A Separated Approach to Control of Markov Jump Nonlinear Systems With General Transition Probabilities

Shen, Mouquan; Park, Ju H.; Ye, Dan

doi:10.1109/tcyb.2015.2459717

Cited by 138 publications

(77 citation statements)

References 35 publications

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“…Remark For the proof of Theorem , Case I is similar to the one in the work of Shen et al For Case II, P l ≤ P i needs to be satisfied in the work of the aforementioned author . This condition can be removed by using a piecewise function in the current work, which means that the condition proposed in this paper is more general.…”

Section: Resultsmentioning

confidence: 91%

“…The transition probabilities of the jumping process { r ( t ), t ≥0} is supposed to be generally uncertain, ie, each of them maybe known, or uncertain, or completely unknown . For example, the matrix of system with s operation modes may be expressed as

([], \begin{matrix} center \\ array π_{11} + {normalΔ}_{11} & array ? & array π_{13} & array ⋯ & array ? \\ array ? & array ? & array π_{23} & array ⋯ & array π_{2 s} + {normalΔ}_{2 s} \\ array ⋮ & array ⋮ & array ⋮ & array ⋱ & array ⋮ \\ array π_{s 1} & array π_{s 2} + {normalΔ}_{s 2} & array ? & array ⋯ & array π_{s s} + {normalΔ}_{s s} \end{matrix}),

where ?…”

Section: Problem Statementmentioning

confidence: 99%

“…However, most of the aforementioned results are based on the assumption that all terms of the transition probability matrix are exactly known. However, to have exact knowledge of the transition probabilities is difficult in practice due to limitation of equipment and influence of uncertain factors . This makes the results on the Markovian jump neural networks with completely known transition probabilities not implementable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

Liu

Park

Guo

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, dissipative synchronization problem for the Markovian jump neural networks with time‐varying delay and general transition probabilities is investigated. An event‐triggered communication scheme is introduced to trigger the transmission only when the variation of the sampled vector exceeds a prescribed threshold condition. The transition probabilities of the Markovian jump delayed neural networks are allowed to be known, or uncertain, or unknown. By employing delay system approach, a new model of synchronization error system is proposed. Applying the Lyapunov‐Krasovskii functional and integral inequality combining with reciprocal convex technique, a delay‐dependent criterion is developed to guarantee the stochastic stability of the errors system and achieve strict (Q,S,R)−α dissipativity. The event‐triggered parameters can be derived by solving a set of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed design method.

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Section: Resultsmentioning

confidence: 91%

([], \begin{matrix} center \\ array π_{11} + {normalΔ}_{11} & array ? & array π_{13} & array ⋯ & array ? \\ array ? & array ? & array π_{23} & array ⋯ & array π_{2 s} + {normalΔ}_{2 s} \\ array ⋮ & array ⋮ & array ⋮ & array ⋱ & array ⋮ \\ array π_{s 1} & array π_{s 2} + {normalΔ}_{s 2} & array ? & array ⋯ & array π_{s s} + {normalΔ}_{s s} \end{matrix}),

where ?…”

Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

Liu

Park

Guo

et al. 2018

Intl J Robust & Nonlinear

Self Cite

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show abstract

“…As is well known, the coupling relationship between the controller gain and the Lyapunov variable is the key obstacle in addressing static output‐feedback control issues (see the work of Shu et al for more details). In this paper, inspired by other works, we introduce the following separation strategy:

\begin{matrix} alignleft \\ align-1 B {normalΦ}_{σ (k)} K_{σ (k)} C {\vec{P}}_{σ (k)} = B {normalΦ}_{σ (k)} {\vec{K}}_{σ (k)} + B {normalΦ}_{σ (k)} {\vec{L}}_{σ (k)}, & align-2 \end{matrix}

where

{\overset{L}{true}}_{σ false(k false)} ≜ K_{σ false(k false)} C {\overset{P}{true}}_{σ false(k false)} - {\overset{K}{true}}_{σ false(k false)}

.…”

Section: Design Of Static Output‐feedback Smc Under Round‐robin Protocolmentioning

confidence: 99%

Static output‐feedback sliding mode control under round‐robin protocol

Song

Wang

Niu

2018

Intl J Robust & Nonlinear

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Summary This paper addresses the static output‐feedback sliding mode control (SMC) problem for a class of uncertain control systems subject to the round‐robin protocol scheduling, in which the communication between the controller and the actuators is regulated by the round‐robin protocol, that is, only one actuator node gets the access to the transmission network at each instant and the other actuators utilize the values stored in the zero‐order holders. A key issue of the addressed problem is how to design both the sliding surface and the sliding mode controller subject to the kind of actuator signals depending on protocol scheduling and zero‐order holders. By only using the measured output information, a linear sliding surface is constructed, and then, a token‐dependent SMC law is designed properly with the aid of an updating rule on actuator input. Moreover, suitable token‐dependent Lyapunov functions are exploited to obtain sufficient conditions for guaranteeing the asymptotic stability of the closed‐loop systems and the reachability of the specified sliding surface. Furthermore, based upon a separation strategy, a convex optimization algorithm is proposed to obtain the controller gains. Finally, the effectiveness of the developed static output‐feedback SMC design scheme is verified in an industrial continuous‐stirred tank reactor system.

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“…Because of two kinds of mechanisms contained, it is very suitable to model such actual systems whose structures or parameters change [1,2]. Over the past years, many research topics on MJSs have been extensively studied, like stability analysis [3][4][5][6], stabilization [7][8][9][10][11], robust control [12][13][14][15], adaptive control [16][17][18][19], ∞ filtering and control [20,21], state estimation [22][23][24][25], synchronization [26][27][28][29][30], and so on.…”

Section: Introductionmentioning

confidence: 99%

Observer Design for Delayed Markovian Jump Systems with Output State Saturation

Wang

Feng

2018

Mathematical Problems in Engineering

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This paper considers the observer design problem of continuous-time delayed Markovian jump systems with output state saturation. Different from the traditionally observer-based saturation control methods, a kind of system output state saturation with a partially delay-dependent property is proposed, where both nondelay and delay states exist at the same time but happen asynchronously. By exploiting the Bernoulli variable, the probability distributions of such two states are described and considered in the observer design. Based on an improved equality applied to deal with saturation terms, sufficient conditions for the designed observer with three kinds of output saturations are all provided with LMI forms. Finally, a numerical example is given to indicate the effectiveness of the obtained results.

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A Separated Approach to Control of Markov Jump Nonlinear Systems With General Transition Probabilities

Cited by 138 publications

References 35 publications

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

Static output‐feedback sliding mode control under round‐robin protocol

Observer Design for Delayed Markovian Jump Systems with Output State Saturation

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