Limit processes in oridinary differential equations
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Trajectory-Based Local Approximations of Ordinary\ Differential\ Equations
SIAM Journal on Control and Optimization
On non-local stability properties of extremum seeking control
Automatica (Journal of IFAC)
Cooperative control and potential games
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Extremum seeking under stochastic noise and applications to mobile sensors
Automatica (Journal of IFAC)
Brief Stability of extremum seeking feedback for general nonlinear dynamic systems
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
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 systems. In this paper, a novel interpretation of extremum seeking is introduced. We show that the trajectories of an extremum seeking system can be approximated by the trajectories of a system which involves certain Lie brackets of the vector fields of the extremum seeking system. It turns out that the Lie bracket system directly reveals the optimizing behavior of the extremum seeking system. Furthermore, we establish a theoretical foundation and prove that uniform asymptotic stability of the Lie bracket system implies practical uniform asymptotic stability of the corresponding extremum seeking system. We use the established results in order to prove local and semi-global practical uniform asymptotic stability of the extrema of a certain map for multi-agent extremum seeking systems.