Evolving Granular Fuzzy Model-Based Control of Nonlinear Dynamic Systems

Unknown nonstationary processes require modeling and control design to be done in real time using streams of data collected from the process. The purpose is to stabilize the closed-loop system under changes of the operating conditions and process parameters. This paper introduces a model-based evolving granular fuzzy control approach as a step toward the development of a general framework for online modeling and control of unknown nonstationary processes with no human intervention. An incremental learning algorithm is introduced to develop and adapt the structure and parameters of the process model and controller based on information extracted from uncertain data streams. State feedback control laws and closed-loop stability are obtained from the solution of relaxed linear matrix inequalities derived from a fuzzy Lyapunov function. Bounded control inputs are also taken into account in the control system design. We explain the role of fuzzy granular data and the use of parallel distributed compensation. Fuzzy granular computation provides a way to handle data uncertainty and facilitates incorporation of domain knowledge. Although the evolving granular approach is oriented to control systems whose dynamics is complex and unknown, for expositional clarity, we consider online modeling and stabilization of the well-known Lorenz chaos as an illustrative example.