Adaptive control of systems with mismatched non-linearities and time-varying delays using state measurements

In this study, the authors develop a new delay-dependent adaptive control design method for a class of nominally linear continuous-time systems with time-varying delays and unknown non-linearities. The parameter uncertainties are convex-bounded and the unknown non-linearities are mismatched time-varying perturbations satisfying Lipschitz conditions in the state and delayed state. A new delay-dependent procedure is constructed based on a new form of Lyapunov–Krasovskii functional (LKF) together with a free-weighting matrix equation and the integral inequality. The feedback gains are determined by convex optimisation over linear matrix inequalities (LMIs) such that closed-loop adaptive controlled system is asymptotically stable. The theoretical developments are then extended to the case of polytopic uncertainties by deploying a parameter-dependent LKF. All the obtained results are tested on representative examples.

[1]  Anuradha M. Annaswamy,et al.  An adaptive Smith-controller for time-delay systems with relative degree n*≤2 , 2003, Syst. Control. Lett..

[2]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..

[3]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[4]  Magdi S. Mahmoud.  Resilient control of uncertain dynamical systems , 2003 .

[5]  M. Mahmoud.  Delay-dependent robust stability and stabilization for systems with mismatched uncertainties , 2000 .

[6]  Y. Cao,et al.  Robust stabilization of uncertain systems with time-varying multistate delay , 1998, IEEE Trans. Autom. Control..

[7]  Wook Hyun Kwon,et al.  A simple receding horizon control for state delayed systems and its stability criterion , 2003 .

[8]  Eugene P. Ryan,et al.  Controlled functional differential equations and adaptive tracking , 2002, Syst. Control. Lett..

[9]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[10]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[11]  Stephan Trenn,et al.  Tracking control: Performance funnels and prescribed transient behaviour , 2005, Syst. Control. Lett..

[12]  M. Mahmoud,et al.  Adaptive stabilization of delay differential systems with unknown uncertainty bounds , 1998 .

[13]  C. Scherer,et al.  Linear Matrix Inequalities in Control , 2011 .

[14]  Said Oucheriah.  Adaptive Variable Structure Control of Linear Delayed Systems , 2005 .

[15]  D. Wang,et al.  Nonlinear state predictor for a class of nonlinear time-delay systems , 2004, Int. J. Syst. Sci..

[16]  Claude H. Moog,et al.  New insights on the analysis of nonlinear time-delay systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[17]  Per Olof Gutman,et al.  Robust Output-Feedback Model Reference Adaptive Control of SISO Plants With Multiple Uncertain, Time-Varying State Delays , 2008, IEEE Transactions on Automatic Control.

[18]  Manuel de la Sen.  Adaptive control of linear singular time-invariant single-input single-output systems with external point delay , 2008, Appl. Math. Comput..

[19]  Jin-Hoon Kim,et al.  Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty , 2001, IEEE Trans. Autom. Control..

[20]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[21]  Magdi S. Mahmoud,et al.  Robust stability and stabilization of a class of uncertain nonlinear systems with delays , 1998 .

[22]  Yuechao Wang,et al.  An LMI approach to stability of systems with severe time-delay , 2004, IEEE Transactions on Automatic Control.

[23]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[24]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[25]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[26]  Wei-Sheng Chen,et al.  Backstepping tracking control for nonlinear time-delay systems * * This project was supported by the , 2006 .

[27]  Hansheng Wu,et al.  Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays , 2004, IEEE Trans. Autom. Control..

[28]  Magdi S. Mahmoud,et al.  Robust Design of Stabilizing Controllers for Interconnected Time-delay Systems , 1998, Autom..

[29]  Hassan K. Khalil,et al.  Robustness of high-gain observer-based nonlinear controllers to unmodeled actuators and sensors , 2002, Autom..

[30]  Said Oucheriah.  Adaptive robust control of a class of dynamic delay systems with unknown uncertainty bounds , 2001 .

[31]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

[32]  Jong-Tae Lim,et al.  Global Asymptotic Stabilization of a Class of Nonlinear Time-Delay Systems by Output Feedback , 2005, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[33]  E. Feron,et al.  History of linear matrix inequalities in control theory , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[34]  Tong Heng Lee,et al.  Adaptive robust control of uncertain time delay systems , 2005, Autom..

[35]  Tielong Shen,et al.  Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach , 2005, IEEE Transactions on Automatic Control.

[36]  R. Yanushevsky.  A class of nonlinear time-delay systems and related optimal problems , 1999 .

[37]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[38]  Qing-Long Han,et al.  New stability criteria for linear systems with interval time-varying delay , 2008, Autom..

[39]  Erik I. Verriest,et al.  Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior , 1994, IEEE Trans. Autom. Control..

[40]  Magdi S. Mahmoud,et al.  Adaptive control of a class of time-delay systems with uncertain parameters , 1996 .

[41]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[42]  George Leitmann,et al.  Continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems: An application to river pollution control , 1988 .

[43]  Gang Feng,et al.  Analysis of a new algorithm for continuous-time robust adaptive control , 1999, IEEE Trans. Autom. Control..