Model-free control of affine chaotic systems

Abstract

In practice, there are many chaotic systems whose models are usually unknown or partially unknown. However, the majority of control schemes focus on model-dependent techniques. The model-free controlling problem for affine chaotic systems is investigated in this Letter. An adaptive higher-order differential feedback controller (HODFC), which does not depend on the model of the controlled chaotic system, is presented. The controller utilizes the information of the measured output and the given objective as well as extracted differentials of those via higher-order differentiator (HOD). Stability, convergence and robustness of the closed-loop system are investigated. The presented adaptive HODFC can successfully control the uncertain Lorenz system, the Chen system, the Duffing–Holmes system, the Rössler system, and a new coined 4-dimensional chaotic system, and can drive their trajectories to desired steady states, unstable periodic orbits, or new chaotic states. Importantly, the controller does not use model functions of these systems above. The control scheme is suitable for both chaotic affine systems and ordinary affine systems without knowing their precise models.