Excitation Conditions for Uniform Exponential Stability of the Cooperative Gradient Algorithm over Weakly Connected Digraphs

Javed, Muhammad Umar; Poveda, Jorge I.; Chen, Xudong

doi:10.23919/acc50511.2021.9483022

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Remark 2 This class of systems is important as it covers a number of interesting cases that appear in adaptive estimation. For instance, when ν " 0 and Apt, jq and Bpt, jq are both symmetric and positive semidefinite, system (13) generalizes the so called gradient system, studied both in continuous and discrete time in the context of identification [2,17] and multi-agent systems [18,41]. The functions A and B may come from expressing outputs and inputs along solutions; namely, for a system 9 z " A z py, uqz, we let Apt, jq :" A z pypt, jq, upt, jqq.…”

Section: Problem Formulation and Standing Hypothesesmentioning

confidence: 99%

“…The function ψψ J defined in (47) The pair pA, Bq is HPE, with K " 2π `1 and µ " 0.21. HPE is less conservative than its counterparts CPE and DPE as it captures the fact that the richness of a signal may be enhanced by an appropriate mingling of exciting flows and jumps, which, otherwise, are insufficient to guarantee that neither (38) nor (41) hold. The latter being necessary, θ Ñ 0 in either case, but θ Ñ 0 under the hybrid gradient-descent algorithm-see Fig.…”

Section: The Hybrid Gradient-descent Algorithmmentioning

confidence: 99%

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Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

Saoud¹,

Maghenem²,

Lorı́a³

et al. 2023

Preprint

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We propose a framework of stability analysis for a class of linear non-autonomous hybrid systems, with solutions evolving in continuous time governed by an ordinary differential equation and undergoing instantaneous changes governed by a difference equation. Furthermore, the jumps may also be triggered by exogeneous hybrid signals. The proposed framework builds upon a generalization of notions of persistency of excitation (PE) and uniform observability (UO), which we redefine to fit the realm of hybrid systems. Most remarkably we propose for the first time in the literature a definition of hybrid persistency of excitation. Then, we establish conditions, under which, hybrid PE implies hybrid UO and, in turn, uniform exponential stability (UES) and input-to-state stability (ISS). Our proofs rely on an original statement for hybrid systems, expressed in terms of Lp bounds on the solutions. We also demonstrate the utility of our results on generic adaptive estimation problems. The first one concerns the so-called gradient systems, reminiscent of the popular gradient-descent algorithm. The second one pertains to the design of adaptive observers/identifiers for a class of hybrid systems that are nonlinear in the input and in the output, and linear in the unknown parameters. In both cases, we illustrate through meaningful examples that the proposed hybrid framework succeeds in scenarii where the classical purely continuousor discrete-time counterparts fail.

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Section: Problem Formulation and Standing Hypothesesmentioning

confidence: 99%

Section: The Hybrid Gradient-descent Algorithmmentioning

confidence: 99%

Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

Saoud¹,

Maghenem²,

Lorı́a³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Distributed adaptive parameter estimation over weakly connected digraphs using a relaxed excitation condition

Garg,

Basu Roy

2024

Adaptive Control & Signal

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SummaryIn this article, a novel distributed adaptive parameter estimation (DAPE) algorithm is proposed for an multi‐agent system over weakly connected digraph networks, where parameter convergence is ensured under a newly coined relaxed excitation condition, called generalized cooperative initial excitation (gC‐IE). This is in contrast to the past literature, where such DAPE algorithms demand cooperative persistent of excitation (C‐PE) and generalized cooperative persistent of excitation (gC‐PE) for strongly connected digraph, and weakly connected digraph networks, respectively, for parameter convergence. The gC‐PE and C‐PE conditions are restrictive in the sense that they require the richness/excitation of information over the entire time‐span of the signal/data, unlike gC‐IE condition where excitation is needed only in the initial time‐span. The newly coined gC‐IE condition is an extension of cooperative initial excitation (C‐IE) condition. While the C‐IE condition is applicable to a strongly connected digraph, the newly proposed gC‐IE condition extends the concept to weakly connected digraph. The proposed algorithm utilizes a novel set of weighted integrator dynamics, which omits the requirement of computationally involved multiples switching mechanisms in past literature, while still ensuring parameter convergence. The proposed algorithm provides global exponential stability of origin of the parameter estimation error dynamics under gC‐IE condition. Furthermore, robustness to unmodeled disturbance is also established in the form of input‐to‐state stability. Simulation results validate the efficacy of the proposed algorithm in contrast to the gC‐PE based algorithm.

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Excitation Conditions for Uniform Exponential Stability of the Cooperative Gradient Algorithm over Weakly Connected Digraphs

Cited by 2 publications

References 16 publications

Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

Distributed adaptive parameter estimation over weakly connected digraphs using a relaxed excitation condition

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