Event-triggered mixed  H_\infty  and passive control for Markov jump systems with bounded inputs

Jin, Liqiang; Yin, Yanyan; Teo, Kok Lay; Liu, Fei

doi:10.3934/jimo.2020024

Cited by 2 publications

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“…Given the deterministic system (11) with the initial condition 𝜼(0), find a control ũ(t ) ∈ Ũ such that the cost function ( 15) is minimised subject to the state inequality constraints (16), where Ũ is the set which contains all control functions satisfying the following constraints.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

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Optimal control of nonlinear Markov jump systems by control parametrisation technique

Jin

Yin

Loxton

et al. 2022

IET Control Theory & Appl

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This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient-based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real-world practical problem involving a bioreactor tank model is solved using the method proposed.

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Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Due to the important nature of such systems, there is a growing interest among research community towards the study of Markov jump systems. See, for instance, stability analysis [6][7][8], controller design [9][10][11], filtering [12][13][14], and fault detection [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of nonlinear Markov jump systems by control parametrisation technique

Jin

Yin

Loxton

et al. 2022

IET Control Theory & Appl

Self Cite

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“…Introduction. In the past decade, uncertain systems with unconstructed or constructed uncertain parameters have attracted much attention from worldwide researchers, and robust control [1] has been used for controller design for such a system [19,7,13,10], controller design for constrained systems is still addressed in some work [11]. In the classical robust control methods, the controllers designed are robust against all the uncertainties so that the system has a good performance under the control, see [20,21,22].…”

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confidence: 99%

Probabilistic robust anti-disturbance control of uncertain systems

Peng¹,

Pan²,

Yin³

et al. 2021

JIMO

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We propose a novel method for constructing probabilistic robust disturbance rejection control for uncertain systems in which a scenario optimization method is used to deal with the nonlinear and unbounded uncertainties. For anti-disturbance, a reduced order disturbance observer is considered and a state-feedback controller is designed. Sufficient conditions are presented to ensure that the resulting closed-loop system is stable and a prescribed H∞ performance index is satisfied. A numerical example is presented to illustrate the effectiveness of the techniques proposed and analyzed.

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Event-triggered mixed H_\infty and passive control for Markov jump systems with bounded inputs

Cited by 2 publications

References 0 publications

Optimal control of nonlinear Markov jump systems by control parametrisation technique

Optimal control of nonlinear Markov jump systems by control parametrisation technique

Probabilistic robust anti-disturbance control of uncertain systems

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