610 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 47, NO. 4, APRIL 2002 Robust Switching Adaptive Control of Multi-Input Nonlinear Systems Elias B. Kosmatopoulos and Petros A. Ioannou, Fellow, IEEE Abstract—During the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear sys- tems with known and unknown constant parameters. New design tools such as adaptive feedback linearization, adaptive back- stepping, control Lyapunov functions (CLFs) and robust control Lyapunov functions (RCLFs), nonlinear damping and switching adaptive control have been introduced. Most of the results devel- oped are applicable to single-input feedback-linearizable systems and parametric-strict-feedback systems. These results, however, cannot be applied to multi-input feedback-linearizable systems, parametric-pure-feedback systems and systems that admit a linear-in-the-parameters CLF. In this paper, we develop a general procedure for designing robust adaptive controllers for a large class of multi-input nonlinear systems. This class of nonlinear sys- tems includes as a special case multi-input feedback-linearizable systems, parametric-pure-feedback systems and systems that admit a linear-in-the-parameters CLF. The proposed approach uses tools from the theory of RCLF and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable. The proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances. Index Terms—Feedback linearizable systems, robust adaptive control, switching control. I. INTRODUCTION D URING the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parame- ters. New design tools such as adaptive feedback linearization [1], [5], [19], adaptive backstepping [6], [12], [20], control Lyapunov functions (CLFs) and robust control Lyapunov functions (RCLFs) [2], [13], [21], [22], nonlinear damping and swapping [11], [12] and switching adaptive control [8], [9] have been introduced. Using these new design tools, globally stabilizing controllers have been constructed for various classes of nonlinear systems such as single-input feedback-linearizable systems [1], [5], [9] and parametric-strict-feedback systems [6], [12], [20]. Despite the success of the aforementioned design tools to resolve a variety of adaptive control problems for nonlinear systems, the problem of adaptive control of nonlinear Manuscript received July 13, 1998; revised January 20, 2000 and July 10, 2001. Recommended by Asociate Editor M. Krstic. This work was supported in part by the National Aeronautics and Space Administration (NASA) under Grant Number NAGW-4103, and in part by the National Science Foundation under Grant Number ECS 9877193. E. B. Kosmatopoulos is with the Department of Production Engineering and Management, Technical University of Crete, Chania 73100, Greece. P. A. Ioannou is with the Department of Electrical Engineering-Systems, Uni- versity of Southern California, Los Angeles, CA 90089-2563 USA. Publisher Item Identifier S 0018-9286(02)03739-X. systems is still very much unexplored. For example, there exists no procedure for designing a globally stable feedback control system for multi-input feedback linearizable systems of the form (1.1) where , denote the state and control input vectors of the system, respectively, , , are con- stant unknown matrices and , are continuous matrix func- tions satisfying and is nonsingular for all . The existing adaptive control designs guarantee [1], [5], [19] closed-loop stability only for the case where the con- stant matrices and are known; an exception is the case where (i.e., the system (1.1) is single-input) and the pair is in a special canonical form [9]. Another example is the system of the form (parametric-pure- feedback system) (1.2) where is a vector of unknown constant parameters, denotes the state vector of the system and , , are continuous functions. The procedures pro- posed in [6], [11], [20] are applicable to this system if both and , , where denotes the esti- mate of ; moreover, these procedures guarantee global stability only in the case where the input vector-field is independent of , i.e., in the case where and the functions are independent of . In this paper, we develop a general procedure for designing robust adaptive controllers for a large class of multi-input non- linear systems with exogenous bounded input disturbances. The class of systems for which the proposed approach is applicable is characterized by the assumption that the function de- pends linearly on unknown constant parameters, where de- notes the input vector field, is a CLF (RCLF) for the system and denotes the Lie derivative of with respect to . This class of nonlinear systems includes as a special case the systems (1.1) and (1.2). The proposed approach combines the theory of CLF (RCLF) and the switching adaptive controller proposed by the authors [9] for overcoming the problem of computing the control law in the case where the estimation model becomes un- controllable. Contrary to the classical adaptive approach where the con- trol law depends on estimates of the system vector-fields, in our case, the control law depends on estimates of the “RCLF term” 0018-9286/02$17.00 © 2002 IEEE Authorized licensed use limited to: TECHNICAL UNIVERSITY OF CRETE. Downloaded on October 6, 2008 at 10:59 from IEEE Xplore. Restrictions apply.