Robust Feedback Control for a Class of Uncertain MIMO Nonlinear Systems

In this paper, a continuous feedback tracking controller is developed for a class of high-order multi-input multi-output (MIMO) nonlinear systems with an input gain matrix that has nonzero leading principal minors but can be nonsymmetric. Under the mild assumption that the signs of the leading minors of the control input gain matrix are known, the controller yields locally uniformly ultimately bounded (UUB) tracking while compensating for unstructured uncertainty in both the drift vector and the input matrix. First, a full-state feedback controller is designed based on limited assumptions on the structure of the system nonlinearities, and the singularity-free controller is proven to yield locally UUB tracking through a Lyapunov-based analysis. Then, it is shown that an output feedback control can be designed based on a high-gain observer. Simulation results are provided to illustrate the performance of the proposed control algorithm.

[1]  Kumpati S. Narendra,et al.  Improving transient response of adaptive control systems using multiple models and switching , 1994 .

[2]  R. Ortega.  On Morse's new adaptive controller: parameter convergence and transient performance , 1993, IEEE Trans. Autom. Control..

[3]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[4]  Daniel E. Miller,et al.  An adaptive controller which provides an arbitrarily good transient and steady-state response , 1991 .

[5]  Petros A. Ioannou,et al.  Performance analysis and improvement in model reference adaptive control , 1994, IEEE Trans. Autom. Control..

[6]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

[7]  I. Kanellakopoulos,et al.  Adaptive output-feedback control of systems with output nonlinearities , 1992 .

[8]  Jing Sun.  A Modified Model Reference Adaptive Control Scheme for Improved Transient Performance , 1991, 1991 American Control Conference.

[9]  Frank L. Lewis,et al.  Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities , 1987 .

[10]  A. Morse.  A gain matrix decomposition and some of its applications , 1993 .

[11]  Liu Hsu,et al.  Lyapunov-based adaptive control of MIMO systems , 2003, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[12]  Miroslav Krstic,et al.  Transient-performance improvement with a new class of adaptive controllers , 1993 .

[13]  B. Ydstie.  Transient performance and robustness of direct adaptive control , 1992 .

[14]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems. I. Linear parameterization , 1993, IEEE Trans. Autom. Control..

[15]  Antonella Ferrara,et al.  Robustness and performance of an indirect adaptive control scheme in presence of bounded disturbances , 1999, IEEE Trans. Autom. Control..

[16]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[17]  Joao P. Hespanha,et al.  Position tracking of underactuated vehicles , 2003, Proceedings of the 2003 American Control Conference, 2003..

[18]  H. Khalil,et al.  A separation principle for the stabilization of a class of nonlinear systems , 1997 .

[19]  A. Teel,et al.  Global stabilizability and observability imply semi-global stabilizability by output feedback , 1994 .

[20]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[21]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[22]  A. Behal,et al.  Adaptive output feedback control for a class of MIMO nonlinear systems , 2006, 2006 American Control Conference.

[23]  R.M. Murray,et al.  The Caltech Multi-Vehicle Wireless Testbed , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[24]  Petros A. Ioannou,et al.  Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds , 2003, IEEE Trans. Autom. Control..

[25]  H. Khalil.  Adaptive output feedback control of nonlinear systems represented by input-output models , 1996, IEEE Trans. Autom. Control..