Direct adaptive stabilization of linear systems using query-based protocols

Query-based inference is a machine learning paradigm which has been used for learning Boolean functions from examples. This paper shows how such a protocol can be used for direct adaptive control of linear systems. The proposed procedure employs the central-cut ellipsoid method to iteratively search for a set of control gains which are feasible solutions to a system of linear inequalities. The value of using this approach is that such inference protocols can be shown to converge after a finite number of updates. This convergence time scales in a polynomial manner, O(n² ln n), with the number, n, of control gains to be determined. The convergence time is also bounded below by a function of the uncontrolled system´s eigenvalues. These results thereby suggest that inductive inference protocols may represent a feasible method for direct adaptive control which can be practical for large scale linear systems