Adaptive stabilization of LTI systems with distributed input delay

SUMMARY We solve stabilization problems of LTI systems with unknown parameters and distributed input delay. The key challenge is that the infinite-dimensional input dynamics are distributed, which makes traditional infinite-dimensional backstepping inapplicable. We resolve this challenge by employing backstepping–forwarding transformations of the finite-dimensional state of the plant and of the infinite-dimensional actuator state. These transformations enable us to design Lyapunov-based update laws. We also design an adaptive controller for rejecting a constant disturbance in the input of the LTI plant, in the case where the parameters of the plant are known. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  Delphine Bresch-Pietri,et al.  Adaptive trajectory tracking despite unknown input delay and plant parameters , 2009, Autom..

[2]  M. Krstić,et al.  Adaptive control of Burgers' equation with unknown viscosity , 2001 .

[3]  R. Ortega,et al.  Globally stable adaptive controller for systems with delay , 1988 .

[4]  Anuradha M. Annaswamy,et al.  Adaptive posicast controller for time-delay systems with relative degree n*<=2 , 2010, Autom..

[5]  Miroslav Krstic,et al.  Adaptive boundary control for unstable parabolic PDEs - Part II: Estimation-based designs , 2007, Autom..

[6]  Z. Artstein.  Linear systems with delayed controls: A reduction , 1982 .

[7]  Delphine Bresch-Pietri,et al.  Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $ , 2010, IEEE Transactions on Automatic Control.

[8]  IASSON KARAFYLLIS.  Stabilization by Means of Approximate Predictors for Systems with Delayed Input , 2011, SIAM J. Control. Optim..

[9]  Mrdjan Jankovic,et al.  Forwarding, backstepping, and finite spectrum assignment for time delay systems , 2007, 2007 American Control Conference.

[10]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[11]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .

[12]  Zongli Lin,et al.  On Input-to-State Stability for Nonlinear Systems with Delayed Feedbacks , 2007, 2007 American Control Conference.

[13]  Miroslav Krstic,et al.  Adaptive Boundary Control for Unstable Parabolic PDEs—Part I: Lyapunov Design , 2008, IEEE Transactions on Automatic Control.

[14]  Miroslav Krstic,et al.  Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch , 2008, 2008 American Control Conference.

[15]  Miroslav Krstic,et al.  Optimal design of adaptive tracking controllers for non-linear systems , 1997, Autom..

[16]  Tianping Zhang,et al.  Adaptive control of time delay nonlinear systems with unknown control direction , 2010, 2010 Chinese Control and Decision Conference.

[17]  Frédéric Mazenc,et al.  Backstepping design for time-delay nonlinear systems , 2006, IEEE Transactions on Automatic Control.

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

[19]  Miroslav Krstic,et al.  Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

[20]  Miroslav Krstic,et al.  Adaptive nonlinear output-feedback schemes with Marino-Tomei controller , 1996 .

[21]  Miroslav Krstic,et al.  Compensating the Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems , 2011, IEEE Transactions on Automatic Control.

[22]  Iasson Karafyllis,et al.  Finite-Time Global Stabilization by Means of Time-Varying Distributed Delay Feedback , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Miroslav Krstic,et al.  Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays , 2011, IEEE Trans. Autom. Control..

[24]  P.-O. Gutman,et al.  Adaptive control of linear time delay systems , 2004, Proceedings of the 2004 American Control Conference.