Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria †

Blair, William P.; Sworder, David D.

doi:10.1080/00207177508922037

Cited by 254 publications

(104 citation statements)

References 5 publications

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“…The vertices of the time-varying transition probability matrix are given by Next, we consider a nonhomogeneous economic system [29], which are aggregated into 3 modes: Table 2 And the vertices of the time-varying transition probability matrix are given below: …”

Section: Simulation Resultsmentioning

confidence: 99%

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Yin

Shi

Liu

et al. 2013

Int. J. Robust Nonlinear Control

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SUMMARYThis paper considers the problem of observer‐based H ∞ controller design for a class of discrete‐time nonhomogeneous Markov jump systems with nonlinear input. Actuator saturation is considered to be a nonlinear input of such system and the time‐varying transition probability matrix in the system is described as a polytope set. Furthermore, a mode‐dependent and parameter‐dependent Lyapunov function is investigated, and a sufficient condition is derived to design observer‐based controllers such that the resulting error dynamical system is stochastically stable and a prescribed H ∞ performance is achieved. Finally, estimation of attraction domain of such nonhomogeneous Markov jump systems is also made. A simulation example shows the effectiveness of developed techniques. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Simulation Resultsmentioning

confidence: 99%

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Yin

Shi

Liu

et al. 2013

Int. J. Robust Nonlinear Control

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“…Motivated by a wide spectrum of applications, for the last thirty years, there has been active research in the analysis [3], [22] and in the design of controllers [10] for Markovian jump linear systems. More specifically, in the last fifteen years, the classical paradigms of optimal control have been re-visited for Markovian jump linear systems, such as the ones defined by H 2 and mixed H 2 /H ∞ measures of performance [13], [17], [15] (see [14] for a more detailed survey of existing work).…”

Section: ) Results On Optimal Control Of Markovian Jump Linear Systemsmentioning

confidence: 99%

Optimal Preview Control of Markovian Jump Linear Systems

Running

Martins

2009

IEEE Trans. Automat. Contr.

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Isr develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government.Isr is a permanent institute of the university of maryland, within the a. James clark school of engineering. It is a graduated national science foundation engineering research center. AbstractIn this paper, we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview (reference look-ahead). For a quadratic cost and given a reference sequence, we obtain the optimal solution for the full information case. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term. We show that the feedback term is identical to the standard optimal linear quadratic regulator for Markovian jump linear systems. We provide explicit formulas for computing the feedforward term, including an analysis of convergence.

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“…A special case of the xindependent JLQ discrete-time problem is considered in Birdwell [15][16][17], and the finite-time horizon x-independent problem is solved in Blair and…”

Section: Nmentioning

confidence: 99%

“…satisfy (16). Straightforward adaptations of standard LQ arguments then allow us first to extend the convergence result to the case of arbitrary terminal cost matrices for the finite horizon problem and, secondly, to…”

Section: Conditionmentioning

confidence: 99%

Discrete-time markovian-jump linear quadratic optimal control

Chizeck

Willsky

Castañón³

1986

International Journal of Control

221

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This. paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite state Markov processes.For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.;ystems Enqgineering Department, Case

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Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria †

Cited by 254 publications

References 5 publications

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Optimal Preview Control of Markovian Jump Linear Systems

Discrete-time markovian-jump linear quadratic optimal control

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Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria †

Cited by 254 publications

References 5 publications

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH ∞ control on nonhomogeneous Markov jump systems with nonlinear input

Optimal Preview Control of Markovian Jump Linear Systems

Discrete-time markovian-jump linear quadratic optimal control

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Product

Resources

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Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input

Observer-basedH_∞control on nonhomogeneous Markov jump systems with nonlinear input