Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method
TL;DR: It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters.
Abstract: This paper considers the problem of adaptive fuzzy backstepping-based output-feedback controller design for a class of uncertain switched nonlinear stochastic systems in lower-triangular form without the measurements of the system states. By combining fuzzy logic systems’ universal approximation ability and dynamic surface control technique in the adaptive backstepping recursive design with a modified average dwell-time scheme, a new adaptive fuzzy control approach is presented for the switched system. More specifically, a switched observer is constructed to reduce the conservativeness aroused by the employ of a common observer, and individual coordinate transformations for subsystems are given up by adopting a common coordinate transformation of all subsystems. It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters. Finally, simulation studies are provided to demonstrate the validity of the proposed control method.
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TL;DR: This paper is concerned with the event-triggered finite-time control problem for networked switched linear systems by using an asynchronous switching scheme, and sufficient conditions are established to guarantee theevent-based asynchronous closed-loop systems are both finite-Time bounded and input-output finite- time stable.
Abstract: This paper is concerned with the event-triggered finite-time control problem for networked switched linear systems by using an asynchronous switching scheme. Not only the problem of finite-time boundedness, but also the problem of input-output finite-time stability is considered in this paper. Compared with the existing event-triggered results of the switched systems, a new type of event-triggered condition is proposed. Sufficient conditions are established to guarantee the event-based asynchronous closed-loop systems are both finite-time bounded and input-output finite-time stable. A set of event-triggered finite-time bounded and input-output finite-time stabilizing controllers are designed under the asynchronous control scheme. It is revealed that the triggered thresholds determine the number of sampling points transmitted to the controller, and the smaller triggered parameters indicate the less-sampled data needed to be transmitted to the controller under the event-triggered scheme. Finally, a boost converter circuit is applied to bring out the advantages of the proposed control scheme.
299 citations
Cites background from "Adaptive Output-Feedback Controller..."
...1) In contrast with [27]–[29], an event-triggered-based asynchronous switching control approach is constructed to resolve the FTB and IO-FTS problem....
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TL;DR: It is proven that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded with full state constraints.
Abstract: The problem of adaptive fuzzy control is investigated for a class of nontriangular structural stochastic switched nonlinear systems with full state constraints in this paper. A remarkable feature of the nontriangular structural nonlinear system is the so-called algebraic loop problem in the existing backstepping-based analysis and design. Properties of fuzzy basis functions are utilized to circumvent this algebraic loop problem. Based on the Barrier Lyapunov function, an adaptive fuzzy stochastic switched control scheme is designed. It is proven that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded with full state constraints. The effectiveness of the proposed control scheme is verified via simulation studies.
297 citations
Cites background from "Adaptive Output-Feedback Controller..."
...INTRODUCTION SWITCHED systems, as a typical class of hybrid systems, have received considerable research attention [1]–[4]....
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TL;DR: This paper considers the problem of sampled-data adaptive output feedback fuzzy stabilization for switched uncertain nonlinear systems associated with asynchronous switching and proposes a scheme that is employed in a mass–spring–damper system to demonstrate its effectiveness.
Abstract: This paper considers the problem of sampled-data adaptive output feedback fuzzy stabilization for switched uncertain nonlinear systems associated with asynchronous switching. A state observer is designed to estimate the unmeasured states and fuzzy logic systems are employed to deal with the unknown nonlinear terms. Sampled-data controller and novel switched adaptive laws are constructed based on the recursive design method and an average dwell time constraint is given to ensure that the closed-loop system is stable. The proposed scheme is employed in a mass–spring–damper system to demonstrate its effectiveness.
201 citations
Cites methods from "Adaptive Output-Feedback Controller..."
...ADT methods offer the advantage of less conservatism and have been widely used [14], [15], [20]–[23], with several adaptive control methods being proposed [14], [20]–[22]....
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TL;DR: A universal formula is presented for constructing an adaptive output-feedback controller of the considered system with only one adaptive parameter by designing a switched state observer and the Lyapunov stability of the overall closed-loop system is ensured in the presence of ADT switching.
Abstract: This paper deals with the issue of adaptive observer-based stabilization for a more general class of uncertain switched stochastic nonlower triangular nonlinear systems with average dwell-time (ADT) switching. The completely unknown nonlinear functions possessing the entire states are handled using the neural networks universal approximation property and the variable separation technique. The main novelty of this paper is that it presents a universal formula for constructing an adaptive output-feedback controller of the considered system with only one adaptive parameter by designing a switched state observer. The theoretical analysis shows that the Lyapunov stability of the overall closed-loop system is ensured in the presence of ADT switching. Finally, the effectiveness and practicability of the obtained design scheme are illustrated by two simulation examples.
