Adaptive Dynamic Inversion via Time-Scale Separation

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.

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

[2]  D. Fontaine,et al.  Approaches to global stabilization of a nonlinear system not affine in control , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[3]  Lingji Chen,et al.  Adaptive Control Design for Nonaffine Models Arising in Flight Control , 2004 .

[4]  Frank L. Lewis,et al.  Neural net backlash compensation with Hebbian tuning using dynamic inversion , 2001, Autom..

[5]  Anthony J. Calise,et al.  A novel error observer-based adaptive output feedback approach for control of uncertain systems , 2002, IEEE Trans. Autom. Control..

[6]  W. Rudin.  Real and complex analysis , 1968 .

[7]  Olav Egeland,et al.  Swinging up of non-affine in control pendulum , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[8]  Wei Lin,et al.  Global asymptotic stabilization of general nonlinear systems with stable free dynamics via passivity and bounded feedback , 1996, Autom..

[9]  Prashanth Krishnamurthy,et al.  A high-gain scaling technique for adaptive output feedback control of feedforward systems , 2004, IEEE Transactions on Automatic Control.

[10]  Anthony J. Calise,et al.  Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks , 2002, IEEE Trans. Neural Networks.

[11]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[12]  Robin J. Evans,et al.  Minimum phase properties for input nonaffine nonlinear systems , 1999, IEEE Trans. Autom. Control..

[13]  Shuzhi Sam Ge,et al.  Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs , 2007, Autom..

[14]  E. Lavretsky,et al.  Dynamic Inversion for Nonaffine-in-Control Systems via Time-Scale Separation. Part I , 2005, Proceedings of the 2005, American Control Conference, 2005..

[15]  Wilfrid Perruquetti,et al.  Stabilization of nonaffine systems: a constructive method for polynomial systems , 2005, IEEE Transactions on Automatic Control.

[16]  Anthony J. Calise,et al.  Adaptive Output Feedback Control of Uncertain Systems using Single Hidden Layer Neural Networks , 2001 .

[17]  B. Paden,et al.  Nonlinear inversion-based output tracking , 1996, IEEE Trans. Autom. Control..

[18]  Shuzhi Sam Ge,et al.  Adaptive neural control of uncertain MIMO nonlinear systems , 2004, IEEE Transactions on Neural Networks.

[19]  Ah Chung Tsoi,et al.  Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods, and Some New Results , 1998, Neural Networks.

[20]  A. Isidori.  Nonlinear Control Systems , 1985 .

[21]  Anthony J. Calise,et al.  Nonlinear adaptive flight control using neural networks , 1998 .

[22]  Anthony J. Calise,et al.  Adaptive output feedback control of nonlinear systems using neural networks , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[23]  E. Lavretsky,et al.  Adaptive dynamic inversion for nonaffine-in-control systems via time-scale separation: part II , 2005, Proceedings of the 2005, American Control Conference, 2005..

[24]  Jason L. Speyer,et al.  Sensor and Actuator Fault Reconstruction , 2004 .

[25]  S. Shankar Sastry,et al.  Analysis and control of flapping flight: from biological to robotic insects , 2003 .

[26]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[27]  Jin Zhang,et al.  Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback , 2003, IEEE Trans. Neural Networks.