Event-triggered optimal control of nonlinear continuous-time systems in affine form by using neural networks

The proposed event-triggered control design uses the adaptive dynamic programming (ADP) technique to solve the infinite-horizon optimal control of nonlinear continuous time system in affine form with complete unknown system dynamics in a forward time and online manner. The approximation property of the neural network (NN) is used to estimate the system dynamics and the value function with event-based sampling of state vector. Subsequently the estimated values are used to design the near optimal control policy. In addition, the NN weights are updated as a jump at every trigger instant, hence aperiodic in nature, to save computation when compared to the traditional NN-based approaches. Further, the closed-loop dynamics are formulated as a nonlinear impulsive dynamical system and the extension of the Lyapunov technique is utilized to prove the locally ultimate boundedness of all the closed-loop signals by deriving an adaptive event-trigger condition. Nonetheless, a positive lower bound on the inter-event time is guaranteed to avoid accumulation point. Finally, the analytical design is evaluated by using an example.