New Style Estimators For Nonlinear Systems And Applications In Control

This paper stresses on the problems of states estimation and control for disturbed time-varying nonlinear system with unknown model. The following innovations are achieved: 1. Proportion-Differential filtering(PDF)is presented for nonlinear discrete time-varying stochastic systems. PDF is derived not only from taking into account minimizing variance of state estimation error, but regarding its rate of change. Therefore, it has higher estimating precision and stability than the extended Kalman filtering. 2. Definition and condition of the locally observability are given for the nonlinear MIMO stochastic system. Neural networks-based adaptive filter is presented for the nonlinear discrete stochastic system with unknown model and stochastic characteristics. 3. A new simple differentiator is proposed, which can extract differential of any smooth nonlinear signals to reach higher accuracy. The stability and convergence of the differentiator are analyzed. 4. A class of asymptotically stable and convergent three orders differentiator is designed, which is able to extract the second order and third order differentials of signal. 5. High order differentiator (HOD) is proposed, which is able to approximate the real signal and extract differentials up to n th-order differentials with high precision and filtering quality. Stability and convergence of the HOD are proved. The HOD doer not rely on the model of the system produced, and only depend on the signal produced from the system. 6. The problem of states estimate is converted into the one of extracting the differential and high orders differentials for nonlinear affine system. Based on the HOD, a new estimator is brought forward, which does not rely on the model of the estimated system and has higher accuracy with a few parameters. 7. Using the estimator that does not rely on the model, an adaptive neural networks controller is designed, which makes the closed-loop nonlinear uncertain system asymptotically stable and robust. 8. Based on the HOD, adaptive high order differentials feedback controller (HODFC) is presented for time-varying nonlinear SISO and MIMO affine systems, which does not rely on the model of the controlled plant. Presents the analysis of stability and robustness of the closed-loop system. Linearized decoupling control is achieved for MIMO system. 9. We applied successfully the proposed adaptive HODFC to the inverted pendulum stabilization and regulation, and the SISO and MIMO chaotic system control synchronization. The controllers do not rely on the models of the inverted pendulum and chaotic systems. 10. A new 4-dimensional autonomous chaotic system is coined, in which each equation contains a coupled cross-product terms with three factors. Chaos properties are analyzed both theory and simulation via Lyapunov-exponents-spectrums and bifurcation graphs. At last, the control and synchronization are achieved for the chaotic system by using the proposed adaptive HODFC.