Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Kao, Yonggui; Yang, Tianjun; Park, Ju H.

doi:10.1002/rnc.3970

Cited by 31 publications

(19 citation statements)

References 33 publications

(31 reference statements)

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“…In this section, we shall derive some new criteria guaranteeing the systems stochastically finite-time bounded and stable. For convenient representation, denote 13 = col{e 11 , e 9 }, 21 = col{e 9 , e 1 }, 22 = col{e 10 , e 3 }, 23 = col{e 11 , e 7 }, 42 = col{e 12 , e 13 },…”

Section: Resultsmentioning

confidence: 99%

“…It is known that the realization of artificial NNs is usually based on electronic circuits (ECs), whereas time‐varying delays (TDs) can not be avoided due to the limited switching speed of amplifiers in ECs and often leads to undesirable dynamic behaviors, such as chaotic, oscillation, and even unstable. In addition, it has been found in modern large‐scale integrated ECs research, the current state of the systems is not only affected to the delayed state but also to the change rate of the delayed state . This means that there exists a phenomenon of neutral behavior in NNs, which can be suitably described by a special kind of NNs, namely, neutral‐type neural networks (NNNs).…”

Section: Introductionmentioning

confidence: 99%

“…In general, these random behaviors can be accurately characterized by a special kind of stochastic process: semi‐Markov process (SMP) . Different from the well‐known Markov process, the sojourn time in the SMP is a random variable that does not follow a memoryless exponential distribution but a more general probability distribution, such as Weibull distribution, Laplace distribution, and so on . As a result, the transition rates will not be constant any more but time‐varying and depends on the sojourn time, which lead to the stability analysis and other synthesis problems of making NNs more challenging.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic robust finite‐time boundedness for semi‐Markov jump uncertain neutral‐type neural networks with mixed time‐varying delays via a generalized reciprocally convex combination inequality

Zhang

Qiu

Liu

et al. 2019

Intl J Robust & Nonlinear

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Summary This article investigates the stochastic robust finite‐time boundedness problem for semi‐Markov jump uncertain (SMJU) neutral‐type neural networks with distributed and additive time‐varying delays (TDs). To derive less conservative stability criteria, a generalized reciprocally convex combination inequality (RCCI) is first proposed, which includes the existing RCCIs as its special cases. By taking full advantage of the characteristics of various TDs and SMJU parameters, a novel suitable Lyapunov‐Krasovskii functional is provided. Then, with the virtue of the new RCCI and other analysis approaches, some new criteria guaranteeing the underlying systems are stochastically robustly finite‐time bounded or stable and are derived in the form of linear matrix inequalities. Finally, three numerical examples are given to show the validity of the approaches presented in this article.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic robust finite‐time boundedness for semi‐Markov jump uncertain neutral‐type neural networks with mixed time‐varying delays via a generalized reciprocally convex combination inequality

Zhang

Qiu

Liu

et al. 2019

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…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%

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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“…For ε-greedy exploration, since the action with the maximal Q-value will be selected for exploitation, the Q-value can be viewed as the switching signal. Thus results on stability analysis for switching systems [18,19] might be beneficial to the analysis of IQL with ε-greedy exploration. Awheda and Schwartz [11] proposed EMA Q-learning and proved its ability to converge to a Nash equilibrium in two-player two-action games.…”

Section: Introductionmentioning

confidence: 99%

EAQR: A Multiagent Q‐Learning Algorithm for Coordination of Multiple Agents

Zhang

Wang

2018

Complexity

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We propose a cooperative multiagent Q-learning algorithm called exploring actions according to Q-value ratios (EAQR). Our aim is to design a multiagent reinforcement learning algorithm for cooperative tasks where multiple agents need to coordinate their behavior to achieve the best system performance. In EAQR, Q-value represents the probability of getting the maximal reward, while each action is selected according to the ratio of its Q-value to the sum of all actions' Q-value and the exploration rate ε. Seven cooperative repeated games are used as cases to study the dynamics of EAQR. Theoretical analyses show that in some cases the optimal joint strategies correspond to the stable critical points of EAQR. Moreover, comparison experiments on stochastic games with finite steps are conducted. One is the box-pushing, and the other is the distributed sensor network problem. Experimental results show that EAQR outperforms the other algorithms in the box-pushing problem and achieves the theoretical optimal performance in the distributed sensor network problem.

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Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Cited by 31 publications

References 33 publications

Stochastic robust finite‐time boundedness for semi‐Markov jump uncertain neutral‐type neural networks with mixed time‐varying delays via a generalized reciprocally convex combination inequality

Stochastic robust finite‐time boundedness for semi‐Markov jump uncertain neutral‐type neural networks with mixed time‐varying delays via a generalized reciprocally convex combination inequality

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

EAQR: A Multiagent Q‐Learning Algorithm for Coordination of Multiple Agents

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