Randomized Algorithms for the Synthesis of Adaptive Controllers

In this paper, we propose the use of randomized algorithms for the synthesis of adaptive control laws which incorporate robustness features with respect to parameter uncertainty. Specifically, at each time instant, the controller is selected so as to optimize the average control performance with respect to a probability distribution describing which models are more likely to be a fair description of the true system. The probability distribution is then updated on-line on the basis of the data gathered from the controlled system enabling the controller to tune to the true system and thus enhancing the control performance. It is the use of randomized methods which makes the minimization of average cost criteria a computationally tractable optimization problem. Simulation results are provided to show the effectiveness of the proposed approach