Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian

Ding, Dong-Sheng; Jovanović, Mihailo R.

doi:10.23919/acc.2019.8815153

Cited by 17 publications

(3 citation statements)

References 25 publications

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“…2) Switched Plants with Average Dwell-Time Constraints: When the switched system (12) does not have a common Lyapunov function, it is still possible to obtain a result of the form (12), provided the switching is slow "on the average". In particular, if the switching signal σ satisfies an average dwelltime constrain of the form…”

Section: Extensionsmentioning

confidence: 99%

Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

Bianchin¹,

Cortés²,

Poveda³

et al. 2021

Preprint

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This paper investigates the problem of regulating in real time a linear dynamical system to the solution trajectory of a time-varying constrained convex optimization problem. The proposed feedback controller is based on an adaptation of the saddle-flow dynamics, modified to take into account projections on constraint sets and output-feedback from the plant. We derive sufficient conditions on the tunable parameters of the controller (inherently related to the time-scale separation between plant and controller dynamics) to guarantee exponential and input-tostate stability of the closed-loop system. The analysis is tailored to the case of time-varying strongly convex cost functions and polytopic output constraints. The theoretical results are further validated in a ramp metering control problem in a network of traffic highways.

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Section: Extensionsmentioning

confidence: 99%

Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

Bianchin¹,

Cortés²,

Poveda³

et al. 2021

Preprint

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“…The proof is a standard stochastic approximation analysis, in which the ODE approximation is precisely the primal-dual flow considered in [22,8] and their references.…”

Section: Batch Cvxq Explicit Updatementioning

confidence: 99%

Convex Q-Learning

Lü

Mehta

Meyn

et al. 2021

2021 American Control Conference (ACC)

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The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of optimal control. The main contributions firstly concern properties of the relaxation, described as a deterministic convex program: we identify conditions for a bounded solution, and a significant relationship between the solution to the new convex program, and the solution to standard Q-learning. The second set of contributions concern algorithm design and analysis: (i) A direct model-free method for approximating the convex program for Q-learning shares properties with its ideal. In particular, a bounded solution is ensured subject to a simple property of the basis functions; (ii) The proposed algorithms are convergent and new techniques are introduced to obtain the rate of convergence in a mean-square sense; (iii) The approach can be generalized to a range of performance criteria, and it is found that variance can be reduced by considering "relative" dynamic programming equations; (iv) The theory is illustrated with an application to a classical inventory control problem. This is an extended version of an article to appear in the forthcoming IEEE Conference on Decision and Control.

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“…These algorithms were studied with primary focus on convergence of iterates to the saddle-point solution and its stability. These algorithms either use a framework of hybrid dynamical systems [9], [13] or an augmented Lagrangian technique that involves projections in the Lagrangian function [14]- [16]. The hybrid dynamical systems approach involves switching in the dual dynamics to handle constraint violations.…”

Section: Introductionmentioning

confidence: 99%

On the Geometry and Linear Convergence of Primal-Dual Dynamics

Bansode¹,

Chinde²,

Wagh³

et al. 2020

Preprint

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The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework is proposed wherein we begin by framing the proposed dynamics in a fiber-bundle setting endowed with a Riemannian metric that captures the geometry of the gradient (of the Lagrangian function). A strongly monotone gradient vector field is obtained by using the natural gradient adaptation on the Riemannian manifold. The Lyapunov stability analysis proves that this adaption leads to a globally exponentially stable saddle-point solution. Further, with numeric simulations we show that the scaling a key parameter in the Riemannian metric results in an accelerated convergence to the saddle-point solution.

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Global exponential stability of primal-dual gradient flow dynamics based on the proximal augmented Lagrangian

Cited by 17 publications

References 25 publications

Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

Convex Q-Learning

On the Geometry and Linear Convergence of Primal-Dual Dynamics

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