Effective digital chaotic orbit tracker and Kalman filtering for nonlinear stochastic hybrid systems

A comprehensive study of a new effective digital chaotic orbit tracker and Kalman filtering scheme for nonlinear stochastic hybrid systems is presented in this dissertation. This includes the following novel features: (i) An effective digital tracker for continuous-time chaotic orbit tracking, which is insensitive to numerical errors, is developed. The design is based on some advanced digital redesign techniques equipped with a predictive feature. (ii) An improved Kalman filtering scheme is proposed. Meanwhile, a new optional linearization methodology is developed to obtain optimal linear models of a class of discrete-time time-invariant nonlinear systems, so that the proposed improved Kalman filter can work properly for both linear and a class of nonlinear stochastic systems. Furthermore, a Kalman innovation filtering algorithm and its variant based on the evolutionary programming optimal-search technique are proposed for discrete-time time-invariant nonlinear systems with unknown-but bounded plant and noise uncertainties. (iii) The new state-space self-tuning control scheme for adaptive digital control of continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, system and measurement noises, and inaccessible system states, is presented. An adjustable auto-regressive moving average (ARMA) based noise model with estimated states is constructed for state-space self-tuning control of continuous-time nonlinear stochastic systems. By taking advantage of the digital redesign methodology and by taking into consideration of the non negligible computation time delay and a relatively long sampling period, a new digitally redesigned predictive tracker/observer is developed for adaptive chaotic orbit tracking.; The methodology developed in this dissertation enables the design of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems. It is expected that the new results will find direct applications in aerospace and industrial engineering in the near future.