Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

Wu, Zhaojing; Xie, Xue‐Jun; Shi, Peng; Xia, Yuanqing

doi:10.1016/j.automatica.2008.12.002

Cited by 248 publications

(124 citation statements)

References 20 publications

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“…Authors in [18] first proposed an adaptive backstepping control design approach for strict-feedback stochastic systems by a risk-sensitive cost criterion. Authors in [19] solved the output feedback stabilization problem of strict-feedback stochastic nonlinear systems by using the quartic Lyapunov function, while authors in [20] and [21] developed backstepping control design approaches for nonlinear stochastic systems with Markovian switching. Meanwhile, by using the linear reduced-order state observer, several different output-feedback controllers are developed for strict-feedback stochastic nonlinear systems with unmeasured states, such as tracking control [22], decentralized control [23], and time-delay systems [24].…”

Section: Introductionmentioning

confidence: 99%

“…Their existence is a source of instability of the control systems, thus the investigations on stochastic systems modeling and control have received considerable attention in recent years [17][18][19][20][21][22][23][24]. Authors in [18] first proposed an adaptive backstepping control design approach for strict-feedback stochastic systems by a risk-sensitive cost criterion.…”

Section: Introductionmentioning

confidence: 99%

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Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

Tong

2011

Nonlinear Dyn

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In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multiinput and multioutput (MIMO) uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Utilizing the designed the fuzzy state observer and by combining the adaptive backstepping control design, an adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. A simulation example is provided to show the effectiveness of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

Tong

2011

Nonlinear Dyn

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“…A weaker sufficient condition for the existence of a unique solution to (4) using a notion of (finite or infinite) escape time under the local Lipschitz continuity condition (6) without the growth condition (7) is given in [41]. Alternatively, existence and uniqueness of solutions even when the uniform Lipschitz continuity condition (6) does not hold are given in ( [38], p. 152).…”

Section: ∂V(x) ∂Xmentioning

confidence: 99%

Stochastic Thermodynamics: A Dynamical Systems Approach

Rajpurohit

Haddad

2017

Entropy

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Abstract:In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time.

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“…They conclude that the optimal strategy is a cutoff strategy when the arms have two types. For other optimal strategies and control approaches, the reader is referred to [9][10][11] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A Common Value Experimentation with Multiarmed Bandits

Gao

Liang

Wang

2018

Mathematical Problems in Engineering

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We study a value common experimentation with multiarmed bandits and give an application about the experimentation. The second derivative of value functions at cutoffs is investigated when an agent switches action with multiarmed bandits. If consumers have identical preference which is unknown and purchase products from only two sellers among multiple sellers, we obtain the necessary and sufficient conditions about the common experimentation. The Markov perfect equilibrium and the socially effective allocation in -armed markets are discussed.

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Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching

Cited by 248 publications

References 20 publications

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

Stochastic Thermodynamics: A Dynamical Systems Approach

A Common Value Experimentation with Multiarmed Bandits

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