A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties

Wheeler, G.; Su, Chun‐Yi; Stepanenko, Y.

doi:10.1016/s0005-1098(98)80024-1

Cited by 166 publications

(65 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, inequality (40) in Corollary 4 is satisfied to assure that the globally exponential adaptive synchronization in mean square of the drive system (34) and the noiseperturbed response system (35) is realized under the adaptive control law (41). Note that the sufficient conditions established in [44] and [45] cannot be utilized to consider this example, due to the difficulty that stems from time-varying delay.…”

Section: Examplesmentioning

confidence: 99%

“…There exist many excellent works on synchronization or chaotic synchronization in engineering applications [33]- [35], such as secure communications, image encryption, chaos generator design, chemical reaction, biological systems, and information science. In recent years, the synchronization problems of chaotic systems have widely been investigated by using some prevalent methods, such as feedback control [36], adaptive control [37], [38], backstepping control [39], sliding-mode control [40], and sampled data control [41], [42]. In [43], the exponential synchronization in pth(p > 1)-moment for stochastic Markov chaotic systems with time-delay has been realized by designing the adaptive feedback controller, and the obtained sufficient conditions are expressed in terms of M-matrix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Chen

Shi

Lim

et al. 2016

IEEE Trans. Cybern.

View full text Add to dashboard Cite

In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained.

show abstract

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Chen

Shi

Lim

et al. 2016

IEEE Trans. Cybern.

View full text Add to dashboard Cite

show abstract

“…Step 2: To obtain control u in the following theorem, let: i.e., inequalities (15) have solutions P (k) 2 R m2m , K(k) 2 R m2(n0m) ; k 2 S, Q(k) 2 R m2(n0m) ; k 2 S, and there exists a constant scalar > 0 such that the following inequalities hold: R(k) 0 11(k) 0 j=1 kj P (j) > P (k) (25) then the following control makes the closed-loop system is bounded in probability: u =0B 01 2 (k)[(311(k)+12(k))y1(t)+(312(k)+Q(k))y2(t)]+uN (26) u N = 0 B y (t) kB y (t)k ; if kB T 2 y 2 (t)k > 0 B y (t) 2 ; if kB T 2 y 2 (t)k (27) and the adaptation laws arê =ĉ(y(t);t)+(y(t);t)ky(t)k (28) _ c(t; y) =q 1 (0 0ĉ + kB T 2 y 2 (t)k) (29) _ (t; y) =q 2 (0 1 + kB T 2 y 2 (t)kky(t)k) (30) where q 1 , q 2 , 0 and 1 are design parameters.…”

Section: )mentioning

confidence: 99%

Adaptive Backstepping Controller Design for Stochastic Jump Systems

Xia

Shi

et al. 2009

IEEE Trans. Automat. Contr.

140

View full text Add to dashboard Cite

In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques.Index Terms-Adaptive control, backstepping control, linear matrix inequality, Markovian jump system, stochastic stability. Manuscript

show abstract

“…Notable exceptions are [15] and the references therein. Here the gain will be allowed to be adaptive.…”

Section: Introductionmentioning

confidence: 99%

“…This adaptation scheme is different to the one in [15]. The choice of the design parameters will be discussed later.…”

Section: Introductionmentioning

confidence: 99%

Fault Tolerant Control of a Civil Aircraft Using a Sliding Mode Based Scheme

Alwi

Edwards

Proceedings of the 44th IEEE Conference on Decision and Control

View full text Add to dashboard Cite

This paper presents a sliding mode control scheme for reconfigurable control of a civil aircraft. The controller is based around a state-feedback sliding mode scheme where the nonlinear unit vector term is allowed to adaptively increase when the onset of a fault is detected. Compared to other fault tolerant controllers which have been implemented on this model, the controller proposed here is relatively simple and yet is shown to work across the entire 'up and away' flight envelope. Unexpected deviation of the switching variables from their nominal condition triggers the adaptation mechanism.

show abstract

A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties

Cited by 166 publications

References 9 publications

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Adaptive Backstepping Controller Design for Stochastic Jump Systems

Fault Tolerant Control of a Civil Aircraft Using a Sliding Mode Based Scheme

Contact Info

Product

Resources

About