Dynamic Re-optimization of a MEMS Controller in Presence of Unmodeled Uncertainties

Online trained neural networks have become popular in recent years in designing robust and adaptive controllers for dynamic systems with uncertainties in their system equations because of their universal function approximation property. This paper discusses a technique that dynamically reoptimizes a Single Network Adaptive Critic (SNAC) based optimal controller in the presence of unmodeled uncertainties. The controller design is carried out in two steps: (i) synthesis of a set of online neural networks that capture the uncertainties in the plant equations on-line (ii) re-optimization of the existing optimal 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 stability of the error dynamics as well as boundedness of the weights. This approach has been applied in the online reoptimization of a micro-electromechanical device controller and numerical results from simulation studies are presented here.