Online trained neural networks have become popular in designing robust and adaptive controllers for dynamic systems with uncertainties in their system equations because of their universal function approximation property. The uniqueness of the method proposed in this work is that the online function approximating network can be used to re-optimize in real time an existing Single Network Adaptive Critic (SNAC) based optimal controller that has already been designed for a nominal system. The controller redesign is carried out in two steps: (i) synthesis of an online neural network that captures the unknown functions in the plant equations on-line (ii) re-optimization of the existing optimal SNAC controller to drive the states of the plant to a desired reference by minimizing a predefined cost function. The neural network weight update rule for the online networks has been derived using Lyapunov theory that guarantees both the stability of the error dynamics as well as boundedness of the weights. This approach has been applied to control the frictional dynamics of a nano-scale array of particles to track a predefined value of average sliding velocity. Here, the system is in an output feedback form where all states are not available for measurement. This is a significant step towards optimal control of systems at nano levels. Numerical results from simulation studies are presented.

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