of uncertainties in the process model. This control law results in a closed-loop stable process with an associated cost function which is bounded for all admissible uncertainties. Moreover, an optimization algorithm is developed to design this law such that it minimizes the upperbound of the closed-loop cost function.

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Section: Preliminaries and Problem Statementmentioning

confidence: 99%

“…In this paper, we develop a solution to the so-called guaranteed cost control problem for differential linear repetitive processes (for the discrete 2-D linear systems case, see [3]). The solution gives a control law which ensures an adequate level of performance as represented by the cost function.…”

mentioning

confidence: 99%

Guaranteed Cost Control of Uncertain Differential Linear Repetitive Processes

Paszke

Gałkowski

Rogers

et al. 2004

IEEE Trans. Circuits Syst. II

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“…In addition, inspired by the Lyapunov stability condition, the problem of stability of 2D systems has been presented in [6]. Robust stability problem and also optimal guaranteed cost control of the uncertain 2D systems are considered in [7], [8] and [9]. As an effective approach, the SMC method is used for 1D continuous and discrete time systems [10] - [12].…”

Section: Introductionmentioning

confidence: 99%

A new approach to applying discrete sliding mode control to 2D systems

Argha

2013

52nd IEEE Conference on Decision and Control

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Abstract-Sliding mode control has been applied previously to a specific form of 2D systems (Roesser model). In this paper a new approach (1D vectorial form) is introduced for this problem. Using 1D form to represent 2D systems can be used as an alternative strategy to reduce the inherent complexity of 2D systems and their applications. Unlike Wave Advanced Model (WAM) form (proposed by Porter and Aravena), the suggested 1D vectorial form, in this paper, has invariable dimension and consequently can be converted to regular form for sliding mode control (SMC). In this paper, the first Fornasini and Marchesini (FM) model of 2D systems which is a second order recursive form is considered. Meantime, the suggested method can be simply deployed to other first or second order 2D models.

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“…Some new results on the stability of 2-D systems have been presented -specifically with regard to the Lyapunov stability condition which has been developed for RM (Lu, 1994). Then, robust stability problem (Wang & Liu, 2003) and optimal guaranteed cost control of the uncertain 2-D systems (Guan et al, 2001;Du & Xie, 2001;Du et al, 2000 ) came to be the area of interest. In addition, an adaptive control method for SISO 2-D systems has been presented (Fan & Wen, 2003).…”

Section: Introductionmentioning

confidence: 99%