Adaptive Optimal Regulation of A Class of Uncertain Nonlinear Systems using Event Sampled Neural Network Approximators

We present a novel approximation-based event-triggered control of multiinput-multioutput uncertain nonlinear continuous-time systems in affine form. The controller is approximated by use of a linearly parameterized neural network (NN) in the context of event-based sampling. After the NN approximation property has been revisited in the context of event-based sampling, a stabilizing control scheme is introduced first and, subsequently, an optimal regulator is designed with use of NNs. A suite of novel weight update laws for tuning the NN weights at the aperiodic event-trigger or sampling instants is proposed to relax the requirement of knowledge of the complete system dynamics and reduce the computation compared with the traditional NN-based control. For analysis of the stability, the event-triggered system is modeled as a nonlinear impulsive dynamical system and the Lyapunov technique is used to both derive an event-trigger or sampling condition and show local ultimate boundedness of all signals. Further, to overcome the unnecessary triggering of events when the system states are inside the ultimate bound, a dead-zone operator is used to reset the event-trigger or sampling errors to zero. Finally, the analytical design is substantiated with numerical results.