Simple example of dual control problem with almost analytical solution

Abstract

Example of dual control of linear uncertain system have been presented. The control task with short horizon (N=2) were solved using dynamic programming. It was shown that the optimal solution is ambiguous, the cost function is non-convex and has many local minima. Optimal control depends in a discontinuous manner on the initial conditions. It was also observed that active learning occurs only when the uncertainty of the initial state exceeds a certain threshold. In this case, the amount of information transmitted from sensor to the controller is much greater than in the case of passive learning.