Related papers: Partial Stability Concept in Extremum Seeking Prob…
In this paper, we describe a broad class of control functions for extremum seeking problems. We show that it unifies and generalizes existing extremum seeking strategies which are based on Lie bracket approximations, and allows to design…
Stability results for extremum seeking control in $\mathbb{R}^n$ have predominantly been restricted to local or, at best, semi-global practical stability. Extending semi-global stability results of extremum-seeking systems to unbounded sets…
In recent years, an approach to extremum seeking control made it possible to design control vector fields that lead to asymptotic stability of the minimum point provided that the minimum value of the function is known a priori. In this…
Extremum seeking feedback is a powerful method to steer a dynamical system to an extremum of a partially or completely unknown map. It often requires advanced system-theoretic tools to understand the qualitative behavior of extremum seeking…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
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…
Extremum seeking systems are powerful methods able to steer the input of a (dynamical) cost function towards an optimizer, without any prior knowledge of the cost function. To achieve their objective, they typically combine time-periodic…
For a control system two major issues can be considered: the stabilizability with respect to a given target, and the minimization of an integral functional (while the trajectories reach this target). Here we consider a problem where…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
We present a novel extremum seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis…
This paper focuses on the further development of the Lie bracket approximation approach for extremum seeking systems. Classical results in this area provide extremum seeking algorithms with exponential convergence rates for quadratic-like…
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
In [22] a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC the extremum seeker itself controls the systems through feedback rather than fine tuning a controller. The ESC…
This paper focuses on the further development of the Lie bracket approximation approach for optimization and control via extremum seeking systems. Classical results in this area provide algorithms with exponential convergence rates for…
This paper deals with the gradient-based extremum seeking control for multivariable maps under actuator saturation. By exploiting a polytopic embedding of the unknown Hessian, we derive a LMI-based synthesis condition to ensure that the…
We introduce a type of safe extremum seeking (ES) controller, which minimizes an unknown objective function while also maintaining practical positivity of an unknown barrier function. We show semi-global practical asymptotic stability of…
This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
This paper proposes the incorporation of static event-triggered control in the actuation path of Newton-based extremum seeking and its comparison with the earlier gradient version. As in the continuous methods, the convergence rate of the…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…