Passivity and Immersion (P&amp;I) Approach for Constructive Stabilization and Control of Nonlinear Systems

Nayyer, Syed Shadab; Wagh, S. R.; Singh, Nanhay

doi:10.1109/lcsys.2022.3226881

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F Stability Analysis1

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2024

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Cited by 7 publications

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“…The Lyapnouv function for the system dynamics with u 1 evaluated through the P&I strategy is mentioned earlier in equation (15). The convergence of the trajectories of the offthe-manifold dynamics to the invariant manifold with the control input u 1 is ensured with the condition (16).…”

Section: F Stability Analysismentioning

confidence: 99%

A New Perspective of Accelerated Gradient Methods: The Controlled Invariant Manifold Approach

Gunjal,

Wagh,

Nayeer

et al. 2023

Preprint

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Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution x* of the optimization problem must be attained in a minimum number of iterations. For this objective, the paper proposes a genesis of an accelerated gradient algorithm through the controlled dynamical system perspective. The objective of optimally reaching the optimal solution x* where the gradient of ∇f(x*) is zero with a given initial condition x(0) is achieved through control.

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Section: F Stability Analysismentioning

confidence: 99%