Discontinuous Feedback and Universal Adaptive Stabilization

Ryan, E. P.

doi:10.1007/978-1-4757-2108-9_12

Cited by 30 publications

(13 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, for all i3J. Therefore, (20) and H5 imply that the set V( *) is positively invariant and, for any x3V( *), all solutions reach a constrained control region R in is uniformly asymptotically stable. )…”

Section: Theorem 56mentioning

confidence: 91%

“…In order to show that a compact set M is globally uniformly asymptotically stable, it is required that (6) and (7) have inde"nite continuation of solutions. As a consequence of the work in Ryan [20] and under the continuity hypotheses stated earlier, every local solution x( ) ) : [t , t ) PX of (6) and (7) can be extended into a solution on a maximal interval of existence [0, ), *t , and if x( ) ) is bounded then "R, that is, every bounded solution can be continued inde"nitely. De"ne…”

Section: Lemma 41mentioning

confidence: 92%

See 1 more Smart Citation

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Goodall

Wang

2001

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYPractical and asymptotic stabilization is investigated for a class of uncertain nonlinear a$ne control systems subject to constraints on the control inputs. The uncertain systems are modelled as non-linear perturbations to a known non-linear idealized system and a problem formulation based on di!erential inclusions is adopted. A class of constrained generalized state-feedback controls (containing both continuous and discontinuous selections) is developed, which guarantees stabilization with a speci"ed region of attraction. In the presence of residual uncertainty, su$cient conditions for global stabilizability are presented, whilst local results are obtained by relaxing these conditions.

show abstract

Section: Theorem 56mentioning

confidence: 91%

Section: Lemma 41mentioning

confidence: 92%

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Goodall

Wang

2001

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Therefore, all maximal solutions of (14) such that x (t 0 ) ∈ Ω c are precompact [24, Definition 2.3] and T = sup I. In the following, arguments similar to [41,Proposition 2] are used to show that precompact solutions are complete.…”

Section: Design Examplesmentioning

confidence: 99%

Invariance-Like Results for Nonautonomous Switched Systems

Kamalapurkar

Rosenfeld

Parikh

et al. 2019

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper generalizes the LaSalle-Yoshizawa Theorem to switched nonsmooth systems. Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A candidate common Lyapunov function that has a negative semidefinite derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle-Yoshizawa results for the switched system. Results for regular and non-regular candidate Lyapunov functions are developed via appropriate generalization of the notion of a time derivative. The developed generalization is motivated by adaptive control of switched systems where the derivative of the candidate Lyapunov function is typically negative semidefinite.Index Terms switched systems, differential inclusions, adaptive systems, nonlinear systems Rushikesh Kamalapurkar is with the School 2 benefit from adaptive methods where the controller adapts to the uncertain dynamics without strictly relying on high gain or high frequency feedback often associated with robust control methods that can lead to overstimulation.Switched dynamics are inherent in a variety of modern adaptation strategies. For example, in sparse neural networks [5], the use of different approximation architectures for different regions of the state-space introduce switching via the feedforward part of the controller. In adaptive gain scheduling methods [6], switching is introduced due to changing feedback gains. Switching is also utilized as a tool to improve transient response of adaptive controllers by selecting between multiple estimated models of stable plants (see, e.g., [7]-[16]). In addition, switched systems theory can be utilized to extend the scope of existing adaptive solutions to more complex circumstances that involve switched dynamics.Lyapunov-based stability analysis of switched nonautonomous adaptive systems is challenging because adaptive update laws typically result in non-strict Lyapunov functions for the individual subsystems. For each subsystem, convergence of the error signal to the origin is typically established using Barbȃlat's lemma (e.g., [17, Lemma 8.2]).In traditional methods that utilize multiple Lyapunov functions (e.g., [18, Theorem 3.2]) the class of admissible switching signals is restricted based on the rate of decay of the cLf (cf. [18, Eq. 3.10]). Since Barbȃlat's lemma provides no information about the rate of decay of the cLf, it alone is insufficient to establish stability of a switched system using multiple Lyapunov functions. Approaches based on common cLfs have been developed for systems with negative definite Lyapunov derivatives; however, common cLf-based approaches do not trivially extend to systems with non-strict Lyapunov functions (cf. [19]-[21] and [18, Example 2.1]). Because of complications resulting from a negative semidefinite Lyapunov derivative, few results are available in literature that examine adaptive control of uncertain nonlinear switched systems. An...

show abstract

“…[to, U ) + W N , with x(to) = zo, satisfying the differential inclusion almost everywhere) and every solution has a maximal extension [31].…”

Section: It Is Readily Verified That F Is An Upper Semicontinuous Mapmentioning

confidence: 99%

A nonlinear universal servomechanism

Ryan

1994

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

A servomechanism problem of controlling a scalar output variable to A-track any reference signal from some prescribed function space R, whilst maintaining internal states bounded, is addressed for a class S of uncertain nonlinearlyperturbed, single-input, single-output, minimum-phase, relativedegree-one, linear systems with nonlinear actuator characteristics (encompassing, for example, hysteresis and dead-zone effects). The actuator characteristics are required only to be contained in the graph of a suitably regular set-valued map. The terminology "A-tracking" is used in the following sense: for arbitrary prescribed A > 0, an (adaptive) feedback strategy is sought which, for every reference signal of class R and every system (unknown to the controller) of class S, ensures that the tracking error is asymptotic to the interval [-A, A] C R. The instantaneous values of the reference signal and scalar output only are available for feedback. Adopting the space W 1 , "(R) as the set R of admissible reference signals and under fairly weak assumptions on the nature of the system nonlinearities, one such (a, S)-universal adaptive feedback solution to this servomechanism problem is constructed. The feedback is continuous and its construction does not invoke an internal model principle.

show abstract

Discontinuous Feedback and Universal Adaptive Stabilization

Cited by 30 publications

References 10 publications

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Invariance-Like Results for Nonautonomous Switched Systems

A nonlinear universal servomechanism

Contact Info

Product

Resources

About