Minimax adaptive control of uncertain plants

In this paper, we formulate a general class of Adaptive FSI (full-state information) optimal control problems, and develop a constructive method to solve it. An Adaptive FSI problem is defined in terms of state dynamics which are linear in the unknown constant parameters and additive state disturbances, but nonlinear otherwise, and a soft-constrained performance function that is quadratic in disturbances and the unknown parameters, but non-quadratic otherwise. In this formulation, the controller is assumed to have access to the current and past values of both the state and its derivative. Using the cost-to-come method, we show that the original problem with partial information can be converted into an equivalent full information (FI) minimax control problem of higher dimension, which can be solved using Dynamic Programming (DP) methods. Both the finite-and-infinite-horizon problems are considered, and in each case, a set of necessary and sufficient conditions are obtained. The methodology is illustrated on a numerical example.