On the Robustness of $\mathcalKL$-stability for Difference Inclusions: Smooth Discrete-Time Lyapunov Functions

Kellett, Christopher M.; Teel, Andrew R.

doi:10.1137/s0363012903435862

Cited by 94 publications

(94 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar discrete-time results for KLstability with respect to two measures were developed in [10], [11], and hence we expect that a similar version of Theorem 1 will hold in discrete-time, providing a generalization of the results found in discrete-time ISS [9].…”

Section: Discussionsupporting

confidence: 68%

A generalization of Input-to-State Stability

Kellett

Dower

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Discussionsupporting

confidence: 68%

A generalization of Input-to-State Stability

Kellett

Dower

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Proof: The proof follows that of [12,Theorem 2.7] where, here, we need not worry about regularity of the Lyapunov function.…”

Section: April 11 2014 Draftmentioning

confidence: 93%

“…(b), "⇒": We prove that if V together with λ ∈ (0, 1) and σ ∈ K satisfies (5), then V also satisfies (12) and (8) withλ…”

Section: Remark 42mentioning

confidence: 99%

“…In the particular case of a V satisfying (3), (8), and (12) (a), "⇒": Let V together with functionsᾱ ∈ K ∞ and χ,φ ∈ K satisfy (7) and (12). We claim that V satisfies (4) with α .…”

Section: Remark 42mentioning

confidence: 99%

“…The implication (12) follows from the upper bound on V and Proposition 4.6: Let V be a function satisfying (3) and (7) for appropriate α 1 , α 2 ,ᾱ ∈ K ∞ and χ ∈ K. Assume that f is continuous in w = 0 uniformly in x in the following sense:…”

Section: Remark 42mentioning

confidence: 99%

See 2 more Smart Citations

ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

Grüne

Kellett

2014

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

Input-to-State Stability (ISS) and the ISS-Lyapunov function are useful tools for the analysis and design of nonlinear systems. Motivated by the fact that many feedback control laws, such as model predictive or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISSLyapunov functions for such systems. ISS-Lyapunov functions were originally introduced in a so-called implication-form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipative form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication-form ISS-Lyapunov function and provide a complete characterization of ISS-Lyapunov functions for discrete-time systems with discontinuous dynamics.

show abstract

Hybrid online learning control in networked multiagent systems: A survey

Poveda

Benosman

Teel

2018

Adaptive Control & Signal

Self Cite

View full text Add to dashboard Cite

This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous-time dynamical systems and discrete-time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning-based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous-time dynamical systems and discrete-time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems. KEYWORDSadaptive control, hybrid dynamical systems, learning, multiagent systems, networked systems 228One of the fields where control systems with learning and adaptation have recently seen increased attention is in the area of networked multiagent systems (MAS), 16,17 which are systems comprised of multiple interacting subsystems, each subsystem having individual dynamics and computational capabilities as well as limited sensing, communication, and actuation. Depending on the structure of the underlying communication graph between the agents of the system, MAS can be centralized or decentralized. In a centralized MAS, there exists one central agent which has access to the state information of all other agents and which is able to compute the control action for all agents of the system. On the other hand, in a decentralized or distributed MAS, agents individually compute their own control signals, which are shared with a subset of the other agents characterized by a communication graph. Figure 1 illustrates three MASs with different communication graphs. Centralized MASs are typically not scalable, and they present the disadvantage of having a single point of failure that could potentially shut down the complete system. 16 Decentralized and distributed systems, on the other hand, are scalable and more robust, and in nonstationary environments, they allow for adaptation and self-organization of the system. 18 Recent technological advances in communication and computation have made MAS ubiquitous, and today, they can be found in several engineering systems such as in power generation and distribution systems, 19-21 teams of ...

show abstract

On the Robustness of $\mathcalKL$-stability for Difference Inclusions: Smooth Discrete-Time Lyapunov Functions

Cited by 94 publications

References 20 publications

A generalization of Input-to-State Stability

A generalization of Input-to-State Stability

ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

Hybrid online learning control in networked multiagent systems: A survey

Contact Info

Product

Resources

About