M20 – BELGRADE 25/04/2016 – 29/04/2016

Optimization and Stabilization Under Large Delays

Miroslav Krstic
University of California, San Diego, USA
      Iasson Karafyllis
      National Technical University of Athens, Greece

Abstract  of the course

Model-free optimization (also known as Extremum Seeking, ES) and model-based stabilization have much in common. While ES deals with unknown setpoints for stable plants, and stabilization deals with known/desired setpoints for unstable plants, both problems employ feedback for setpoint convergence. The recent confluence of ES and stabilization allows a beginner to get into both subjects with greater ease than previously possible. In addition, advances in delay compensation allow both optimization and stabilization to be solved under arbitrarily large delays on inputs and measurements.

Our course will cover both ES and predictor-based control of nonlinear systems with delays. The course starts with a review of the most important ES techniques for static and dynamic systems, using deterministic and stochastic perturbations, emulating gradient- and Newton-based optimization, and addressing both single-agent optimization and non-cooperative multi-agent games. The course’s second half covers control of nonlinear systems under delays on inputs and outputs, with implementations over networks with delay uncertainty and using sampled-data, and using approximations of predictor mappings. (This is the only EECI course this year covering general nonlinear networked-based designs under arbitrarily large and uncertain delays.) The course concludes with an application of the predictor tools to ES algorithms under large input or measurement delays.

No knowledge of time-delay systems is required and all concepts are explained by means of numerous examples and illustrated by applications in energy systems (renewable and combustion based), robotics, aerospace, biology, economics, manufacturing, and chemical engineering.


• Review of ES techniques for single agent optimization problems
• ES for non-cooperative multi-agent games
• Predictor Feedback for Delay Systems
• Predictor Feedback under partial measurement