Data-based Analysis and Control for Nonlinear Dynamical Systems

We developed some data-based methods for system analysis, and also for nonlinear dynamical systems control under the condition of no explicit mathematical models. We analyzed the controllability, observability, stability and domain of attraction for both linear and nonlinear discrete-time systems, only using measured data, without identifying the system parameters. We then developed the direct and indirect data-based output feedback control methods for a class of nonlinear systems. The direct methods applied a fast sampling technique to estimate system Jacobian matrices; while the indirect method utilized neural network and nonlinear programming methods to estimate them. They all designed the feedback controllers based on these Jacobian metrices and the measured output data.