Interconnection conditions for the stability of nonlinear sampled-data extremum seeking schemes

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.