Adaptive stabilization of a class of time-varying systems with an uncertain delay

Handling delays and uncertain parameters in control systems is an interesting and challenging class of problems. In this paper, we consider the problem of “bounded-input bounded-output stabilizing” a class of single-input single-output, linear time-varying plant models with a time-delay margin as large as desired and a considerable amount of uncertainty in the input matrix of the state-space model. The proposed controller, while periodic and mildly nonlinear, is of low complexity; it tolerates slow variations in the delay and the elements of the input matrix as well as occasional jumps in these parameters, and guarantees that the effect of the initial condition decays exponentially to zero, even in the presence of noise.

[1]  Nikolaos Bekiaris-Liberis,et al.  Nonlinear Control Under Nonconstant Delays , 2013, Advances in design and control.

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

[3]  Daniel E. Miller.  Near Optimal LQR Performance for a Compact Set of Plants , 2006, IEEE Transactions on Automatic Control.

[4]  B. Francis,et al.  Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers , 1988, 1988 American Control Conference.

[5]  Wim Michiels,et al.  Continuous pole placement for delay equations , 2002, Autom..

[6]  Delphine Bresch-Pietri,et al.  Robust compensation of a chattering time-varying input delay , 2014, 53rd IEEE Conference on Decision and Control.

[7]  P. Khargonekar,et al.  Non-Euclidian metrics and the robust stabilization of systems with parameter uncertainty , 1985 .

[8]  Daniel E. Miller,et al.  Stabilization in the presence of an uncertain arbitrarily large delay , 2005, IEEE Transactions on Automatic Control.

[9]  Daniel E. Miller,et al.  Stabilizing a SISO LTI Plant With Gain and Delay Margins as Large as Desired , 2014, IEEE Transactions on Automatic Control.

[10]  Delphine Bresch-Pietri,et al.  Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type , 2014, IEEE Transactions on Automatic Control.

[11]  Carlos Silvestre,et al.  A Synthesis Method of LTI MIMO Robust Controllers for Uncertain LPV Plants , 2014, IEEE Transactions on Automatic Control.

[12]  Daniel E. Miller,et al.  Stabilizing any SISO LTI plant with an arbitrarily large unknown delay and unknown B matrix , 2013, 52nd IEEE Conference on Decision and Control.

[13]  Jonathan Chauvin,et al.  Adaptive control scheme for uncertain time-delay systems , 2012, Autom..

[14]  Daniel E. Miller,et al.  On the Achievable Delay Margin Using LTI Control for Unstable Plants , 2007, IEEE Transactions on Automatic Control.

[15]  Genshiro Kitagawa,et al.  An algorithm for solving the matrix equation X = FXF T + S , 1977 .

[16]  Daniel E. Miller,et al.  Stabilizing any SISO LTI plant with an arbitrarily large uncertain gain and delay , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[17]  Hazem N. Nounou,et al.  Resilient adaptive control of uncertain time-delay systems - a delay-dependent approach , 2008, 2008 47th IEEE Conference on Decision and Control.

[18]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

[19]  O Smith,et al.  CLOSER CONTROL OF LOOPS WITH DEAD TIME , 1957 .

[20]  Daniel E. Miller,et al.  Sampled Data Adaptive Controllers for Systems with Unknown Time Delays , 2011 .

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

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