Switching‐based state tracking of model reference adaptive control systems in the presence of intermittent failures of all actuators

Self Cite

This paper investigates the adaptive quasi-passification-based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasipassification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi-passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods. KEYWORDSadaptive quasi-passification, recursive feedback quasi-passification, global practical stability, switched nonlinear systems, average dwell timeAs a special kind of hybrid dynamical systems, a switched system is composed of a family of continuous-time subsystems and a rule that governs the switching among them. Switched systems have attracted a great amount of attention because of their importance from both theoretical and practical points of view. 1-4 Many practical systems, such as aircraft control systems, mechanical systems and electrical systems, can be modeled as switched systems. 2,4-6 Stability analysis and stabilization problems for switched systems have been extensively studied. Since uncertainties which may cause instability and undesirable performance exist widely in real world systems, one should consider these effects on plant. H ∞ control, robust control and adaptive control are often used to deal with uncertainties. 7-13 For parametric uncertainties, adaptive control has been one of the most effective methods. The asymptotic stability is often the desired performance. 3,5,10,11,14 However, in many practical applications, asymptotic stability may be difficult to obtain due to large uncertainties. From an engineering point of view, the global practical stability can be often satisfactory. 12,13 On the other hand, passivity, introduced by Willems, 15 provides an effective tool for solving the problems of stability analysis and stabilization. 15-17 When a system involves unknown parameters, the adaptive passification and adaptive passivity-based stabilization problems were solved in. 6,18-21 However, the exact feedback passification and asymptotical stabilization problems were intractable because of the large system uncertainties. Therefore, the development of passivity-based methodology for this case would be desirable. The convention passivity property was extended to quasipassivity, 22,23 which were used to investigate the ultimate boundedness of state trajectories of nonlinear uncertain systems. Similar to the concept of strict quasi-passivity, the concepts of passivity with respect to a set and semipassivity were proposed to derive a stability property of the set....

Section: Lemma 3 (40)mentioning

confidence: 71%

“…

This paper investigates the adaptive quasi-passification-based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. 12,13 On the other hand, passivity, introduced by Willems, 15 provides an effective tool for solving the problems of stability analysis and stabilization. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters.

…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

Pang

Zhao

2017

Self Cite

This paper investigates the adaptive quasi-passification-based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasipassification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi-passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods. KEYWORDSadaptive quasi-passification, recursive feedback quasi-passification, global practical stability, switched nonlinear systems, average dwell timeAs a special kind of hybrid dynamical systems, a switched system is composed of a family of continuous-time subsystems and a rule that governs the switching among them. Switched systems have attracted a great amount of attention because of their importance from both theoretical and practical points of view. 1-4 Many practical systems, such as aircraft control systems, mechanical systems and electrical systems, can be modeled as switched systems. 2,4-6 Stability analysis and stabilization problems for switched systems have been extensively studied. Since uncertainties which may cause instability and undesirable performance exist widely in real world systems, one should consider these effects on plant. H ∞ control, robust control and adaptive control are often used to deal with uncertainties. 7-13 For parametric uncertainties, adaptive control has been one of the most effective methods. The asymptotic stability is often the desired performance. 3,5,10,11,14 However, in many practical applications, asymptotic stability may be difficult to obtain due to large uncertainties. From an engineering point of view, the global practical stability can be often satisfactory. 12,13 On the other hand, passivity, introduced by Willems, 15 provides an effective tool for solving the problems of stability analysis and stabilization. 15-17 When a system involves unknown parameters, the adaptive passification and adaptive passivity-based stabilization problems were solved in. 6,18-21 However, the exact feedback passification and asymptotical stabilization problems were intractable because of the large system uncertainties. Therefore, the development of passivity-based methodology for this case would be desirable. The convention passivity property was extended to quasipassivity, 22,23 which were used to investigate the ultimate boundedness of state trajectories of nonlinear uncertain systems. Similar to the concept of strict quasi-passivity, the concepts of passivity with respect to a set and semipassivity were proposed to derive a stability property of the set....

