Observer design for constrained nonlinear systems with application to secure communication

In this paper, a constrained regularized least square (RLS) state estimator is developed for deterministic discrete-time nonlinear dynamical systems subject to a set of equality and/or inequality constraints. The stability of the estimation error is rigorously analyzed. The proposed estimator is then used to handle the important problem of secure communication. At the transmitting end, the output of the constrained unified chaotic system is used as a chaotic mask to achieve a satisfactory and typical secure communication scheme. The encrypted data signal is injected into the transmitter and simultaneously transmitted to the receiver through a public channel. At the receiving end, the constrained RLS estimator is used to reconstruct the states of the constrained unified chaotic system. Simulation results are presented to show the impact of the imposed constraints on the waveform and the pattern of the generated chaotic signal as well as the ability of the proposed estimator to synchronize the actual and estimated states of the constrained unified chaotic system. Moreover, the proposed estimator is applied to recover discrete signals such as digital images where computer simulation results are provided to show the effectiveness of the proposed estimation scheme.