Backstepping Designs in the Presence of Non-constant Delays on the Virtual Input

We present results on stabilization of nonlinear systems in the strict-feedback form with delays affecting the virtual inputs. We consider systems with constant and time-varying delays, as well as systems with delays that depend on the current or past states, which arise in numerous applications, such as, for example, in cooling systems. The design methodology is based on the concepts of infinite-dimensional backstepping and nonlinear predictor feedback. Several illustrative examples are provided.

[1]  Nathan van de Wouw,et al.  Stability of Networked Control Systems With Uncertain Time-Varying Delays , 2009, IEEE Transactions on Automatic Control.

[2]  Mrdjan Jankovic,et al.  Compensation of state-dependent state delay for nonlinear systems , 2012, 2012 American Control Conference (ACC).

[3]  Yusuf Altintas,et al.  Analytical Stability Prediction and Design of Variable Pitch Cutters , 1998, Manufacturing Science and Engineering.

[4]  Miroslav Krstic,et al.  Delay-Adaptive Control for Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[5]  Carlos Canudas-de-Wit,et al.  Remote Stabilization Via Communication Networks With a Distributed Control Law , 2007, IEEE Transactions on Automatic Control.

[6]  Bernhard Maschke,et al.  Mass Transport Equation with Moving Interface and Its Control As an Input Delay System , 2013, TDS.

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

[8]  Miroslav Krstic,et al.  Control of thermodynamical system with input-dependent state delays , 2013, 52nd IEEE Conference on Decision and Control.

[9]  Hiroshi Ito,et al.  On Saturation, Discontinuities, and Delays, in iISS and ISS Feedback Control Redesign , 2012, IEEE Transactions on Automatic Control.

[10]  Miroslav Krstic,et al.  Nonlinear control under delays that depend on delayed states , 2013, Eur. J. Control.

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

[12]  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.

[13]  Karl Henrik Johansson,et al.  Nonlinear state-dependent delay modeling and stability analysis of internet congestion control , 2010, 49th IEEE Conference on Decision and Control (CDC).

[14]  Pierdomenico Pepe.  On Sontag's formula for the input-to-state practical stabilization of retarded control-affine systems , 2013, Syst. Control. Lett..

[15]  Alfredo Germani,et al.  An observer for a class of nonlinear systems with time varying observation delay , 2010, Syst. Control. Lett..

[16]  Joon-Young Choi,et al.  Global asymptotic stability of FAST TCP in the presence of link dynamics , 2009 .

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

[18]  Wim Michiels,et al.  A systems theoretic analysis of fast varying and state dependent delays , 2011, IEEE Conference on Decision and Control and European Control Conference.

[19]  M. Krstić.  Delay Compensation for Nonlinear, Adaptive, and PDE Systems , 2009 .

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

[21]  Erik I. Verriest.  Inconsistencies in systems with time-varying delays and their resolution , 2011, IMA J. Math. Control. Inf..

[22]  Mrdjan Jankovic,et al.  Integrator forwarding: A new recursive nonlinear robust design , 1997, Autom..

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

[24]  Nikolaos Bekiaris-Liberis,et al.  Compensation of state-dependent input delay for nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[25]  Michael Malisoff,et al.  Asymptotic stabilization for feedforward systems with delayed feedbacks , 2013, Autom..

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

[27]  Frédéric Mazenc,et al.  Generating positive and stable solutions through delayed state feedback , 2011, Autom..

[28]  Erik I. Verriest,et al.  Estimator design for a subsonic rocket car (soft landing) based on state-dependent delay measurement , 2013, 52nd IEEE Conference on Decision and Control.

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

[30]  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.

[31]  Michael Malisoff,et al.  Stabilization of a chemostat model with Haldane growth functions and a delay in the measurements , 2010, Autom..

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

[33]  Jan Dimon Bendtsen,et al.  Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow , 2011 .

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

[35]  Dirk Helbing,et al.  On Stability Analysis and Parametric Design of Supply Networks Under the Presence of Transportation Delays , 2006 .

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

[37]  Iasson Karafyllis,et al.  Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold , 2012, IEEE Transactions on Automatic Control.

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

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

[40]  Iasson Karafyllis,et al.  Global stabilisation of nonlinear delay systems with a compact absorbing set , 2014, Int. J. Control.

[41]  Iasson Karafyllis,et al.  Stabilization of nonlinear delay systems using approximate predictors and high-gain observers , 2013, Autom..

[42]  Miroslav Krstic,et al.  Robustness of nonlinear predictor feedback laws to time- and state-dependent delay perturbations , 2012, Autom..

[43]  Sabine Mondié,et al.  Global asymptotic stabilization of feedforward systems with delay in the input , 2004, IEEE Transactions on Automatic Control.

[44]  S. P. Travis,et al.  A One-Dimensional Two-Body Problem of Classical Electrodynamics , 1975 .

[45]  Miroslav Krstic,et al.  Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary , 2015 .

[46]  Hans-Otto Walther,et al.  On a Model for Soft Landing with State-Dependent Delay , 2007 .

[47]  Warren E. Dixon,et al.  Saturated control of an uncertain nonlinear system with input delay , 2013, Autom..

[48]  Zhong-Ping Jiang,et al.  Construction of Lyapunov-Krasovskii functionals for networks of iISS retarded systems in small-gain formulation , 2013, Autom..

[49]  A. Teel.  Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem , 1998, IEEE Trans. Autom. Control..

[50]  Mrdjan Jankovic,et al.  Cross-Term Forwarding for Systems With Time Delay , 2009, IEEE Transactions on Automatic Control.

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