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

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