Adaptive Control of Linear Time-Varying Interval Systems

In this paper, we consider the adaptive control problem for a class of systems governed by linear time-varying interval differential equations having unknown (interval) parameters. Using the fact that system output posses lower and upper bounds, we have converted the interval differential equation into two sets of ordinary differential equations that describe the behavior of lower and upper bounds of system output. With this approach, interval analysis could be replaced by real analysis, and hence, adaptive control of interval systems can be treated as an ordinary adaptive control problem. Using variation arguments, we have developed the necessary conditions of optimality for the equivalent adaptive control problem. Finally, we present a numerical example to illustrate the effectiveness of the proposed (interval) control scheme.