Pattern-moving-based dynamic description for a class of nonlinear systems using the generalized probability density evolution

For a class of complex nonlinear systems governed by statistical laws, a new pattern-moving-based description method using the generalized probability density evolution was proposed. Due to the fact that the states and outputs of such systems typically exhibit a probability distribution rather than deterministic variables, and the outputs obtained by the system under similar operating conditions typically exhibit similar performance, a pattern class variable was constructed to describe such systems and effectively estimate their outputs or states. The mapping relationship between states and pattern class variables was established through the probability density evolution of the system. First, the dynamic description based on pattern moving is constructed by classification metric mapping. Then, the prior probability of the system state was predicted by solving the generalized density evolution equation. Next, the posterior probability was updated recursively according to Bayesian formula. Finally, the maximum a posteriori probability criterion is used to estimate the system state. The feasibility and effectiveness of the proposed algorithm were verified by numerical examples.