Simultaneous Compensation of Unknown Time-Varying State and Input Delays for Uncertain Nonlinear Systems

The paper presents the design of a robust control law for a class of nonlinear dynamical systems subjected to parametric uncertainty and simultaneous unknown, variable state and input delays. Knowing a bound of the input delay, we develop a novel controller using a filtered tracking error and integral of past control values. Lyapunov-Krasovskii functionals based stability analysis guarantees a global uniformly ultimately bounded (GUUB) tracking result where sufficient conditions on controller gains and maximum allowable delay are derived. The performance and robustness of the controller is evaluated by simulation on a two-link robot manipulator for different combinations of time-varying state and input delays.

[1]  Jong Hae Kim,et al.  Robust control for parameter uncertain delay systems in state and control input , 1996, Autom..

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

[3]  Yong He,et al.  Delay-dependent stabilization of linear systems with time-varying state and input delays , 2005, Autom..

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

[5]  M. Ikeda,et al.  Stabilization of Linear Systems with Delay , 1977 .

[6]  M. Nihtila.  Adaptive control of a continuous-time system with time-varying input delay , 1989 .

[7]  Myung Jin Chung,et al.  Memoryless stabilization of uncertain dynamic systems with time-varying delayed states and controls , 1995, Autom..

[8]  Guang-Ren Duan,et al.  Stabilization of some linear systems with both state and input delays , 2012, Syst. Control. Lett..

[9]  Miroslav Krstic,et al.  Compensation of Time-Varying Input and State Delays for Nonlinear Systems , 2012 .

[10]  Mrdjan Jankovic,et al.  Recursive predictor design for state and output feedback controllers for linear time delay systems , 2010, at - Automatisierungstechnik.

[11]  Rogelio Lozano,et al.  Robust prediction-based control for unstable delay systems , 2003 .

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

[13]  Vladimir L. Kharitonov.  Prediction-based control for systems with state and several input delays , 2017, Autom..

[14]  O. J. M. Smith,et al.  A controller to overcome dead time , 1959 .

[15]  Bin Zhou,et al.  Input delay compensation of linear systems with both state and input delays by nested prediction , 2014, Autom..

[16]  Shubhendu Bhasin,et al.  Uniformly Ultimately Bounded Tracking for Uncertain Euler-Lagrange Systems with Unknown Time-Varying Input Delay , 2017 .

[17]  W. Rudin.  Principles of mathematical analysis , 1964 .

[18]  M. Krstic.  Lyapunov Stability of Linear Predictor Feedback for Time-Varying Input Delay , 2010, IEEE Trans. Autom. Control..

[19]  Delphine Bresch-Pietri,et al.  Prediction-Based Control for Linear Systems with Input- and State- Delay – Robustness to Delay Mismatch , 2014 .

[20]  Dong Yue,et al.  Delayed feedback control of uncertain systems with time-varying input delay , 2005, Autom..

[21]  Peter Goldsmith,et al.  Improvement on robust control of uncertain systems with time-varying input delays , 2007 .

[22]  Vladimir L. Kharitonov,et al.  An extension of the prediction scheme to the case of systems with both input and state delay , 2014, Autom..

[23]  Jie Yang,et al.  Adaptive control for a class of nonlinear systems with time-varying delays in state and input , 2011 .

[24]  Nikolaos Bekiaris-Liberis.  Simultaneous compensation of input and state delays for nonlinear systems , 2014, Syst. Control. Lett..

[25]  Delphine Bresch-Pietri,et al.  Prediction-based control for nonlinear state- and input-delay systems with the aim of delay-robustness analysis , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[26]  Miroslav Krstic,et al.  Predictor-feedback for multi-input LTI systems with distinct delays , 2015, 2015 American Control Conference (ACC).

[27]  Warren E. Dixon,et al.  Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems , 2015, IEEE Transactions on Automatic Control.