Complex engineering solutions often rely on control strategies that can be adapted to changing system parameters with little data and little time available. Often, this requires human input. A prime example is the success of pilots learning in real time to fly and safely land an airplane after it has been damaged. How could an autonomous system learn such adaptive control strategies? Motivated by this fundamental problem in control theory, this work studies simplified control scenarios to develop adaptive strategies with theoretical guarantees. We are particularly interested in agnostic problems, where the parameters of the underlying system dynamics are a priori completely unknown. We study systems with an unknown drift and systems with unknown feedback. In both cases, we propose strategies that are optimal or almost optimal with respect to multiplicative regret (also known as competitive ratio).
- J. Carruth, M. F. Eggl, C. L. Fefferman, C. W. Rowley, M. Weber (2021): Controlling Unknown Linear Dynamics with Bounded Multiplicative Regret. Revista Matemática Iberoamericana, to appear. [pdf]
- C. L. Fefferman, B. Guillen Pegueroles, C. W. Rowley, M. Weber (2021): Optimal control with learning on the fly: a toy problem. Revista Matemática Iberoamericana 37 (1). [pdf]