Adaptive Fuzzy Inverse Optimal Control for A Class of Two Order Nonlinear Systems

This study develops an adaptive fuzzy inverse optimal control method for a class of two order nonlinear systems with unknown nonlinear dynamics. By using the knowledge of a control Lyapunov function and the universal approximation property of a fuzzy logic system, the inverse optimal control design and unknown nonlinear dynamics problems are solved, respectively. A new adaptive fuzzy optimal controller is constructed based on backstepping design principle, and the stability and optimality are proven by using rigorous mathematical reasoning.

[1]  T. Basar,et al.  Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[2]  T. Başar,et al.  Backstepping Controller Design for Nonlinear Stochastic Systems Under a Risk-Sensitive Cost Criterion , 1999 .

[3]  M. Krstić,et al.  Stochastic nonlinear stabilization—II: inverse optimality , 1997 .

[4]  Kevin Fiedler,et al.  Robust Nonlinear Control Design State Space And Lyapunov Techniques , 2016 .

[5]  Min-Jea Tahk,et al.  The Inverse Optimal Control Problem for a Three-Loop Missile Autopilot , 2018 .

[6]  Cristian Sminchisescu,et al.  Action from Still Image Dataset and Inverse Optimal Control to Learn Task Specific Visual Scanpaths , 2013, NIPS.

[7]  M. Krstić,et al.  Stochastic nonlinear stabilization—I: a backstepping design , 1997 .

[8]  Tong Zhang,et al.  Design of Highly Nonlinear Substitution Boxes Based on I-Ching Operators , 2018, IEEE Transactions on Cybernetics.

[9]  M. Krstic,et al.  Inverse optimal design of input-to-state stabilizing nonlinear controllers , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[10]  P. Florchinger.  Lyapunov-Like Techniques for Stochastic Stability , 1995 .

[11]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[12]  Miroslav Krstic,et al.  Inverse optimal stabilization of a rigid spacecraft , 1999, IEEE Trans. Autom. Control..

[13]  C. L. Philip Chen,et al.  I-Ching Divination Evolutionary Algorithm and its Convergence Analysis , 2017, IEEE Transactions on Cybernetics.

[14]  Miroslav Krstic,et al.  Stabilization of Nonlinear Uncertain Systems , 1998 .

[15]  Yungang Liu,et al.  Design of satisfaction output feedback controls for stochastic nonlinear systems under quadratic tracking risk-sensitive index , 2007, Science in China Series F: Information Sciences.

[16]  Paolo Mason,et al.  On Inverse Optimal Control Problems of Human Locomotion: Stability and Robustness of the Minimizers , 2013 .

[17]  P. Florchinger.  A universal formula for the stabilization of control stochastic differential equations , 1993 .

[18]  P. Kokotovic,et al.  Inverse Optimality in Robust Stabilization , 1996 .