A universal feedback controller for discontinuous dynamical systems using nonsmooth control Lyapunov functions

Sadikhov, Teymur; Haddad, Wassim M.; Malisoff, Michael

doi:10.1109/acc.2014.6859134

Cited by 3 publications

(4 citation statements)

References 19 publications

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“…Suppose that we fix the gains γ i . Then, the model is consistent with (10) in the sense that, given the boundedness of the discrete solutions of (29), (32), (36), uniformly on h, it is not difficult to show that these converge to a solution of (16) as h goes to zero. The proof follows along the lines of [21,Theorem 6].…”

Section: Discussionmentioning

confidence: 67%

“…We also remark that, because of the presence of the mismatched uncertain terms, it is in general impossible to drive the whole state to the origin. In fact, system (10) does not contain an assignable equilibrium at the origin, unless ζ 1 vanishes at the origin. Thus, we aim for stability of a set rather than just a point.…”

Section: Remark 11mentioning

confidence: 99%

“…knowledge of such a Lyapunov function yields a control law that is also optimal in some meaningful sense. A nonsmooth version of the technique is developed in [10].…”

Section: Introductionmentioning

confidence: 99%

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Continuous and discrete-time stability of a robust set-valued nested controller

2019

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We propose a set-valued controller with a signum multifunction nested inside another one. We prove that the controller is well posed and achieves robust ultimate boundedness in the presence of mismatched, non-vanishing disturbances. Even more, the selected output can be made arbitrarily small. Also, by applying an implicit/explicit Euler scheme similar to the one introduced by Acary and Brogliato [15] for matched disturbances, we derive a selection strategy for the discrete-time implementation of the set-valued control law. Simulations demonstrate that the discrete scheme diminishes chattering substantially, compared with a fully explicit method.

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Section: Discussionmentioning

confidence: 67%

Section: Remark 11mentioning

confidence: 99%

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Continuous and discrete-time stability of a robust set-valued nested controller

2019

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“…Filippov and Krasovskii), and perhaps enters the broader context of differential inclusions instead of systems (1.1). However, while these other questions may admit clean characterizations in their own respective contexts (e.g., [1,7,12,17,23]), the question of stabilizability by continuous feedback in the classical sense remains unsolved by control-Lyapunovian methods. The deficiencies of the control Lyapunov approach in this setting are primarily due to the substantial departure control Lyapunov functions take from the characterization of stability that classical Lyapunov functions enable for non-control systems.…”

Section: Introductionmentioning

confidence: 99%

Continuous feedback stabilization of nonlinear control systems by composition operators

2022

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The ability to asymptotically stabilize control systems through the use of continuous feedbacks is an important topic of control theory and applications. In this paper, we provide a complete characterization of continuous feedback stabilizability using a new approach that does not involve control Lyapunov functions. To do so, we first develop a slight generalization of feedback stabilization using composition operators and characterize continuous stabilizability in this expanded setting. Employing the obtained characterizations in the more general context, we establish relationships between continuous stabilizability in the conventional sense and in the generalized composition operator sense. This connection allows us to show that the continuous stabilizability of a control system is equivalent to the stability of an associated system formed from a local section of the vector field inducing the control system. That is, we reduce the question of continuous stabilizability to that of stability. Moreover, we provide a universal formula describing all possible continuous stabilizing feedbacks for a given system.

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