Applications of Optimally Sensitive Control to Systems Involving Time-Varying Uncertainties

The implementation of control systems capable of identifying and adapting to time-varying unknown parameters has become increasingly important in air-traffic control and other applications. In the recent literature the control problem, in which both the initial state vector as well as a vector of constant plant parameters are unknown, has been treated utilizing sensitivity techniques referred to as optimally sensitive control. The concepts of optimally sensitive control as developed by Kokotovic, Perkins, Cruz, and others are extended to the problem in which the state dynamics contain a vector of stochastic inputs which can be represented as Martingale processes. The resulting optimally sensitive system is shown to be an effective and realistic adaptive controller for systems containing unknown time-varying parameters. A numerical example is presented to demonstrate the effectiveness of the resulting control system at identifying and adapting to the levels of the unknown time-varying inputs.