Related papers: Fixed-Time Extremum Seeking
We address the Nash equilibrium problem in a partial-decision information scenario, where each agent can only observe the actions of some neighbors, while its cost possibly depends on the strategies of other agents. Our main contribution is…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
Although persistent excitation is often acknowledged as a sufficient condition to exponentially converge in the field of adaptive parameter estimation, it must be noted that in practical applications this may be unguaranteed. Recently, more…
Optimization plays a central role in intelligent systems and cyber-physical technologies, where speed and reliability of convergence directly impact performance. In control theory, optimization-centric methods are standard: controllers are…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
In this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the…
Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…
This paper focuses on stochastic methods for solving smooth non-convex strongly-concave min-max problems, which have received increasing attention due to their potential applications in deep learning (e.g., deep AUC maximization,…
The controller of an input-affine system is determined through minimizing a time-varying objective function, where stabilization is ensured via a Lyapunov function decay condition as constraint. This constraint is incorporated into the…
This paper presents a novel extremum seeking control (ESC) approach for the vibrational stabilization of a class of mechanical systems (e.g., systems characterized by equations of motion resulting from Newton second law or Euler-Lagrange…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
This paper proposes a non-adaptive control solution framework to the practical output regulation problem (PORP) for a class of nonlinear systems with uncertain parameters, unknown control directions and uncertain exosystem dynamics. The…
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…
Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…
In this paper, we study the problem of extremum seeking control for mechanical systems in dissipation-free environments. This includes attitude control of satellites in space and displacement control of rigid bodies in ideal fluids. The…
We propose a new framework to design and analyze accelerated methods that solve general monotone equation (ME) problems $F(x)=0$. Traditional approaches include generalized steepest descent methods and inexact Newton-type methods. If $F$ is…