Robust Output Regulation of Strongly Passive Linear Systems With Multivalued Maximally Monotone Controls

Miranda-Villatoro, Félix A.; Castaños, Fernando

doi:10.1109/tac.2016.2544926

Cited by 14 publications

(14 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We recover the saturation function as the Yosida approximant of the signum multifunction, coherently with the discussion in section 2.5. Other examples of mappings are given in [83,86,85], like…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Digital implementation of sliding‐mode control via the implicit method: A tutorial

Brogliato

Polyakov

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

The objective of this article, is to provide a clear presentation of the discretization of continuoustime sliding-mode controllers, also known in the Automatic Control literature as the emulation method, when the implicit (backward) Euler scheme is used. First-order, second-order and homogeneous controllers are considered. The main theoretical results are recalled in each case, and the focus is put on the discrete-time implementation structure and on the algorithms which allow the designer to solve, at each time-step, the one-step generalized equations which are needed to compute the controllers. The article ends with some open issues.

show abstract

Section: Remarkmentioning

confidence: 99%

“…• Infinite dimensional homogeneous systems [99] (would maximal monotone operators as used for the first time in sliding-mode control in [83,86,85,87], be useful in this context? ).…”

Section: Open Problems and Conclusionmentioning

confidence: 99%

Digital implementation of sliding‐mode control via the implicit method: A tutorial

Brogliato

Polyakov

2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Set-valued control laws are common in sliding-mode control theory, where in particular the sign multifuction plays an essential role [37], but not much work has been done exploring other possibilities of multifunctions. Recently maximal monotone operators have been studied in this context [4,10,28,36]. The continuoustime part of the present work is a nontrivial extension of the results in [4,32,33,34] and is strongly based on the theory of maximal monotone operators together with convex analysis tools.…”

Section: Introductionmentioning

confidence: 95%

Multivalued Robust Tracking Control of Lagrange Systems: Continuous and Discrete-Time Algorithms

Miranda-Villatoro

Brogliato

Castaños

2017

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

In this paper the robust trajectory tracking problem of a class of nonlinear systems described by the Euler-Lagrange equations of motion is studied. We start considering a plant under the effects of an unknown external perturbation and also with uncertainties on its parameters. After that a class of passivity-based multivalued control laws is proposed and the well-posedness together with the stability of the closed-loop are established in the continuous-time setting. The discrete-time version of the plant and the controller are studied and well-posedness together with stability results are obtained, using the so-called implicit discretization approach introduced in [1, 2]. Numerical simulations are presented and demonstrate the effectiveness of the proposed discrete-time controller.

show abstract

“…• The related topic of design and stability analysis of state observers has been analysed for MDIs like FOSwP with convex and prox-regular sets [522,524] with AC or BV solutions (hence allowing for Zeno solutions), SOSwP in (4.10) [523], vibro-impact dynamics (i.e., no persistent contact phases) in [252,262,411,417,419,418]. • Finite-time stability and convergence in continuous-time and in discrete-time systems [459,458,385,547,16,146,10,255,253,423,421,422]: finite-time can be obtained by means of "plastic" impact (or accumulation of impact times), or using non-Lipschitz dynamics near the equilibrium (set-valued friction, slidingmode control). • Stability of equilibria or periodic trajectories in vibro-impact systems using impact Poincaré maps [68,380,567] [130, Section 7.3].…”

Section: Sufficient Lyapunov Conditions Let Us Now Provide Brief Insmentioning

confidence: 99%

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

Brogliato¹,

Tanwani²

2020

SIAM Rev.

119

View full text Add to dashboard Cite

This survey article addresses the class of continuous-time systems where a system modeled by ordinary differential equations (ODEs) is coupled with a static and time-varying setvalued operator in the feedback. Interconnections of this form model certain classes of nonsmooth systems including sweeping processes, differential inclusions with maximal monotone right-hand side, complementarity systems, differential and evolution variational inequalities, projected dynamical systems, some piecewise linear switching systems. Such mathematical models have seen applications in electrical circuits, mechanical systems, hysteresis effects, and many more. When we impose a passivity assumption on the open-loop system, and regard the set-valued operator in the feedback as maximally monotone, we obtain a set-valued Lur'e dynamical system. In this article we review the mathematical formalisms, their relationships, main application fields, well-posedness (existence, uniqueness, continuous dependence of solutions), and stability of equilibria. An exhaustive bibliography is provided.

show abstract

Robust Output Regulation of Strongly Passive Linear Systems With Multivalued Maximally Monotone Controls

Cited by 14 publications

References 24 publications

Digital implementation of sliding‐mode control via the implicit method: A tutorial

Digital implementation of sliding‐mode control via the implicit method: A tutorial

Multivalued Robust Tracking Control of Lagrange Systems: Continuous and Discrete-Time Algorithms

Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability

Contact Info

Product

Resources

About