Output controller for uncertain nonlinear systems with structural, parametric, and signal disturbances

We design the output feedback controller for a class of nonlinear systems with a state delay, structural and external disturbances. The external perturbation is bounded. Structural disturbance means the unmodeled and unknown stable dynamics in the control loop. In this paper we consider the problem of exponential stability for disturbed systems which can be represented as a feedback connection of a linear dynamical system with unknown parameters and a uncertain nonlinearity satisfying a sector constraint. Proposed approach is extended for the case of unknown relative degree of the system by modification of the control law.

[1]  A. Astolfi,et al.  Global asymptotic stabilization by output feedback under a state norm detectability assumption , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[2]  Miroslav Krstic,et al.  Rejection of sinusoidal disturbance of unknown frequency for linear system with input delay , 2010, Proceedings of the 2010 American Control Conference.

[3]  Murat Arcak,et al.  Constructive nonlinear control: a historical perspective , 2001, Autom..

[4]  Anton A. Pyrkin.  Adaptive algorithm to compensate parametrically uncertain biased disturbance of a linear plant with delay in the control channel , 2010 .

[5]  Alexey A. Bobtsov,et al.  Fradkov theorem-based design of the control of nonlinear systems with functional and parametric uncertainties , 2005 .

[6]  H. Khalil,et al.  Adaptive stabilization of a class of nonlinear systems using high-gain feedback , 1987 .

[7]  Sergey A. Kolyubin,et al.  Compensation of unknown multi-harmonic disturbances in nonlinear plants with delayed control , 2010 .

[8]  T. A. Burton,et al.  Stability and Periodic Solutions of Ordinary and Functional Differential Equations , 1986 .

[9]  Sergey A. Kolyubin,et al.  Output control approach “consecutive compensator” providing exponential and L∞-stability for nonlinear systems with delay and disturbance , 2011, 2011 IEEE International Conference on Control Applications (CCA).

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

[11]  Petros A. Ioannou,et al.  Robust redesign of adaptive control , 1984 .

[12]  Miroslav Krstic,et al.  Output Control Algorithm for Unstable Plant with Input Delay and Cancellation of Unknown Biased Harmonic Disturbance , 2010 .

[13]  Wei Lin,et al.  Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm , 2002, IEEE Trans. Autom. Control..

[14]  Rabah W. Aldhaheri,et al.  Effect of unmodeled actuator dynamics on output feedback stabilization of nonlinear systems , 1996, Autom..

[15]  Michael Athans,et al.  Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics , 1985 .

[16]  P.V. Kokotovic,et al.  Adaptive nonlinear output-feedback schemes with Marino-Tomei controller , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[17]  Alexey A. Bobtsov.  Output control algorithm with the compensation of biased harmonic disturbances , 2008 .

[18]  Naira Hovakimyan,et al.  L1 adaptive controller for systems in the presence of unmodelled actuator dynamics , 2007, 2007 46th IEEE Conference on Decision and Control.

[19]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

[20]  Alexey A. Bobtsov,et al.  Output control for nonlinear system with time-varying delay and stability analysis , 2011, IEEE Conference on Decision and Control and European Control Conference.

[21]  Alexey A. Bobtsov,et al.  New approach to the problem of globally convergent frequency estimator , 2008 .

[22]  Zongli Lin,et al.  Robust semiglobal stabilization of minimum-phase input-output linearizable systems via partial state and output feedback , 1995, IEEE Trans. Autom. Control..

[23]  Alexey A. Bobtsov,et al.  Output control for time-delay nonlinear system providing exponential stability , 2011, 2011 19th Mediterranean Conference on Control & Automation (MED).

[24]  K. Narendra,et al.  A new adaptive law for robust adaptation without persistent excitation , 1987 .

[25]  H. Khalil,et al.  Semiglobal stabilization of a class of nonlinear systems using output feedback , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[26]  Alexey A. Bobtsov,et al.  Output control of linear systems with unmodeled dynamics , 2009 .

[27]  K. Narendra,et al.  A New Adaptive Law for Robust Adaptation without Persistent Excitation , 1986, 1986 American Control Conference.

[28]  A. A. Bobtsov,et al.  A Robust Control Algorithm for Tracking the Command Signal with Compensation for the Parasitic Effect of External Unbounded Disturbances , 2005 .

[29]  L. Praly.  Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[30]  Alexey A. Bobtsov,et al.  Adaptive control of libration angle of a satellite , 2007 .

[31]  Alexander Fradkov.  Passification of nonsquare linear systems , 2001, 2001 European Control Conference (ECC).

[32]  Hassan K. Khalil.  Comparison of different techniques for nonlinear output feedback adaptive control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[33]  Alexey A. Bobtsov.  A note to output feedback adaptive control for uncertain system with static nonlinearity , 2005, Autom..