Abstract
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.
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References
Mohler R (1973) Bilinear control processes. Academic, New York
Mohler RR (1991) Nonlinear systems volume I, dynamics and control. Prentice–Hall, Englewood Cliffs
Mohler RR (1991) Nonlinear systems volume II, applications to bilinear control. Prentice–Hall, Englewood Cliffs
Chen F, Liu C (1994) Adaptively controlling nonlinear continuous-time systems using multilayer neural networks. IEEE Trans Autom Control 39:1306–1310
Sanner R, Slotine J (1992) Gaussian networks for direct adaptive control. IEEE Trans Neural Netw 3:837–863
Yesidirek A, Lewis F (1995) Feedback linearization using neural network. Automatica 31:1659–1664
Lewis F, Yesidirek A, Liu K (1995) Neural net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 6:703–715
Polycarpou M (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Autom Control 41:447–451
Chen D, Mohler R (1999) Nonlinear adaptive control with potential FACTS applications. In: Proceeding of American control conference. San Diego, June 1999, pp 1077–1081
Chen D, Mohler R, Shahrestani S, Hill D (1999) Neural-net-based nonlinear control for prevention of voltage collapse. In: Proceedings of 38th IEEE conference on decision and control, Phoenix, December 1999, pp 2156–2161
Chen D, Yang J (2005) Robust adaptive neural control applied to a class of nonlinear systems. In: Proceedings of 17th IMACS World congress: scientific computation, applied mathematics and simulation. Paris, July 2005, Paper T5-I-01-0911
Chen D (1998) Nonlinear neural control with power systems applications. Ph. D Dissertation, Oregon State University
Chen D, Mohler R, Chen L (1999) Neural-network-based adaptive control with application to power systems. In: Proceedings of American control conference. San Diego, June 1999, pp 3236–3240
Chen D, Mohler R, Chen L (2000) Synthesis of neural controller applied to power systems. IEEE Trans Circuits Syst I 47:376–388
Lee EB, Markus L (1967) Foundations of optimal control theory. Wiley, New York
Rugh WJ (1993) Linear system theory. Prentice–Hall, Englewood Cliffs
Moon SF (1969) Optimal control of bilinear systems and systems linear in control. PhD Dissertation, The University of New Mexico
Moon SF, Mohler RR (1969) Optimal control of bilinear systems and systems linear in control. Technical Report, The University of New Mexico
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Chen, D., Yang, J. & Mohler, R.R. On near optimal neural control of multiple-input nonlinear systems. Neural Comput & Applic 17, 327–337 (2008). https://doi.org/10.1007/s00521-007-0126-6
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DOI: https://doi.org/10.1007/s00521-007-0126-6