Title :
Interconnection conditions for the stability of nonlinear sampled-data extremum seeking schemes
Author :
Kvaternik, Karla ; Pavel, Lacra
Author_Institution :
Edward S. Rogers Dept. of Electr. & Comput. Eng., Univ. of Toronto, Toronto, ON, Canada
Abstract :
The application of numerical optimization methods to the problem of extremum seeking control (ESC) has the potential to greatly diversify the types and capabilities of ESC schemes. The first uniform treatment of such sampled-data ESC schemes was given in [1]. We approach the problem from the point of view of interconnected systems´ theory, deriving a different, more structurally concrete set of conditions that guarantee the closed-loop stability of such schemes. Our main assumptions concern the interconnection terms arising from the dynamic coupling between a numerical optimization algorithm and a continuous-time nonlinear plant. We demonstrate how these assumptions are satisfied for a special case involving an approximate gradient descent. Our primary motivation in deriving these new conditions is their natural suitability for the development and analysis of decentralized ESC schemes.
Keywords :
approximation theory; closed loop systems; continuous time systems; decentralised control; gradient methods; interconnected systems; nonlinear control systems; numerical analysis; optimal control; optimisation; sampled data systems; stability; approximate gradient descent method; closed loop stability; continuous time nonlinear plant; decentralized ESC schemes; dynamic coupling; extremum seeking control; interconnected system theory; nonlinear sampled data extremum seeking scheme stability; numerical optimization algorithm; Algorithm design and analysis; Heuristic algorithms; Numerical stability; Optimization; Stability analysis; Trajectory; Vectors;
Conference_Titel :
Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-61284-800-6
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2011.6161170