Neural Computing and Applications

, Volume 24, Issue 3, pp 637–648

Deterministic learning and neural control of a class of nonlinear systems toward improved performance

Original Article

DOI: 10.1007/s00521-012-1229-2

Cite this article as:
Wen, B., Wang, C. & Liu, T. Neural Comput & Applic (2014) 24: 637. doi:10.1007/s00521-012-1229-2


A deterministic learning theory was recently presented which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of nonlinear systems in normal form. In this paper, we further investigate deterministic learning of the class of nonlinear systems with relaxed conditions, and neural control of the class of system toward improved performance. Firstly, without the assumption on the upper bound of the derivative of the unknown affine term, an adaptive neural controller is proposed to achieve stability and tracking of the plant states to that of the reference model. When output tracking is achieved, a partial PE condition is satisfied, and deterministic learning from adaptive neural control of the class of nonlinear systems is implemented without the priori knowledge on the upper bound of the derivative of the affine term. Secondly, by utilizing the obtained knowledge of system dynamics, a neural controller with constant RBF networks embedded is presented, in which the learned knowledge can be effectively exploited to achieve stability and improved control performance. Simulation studies are included to demonstrate the effectiveness of the results.


Deterministic learning Input-to-state stability Small-gain theorem Adaptive neural control Learning control 

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.School of Automation and the Center for Control and OptimizationSouth China University of TechnologyGuangzhouPeople’s Republic of China
  2. 2.Department of Electrical and Computer Engineering, Six Metrotech Center, Polytechnic InstituteNew York UniversityBrooklynUSA

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