Direct Adaptive Control
This chapter is devoted to the development of direct adaptive neurocon-trollers for afflne in the control nonlinear dynamical systems possessing unknown nonlinearities. The recurrent high-order neural networks are used as models of the unknown plant, practically transforming the original unknown system into a RHONN model which is of known structure, but contains a number of unknown constant-value parameters, known as synaptic weights. When the RHONN model matches the unknown plant, we provide a comprehensive and rigorous analysis of the stability properties of the closed loop system. Convergence of the state to zero plus boundedness of all other signals in the closed loop is guaranteed without the need of parameter (weight) convergence, which is assured only if a sufficiency-of-excitation condition is satisfied. Moreover, certain sources of instability mechanisms, namely modeling errors, uncertainty in model order and external disturbances acting both additively and multiplicatively, are also considered. Modifications on the control and update laws are provided, to guarantee a certain robustness level.
KeywordsModeling Error Synaptic Weight Projection Algorithm Projection Modification Unmodeled Dynamic
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