Adaptive Control of Linear Time Invariant Systems via a Wavelet Network and Applications to Control Lorenz Chaos

Compactly supported orthogonal wavelets have certain properties that are useful for controller design. In this paper, we explore the mechanism of a wavelet controller by integrating the controller with linear time-invariant systems (LTI). A necessary condition for effective control is that the compact support of the wavelet network covers the state space where the state trajectories stay. Closed-form bounds on the design parameters of the wavelet controller are derived, which guarantee asymptotic stability of wavelet-controlled LTI systems. The same wavelet controller is then applied to the Lorenz equations. The control objective is to stabilize the Lorenz system well into its normally chaotic region at one of its equilibria