Delay, state, and parameter estimation in chaotic and hyperchaotic delayed systems with uncertainty and time-varying delay

A novel approach is proposed for simultaneous estimation of states, delay and parameters of nonlinear chaotic and hyperchaotic delayed systems with constant delay as well as simultaneous estimation of states and parameters for such delayed systems with time-varying delay. The approach exploits continuous time approximation and stochastic optimal filtering. Also, an innovative technique is proposed to approximately compute the Lyapunov exponents of a nonlinear delayed system in order to determine the parameter values for which the system becomes chaotic or hyperchaotic. The model used in this approach contains two different source of considerable uncertainty. The approach is successfully implemented for state, parameter and delay estimation on various forms of time delayed Lorenz system and delayed Hopfield neural network including chaotic and hyperchaotic cases with constant and time-varying delays. In case of delayed Hopfield neural network, the performance of the approach is shown to be superior compared with two other existing approaches.