155 citations
Cites background from "Adaptive Output-Feedback Controller..."
...Therefore, when the common Lyapunov function of all subsystems does not exist or is difficult to find, a thorough study on the stability of switched systems with average dwell-time (ADT) switching schemes is of momentous theoretical and practical significance [16]–[21]....
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TL;DR: The concept of semi-globally uniformly ultimately bounded (SGUUB) stability that is widely used for smooth nonlinear systems in lower triangular form is applied to the nonsmooth case, and such a concept provides a theory foundation for the subsequent backstepping control design.
Abstract: This paper investigates the problems of backstepping control for a class of nonsmooth nonlinear systems. With the help of set-valued functions (or maps) and set-valued derivatives, a new Lyapunov criterion is developed for nonsmooth systems. The concept of semi-globally uniformly ultimately bounded (SGUUB) stability that is widely used for smooth nonlinear systems in lower triangular form is, for the first time, applied to the nonsmooth case, and such a concept provides a theory foundation for the subsequent backstepping control design. Then, two types of continuous controllers are designed based on the backstepping technique and adaptive neural network (NN) algorithm. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. Then, the first type of controller can be efficiently designed by using the traditional backstepping technique. On the other hand, when the unknown uncertainty is taken into account in the equivalent systems, another type of controller is designed based on adaptive NN control strategy. It is proved that in both cases, all the closed-loop signals are SGUUB by using our proposed controllers. Finally, a numerical example with two types of controllers is supplied to show the availability of the provided control schemes.
142 citations
References
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Book•
24 Jun 2003
TL;DR: I. Stability under Arbitrary Switching, Systems not Stabilizable by Continuous Feedback, and Systems with Sensor or Actuator Constraints with Large Modeling Uncertainty.
Abstract: I. INTRODUCTION 1. Basic Concepts II . STABILITY OF SWITCHED SYSTEMS 2. Stability under Arbitrary Switching 3. Stability under Constrained Switching III. SWITCHING CONTROL 4. Systems not Stabilizable by Continuous Feedback 5. Systems with Sensor or Actuator Constraints 6. Systems with Large Modeling Uncertainty IV. SUPPLEMENTARY MATERIAL A. Stability B. Lie Algebras Notes and References Bibliography Index
5,844 citations
"Adaptive Output-Feedback Controller..." refers background in this paper
...Definition 1 [1]: For a switching signal σ(t) and any t > τ > 0, denote by Nσ (τ, t) the number of switchings of σ(t) on the interval (τ, t)....
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...2597305 their widespread real applications, fruitful achievements for such systems have been reported [1]–[12]....
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TL;DR: Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy.
Abstract: Fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions. Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy. Based on the fuzzy basis function representations, an orthogonal least-squares (OLS) learning algorithm is developed for designing fuzzy systems based on given input-output pairs; then, the OLS algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system. The fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system, and the simulation results show that the control performance is improved by incorporating some common-sense fuzzy control rules. >
2,575 citations
"Adaptive Output-Feedback Controller..." refers background in this paper
...Lemma 1 [59]: Assume that f (x) is a continuous function, which is defined on a compact set ....
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...Nevertheless, it should be also emphasized that 0 < ST i (Zi)Si(Zi) ≤ 1 can be learned from the theories in [59]....
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07 Dec 1999
TL;DR: In this article, it was shown that scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of adaptive control systems.
Abstract: It is shown that switching among stable linear systems results in a stable system provided that switching is "slow-on-the-average". In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.
2,197 citations
"Adaptive Output-Feedback Controller..." refers background or methods in this paper
...4) The traditional ADT method in [13] and the presented ADT method in [53] and [55] cannot be directly used to deal with the problem of adaptive fuzzy output-feedback controller design of switched uncertain stochastic nonlinear system since mathematical expectation, which is one of the important digital features of random variable, should be exerted in the proof process....
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...It has been well known that the average dwell time (ADT) scheme is a relatively effective tool of designing stable switching signals to stabilize a switched system [13]–[18]....
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01 Jan 1999
TL;DR: In this article, it was shown that switching among stable linear systems results in a stable system provided that switching is slow-on-the-average, i.e., the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small.
Abstract: It is shown that switching among stable linear systems results in a stable system provided that switching is \slow-on-the-average." In particular, it is proved that exponential stability is achieved when the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.
2,028 citations
TL;DR: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form and it is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice.
Abstract: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, /spl tau/-1 low pass filters are included in the design where /spl tau/ is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.
1,901 citations
Additional excerpts
...In order to eliminate the explosion of complexity problem, the work [46] first proposed the so-called dynamic surface control (DSC) technique for a class of nonlinear lower-triangular systems with unknown functions....
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