Dissipative control for a class of uncertain nonlinear control systems

A general dissipative controller is proposed to achieve robust tracking control performance for a class of uncertain single-input single-output (SISO) nonlinear systems. The feedback linearization technique is employed to transform the nonlinear system into an assignable inner linear system with a differential control input so that the relationship of the external (input) power and the stored energy of system can be shown clearly. Then, a dissipative controller with an assignable attenuation level is proposed to make the system energy dynamics fit a required dissipative inequality. The unstable factors of the system can then be attenuated accordingly. The system stability is guaranteed even if the system has permanent unavoidable uncertainties. The proposed design can be achieved without the use of traditional means, i.e. optimal control, which requires solution of a Hamilton inequality (or Riccati equation). The Lyapunov stable condition is assured in our approach when the system uncertainties belong to L 8. Moreover, due to the compatibility of the proposed controller, the controller can be embedded into the designs of other controllers. In those designs, knowledge of the system functions is not required. Basically, the proposed dissipative controller is independent of the system functions. The use of the bounds of the system function is considered to prove the system stability only. Two simulations are given to illustrate the effectiveness of the proposed controller. Copyright (C) 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society