Reducing memory requirement of cell state space based fuzzy logic controller design approaches using k-d trees

The memory requirement makes cell state space based fuzzy logic controller (FLC) design approaches prohibitive for high order systems. The paper presents a specially modified k-d tree data structure to minimize memory requirements. Based on the k-d tree representation of the cell state space, an optimal control table (OCT) can be built and further be used to optimize a Takagi-Sugeno (TS) type FLC with least mean square (LMS) learning algorithm. However, for high order systems, due to physical memory limit and the complexity of system dynamics, even with k-d trees, an OCT may not have desirable resolution that is critical in FLC optimization. A method to overcome this problem is presented. The method involves interpolating the control actions in an OCT to obtain some optimal trajectories. A FLC will learn from the sampling data along the trajectories instead of learning from the OCT. A 4D inverted pendulum is studied in the paper. The performance of the FLC designed with the new approaches compares favorably with a linear quadratic regulator