Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Robust Continuous-Time Optimization Algorithms for Time-Varying Constrained Cost

Zeinab Ebrahimi, Mohammad Deghat

TL;DR

A distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances, and an integral sliding mode control for disturbance mitigation is proposed.

Abstract

This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By incorporating tools such as log-barrier penalty functions to address inequality constraints, an integral sliding mode control for disturbance mitigation is proposed. The algorithm ensures asymptotic tracking of the optimal solution, achieving a tracking error of zero. The convergence of the introduced algorithms is demonstrated through Lyapunov analysis and nonsmooth techniques. Furthermore, the framework's effectiveness is validated through numerical simulations considering two scenarios for the communication networks.

Distributed Robust Continuous-Time Optimization Algorithms for Time-Varying Constrained Cost

TL;DR

A distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances, and an integral sliding mode control for disturbance mitigation is proposed.

Abstract

This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By incorporating tools such as log-barrier penalty functions to address inequality constraints, an integral sliding mode control for disturbance mitigation is proposed. The algorithm ensures asymptotic tracking of the optimal solution, achieving a tracking error of zero. The convergence of the introduced algorithms is demonstrated through Lyapunov analysis and nonsmooth techniques. Furthermore, the framework's effectiveness is validated through numerical simulations considering two scenarios for the communication networks.
Paper Structure (10 sections, 4 theorems, 35 equations, 3 figures)

This paper contains 10 sections, 4 theorems, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Notations and preliminaries
  3. Notations
  4. Graph Theory
  5. Definitions and Lemmas
  6. Problem Formulation and Main Results
  7. numerical simulation results
  8. Connected network depicted in Fig. 1(a)
  9. Less-connected network depicted in Fig. 1(b)
  10. conclusion

Key Result

Lemma 1

Consider the nonlinear dynamical system $\dot{x}(t) = f(x, t)$, with $x \in \mathbb{R}^n$ and $f: \mathbb{R}^n \times \mathbb{R}_+ \to \mathbb{R}^n$. If a Lyapunov function $V(x)$ exists, satisfying $\dot{V}(x) \leq -\alpha V^p(x) - \beta V^q(x)$, where $\alpha > 0$, $\beta > 0$, $0 < p < 1$, and $q

Figures (3)

  • Figure 1: Network topology of four agents
  • Figure 2: Simulation results of all agents with first-order dynamics under the proposed controller. (a) State trajectories. (b) The constraint results.
  • Figure 3: Simulation results of all agents with first-order dynamics under the proposed controller. (a) State trajectories. (b) The constraint results.

Theorems & Definitions (13)

  • Definition 1: Filippov Solution
  • Definition 2: Clarke's Generalized Gradient
  • Definition 3: Chain Rule
  • Lemma 1: polyakov2011nonlinear
  • Lemma 2: andrieu2008homogeneous
  • Lemma 3: zuo2014new
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • ...and 3 more