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

Document Type



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.


Adaptive control systems; Chaos; Chaotic behavior in systems; Lorenz system; Immersion; Invariance; Non-certainty-equivalent adaptive control; NCEA; Nonlinear control; Parametric uncertainties; Simulation; Trajectory control


Use Find in Your Library, contact the author, or use interlibrary loan to garner a copy of the article. Publisher copyright policy allows author to archive post-print (author’s final manuscript). When post-print is available or publisher policy changes, the article will be deposited

UNLV article access

Search your library