Non-Certainty-Equivalent Adaptive Control of Chaos in Lorenz System

The paper presents the design of a new non-certainty-equivalent adaptive (NCEA) control system for the control of chaos in Lorenz system for large parametric uncertainties, based on the immersion and invariance (I&I) theory. A backstepping procedure is used for the derivation of the NCEA law. This NCEA law differs from the traditional certainty-equivalent adaptive (CEA) laws. For synthesis, certain filters are introduced. By Lyapunov analysis, it is shown that in the closed-loop system, the output trajectory error tends to zero. Interestingly, the system trajectories of this NCEA system converge to certain manifold in an extended state space, and the system recovers the performance of a deterministic control system. Simulation results are presented which show that trajectory control and control of chaos are accomplished, despite large parameter uncertainties