“…During the past decades, a large number of results have been published for switched systems [2,3], many of which are about stability of switched systems. Therefore, global practical stability has attracted growing attention in the control theory field [6]. However, in many practical applications, such conditions may be difficult to satisfy, especially when systems contain large uncertainties.…”

Section: Introductionmentioning

confidence: 99%

“…Global practical stability is such a desirable property for switched systems. Therefore, global practical stability has attracted growing attention in the control theory field [6].…”

Section: Introductionmentioning

confidence: 99%

Model reference adaptive control for nonlinear switched systems under asynchronous switching

Xie

Zhao

2016

Self Cite

In this paper, the problem of model reference adaptive control for nonlinear switched systems with parametric uncertainties is investigated. Asynchronous switching between subsystems and adaptive controllers is also considered. Firstly, a state feedback adaptive controller is designed. Then, sufficient conditions ensuring the global practical stability of the error switched system with average dwell time are proposed. The boundedness of all signals in the closed-loop system is guaranteed by the proposed adaptive controller. Finally, a practical example is given to demonstrate the validity of the main results.(MRAC) philosophy to piecewise smooth systems. For MIMO dynamical systems with partially known dynamics, [15] proposed the composite model reference adaptive control tracking design technique to improve tracking performance.Uncertainties also exist extensively in switched systems, which brings considerable difficulties for researchers. The main problem is that we need to compare the values of the adjacent Lyapunov functions at the switching instants. However, for switched systems with parametric uncertainties, as parametric estimation errors exist in Lyapunov functions, it is impossible to exactly know the values of the Lyapunov functions at a switching instant, which makes the existing stability conditions inapplicable. Some attempt has been made to overcome this obstacle. By the parameter projection adaptive law, a small tracking error is achieved based on the dwell time method [14,16]. Inspired by Sang and Tao [14], Wu et al.[6] developed a novel method that the conditions of the dwell time method are satisfied outside a ball centered at the origin with a given radius, then the global practical stability is obtained. However, for nonlinear switched systems with parametric uncertainties, the problem becomes much more complicated because of the existence of nonlinear terms. Up to now, few results on MRAC for nonlinear switched systems have been reported, which motivates us on this note.What is more, in practice, the switching signal available to the controllers is often later than the switching of subsystems, which results in asynchronous switching in the closed-loop system. It is worth noting that, asynchronous switching causes unavailability of matching conditions for MRAC, which may lead to instability. In recent years, asynchronous switching has become a hot research direction, and a lot of results have been developed [17][18][19]. However, in practice, uncertainties and asynchronous switching can coexist in a switched system, which brings out a challenge. In [19], by the dwell time method, the MRAC was studied under asynchronous switching for a class of linear switched systems. However, for nonlinear switched systems, there is a lack of study. This is another motivation of the present study.In this paper, we present an MRAC scheme for nonlinear switched systems based on the average dwell time method under asynchronous switching. Compared with the existing literature on MRAC for switched systems, the res...

Intermittent fault detection in nonstationary processes via a Wald‐based control chart

Liu,

Zhao,

Gao

et al. 2024

SummaryIn this article, the problem of intermittent fault (IF) detection is investigated for nonstationary processes in the multivariate statistics framework. By combining the moving window technique with maximum likelihood estimation (MLE), the moving window Wald‐based control chart is proposed to realize the detection of IFs in nonstationary processes. The computational efficiency and the convergence properties are discussed for the designed iterative algorithm of MLE. Then, necessary and sufficient conditions are presented to guarantee the detectability of IFs with the consideration of window lengths. Moreover, the alarm delays are analyzed for the appearance and disappearance of IFs. In virtue of the above analysis, the optimal window length is derived by minimizing the supremum of alarm delays. In order to estimate the time of IFs' appearance and disappearance, an algorithm is designed with the inspiration of simulated annealing strategy. Finally, a simulation on rotary steerable drilling tool system is provided to verify the effectiveness of the proposed method.