Differential neural networks observer for second order systems with sampled and quantized output

Real instrumentation of control systems in digital devices introduces the necessity of considering quantization and sampling information used in the control and estimator design. The aim of this study is designing a state estimator for uncertain second order nonlinear systems based on the approximation enforced by differential neural networks (DNN) with quantized and time-varying sampled output information. The effect of sampling output information is considered as a time-varying delay. The DNN estimates the set of non-linearities in the system structure with the applications of an adaptive approximation. A Lyapunov-Krasovskii functional served to justify the design of the law that adjusted the weights of the DNN. The origin of the estimation error space is practically stable with the approximation enforced by the DNN. Experimental results implement the DNN observer to reconstruct the states of the Van Der Pol Oscillator. The estimation attained with the proposed observer is compared with the results provided by classical linear observer. The evaluation of the least mean square error demonstrates the superior performance of the solution suggested in this study. The Lyapunov-Krasovskii methodology estimates the region of convergence depending on the sampled period and the level of quantization.