On near optimal neural control of multiple-input nonlinear systems

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.

[1]  R. R. Mohler,et al.  Nonlinear adaptive control with potential FACTS applications , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[2]  R. Mohler,et al.  Neural-network-based adaptive control with application to power systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[3]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[4]  Zengqi Sun,et al.  Robust adaptive neural control of a class of nonlinear systems , 2007 .

[5]  Chen-Chung Liu,et al.  Adaptively controlling nonlinear continuous-time systems using multilayer neural networks , 1994, IEEE Trans. Autom. Control..

[6]  Frank L. Lewis,et al.  Feedback linearization using neural networks , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[7]  Dingguo Chen,et al.  Synthesis of neural controller applied to flexible AC transmission systems , 2000 .

[8]  Ronald R. Mohler.  Dynamics and control , 1991 .

[9]  Dingguo Chen,et al.  Nonlinear neural control with power systems applications , 1998 .

[10]  W. Rugh.  Linear System Theory , 1992 .

[11]  Ronald R. Mohler,et al.  Natural Bilinear Control Processes , 1970, IEEE Trans. Syst. Sci. Cybern..

[12]  Frank L. Lewis,et al.  Feedback linearization using neural networks , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[13]  Seyed A Shahrestani,et al.  Neural-net-based nonlinear control for prevention of voltage collapse , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[14]  R. R. Mohler,et al.  Nonlinear systems (vol. 2): applications to bilinear control , 1991 .

[15]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[16]  Frank L. Lewis,et al.  Neural net robot controller with guaranteed tracking performance , 1993, Proceedings of 8th IEEE International Symposium on Intelligent Control.

[17]  Marios M. Polycarpou,et al.  Stable adaptive neural control scheme for nonlinear systems , 1996, IEEE Trans. Autom. Control..