Using least mean square learning error to improve Takagi-Sugeno type fuzzy logic controller optimization

An algorithm called Incremental Best Estimate Directed Search (IBEDS) was proposed for Takagi-Sugeno type fuzzy logic controller (FLC) automatic optimization. IBEDS starts with an initial training set that may be empty, an FLC with randomly initialized rule output parameters is trained by least mean square (LMS) learning algorithm in an iterative procedure. In each iteration, the trained FLC is evaluated with cell state space based global and local performance measures, the training set is then updated based on the evaluation under best kept policy, which only keeps the best control commands found so far. In this way, the training set is optimized in every iteration, and the FLC trained by the training set is also optimized progressively. The philosophy behind IBEDS is that the parameters of an FLC do not represent the performance of the controller directly although the goal of the optimization is to find an optimal controller parameter set so that the controller can have optimal global performance. However, the parameter set of an FLC with suboptimal performance may well represent a point in the parameter search space where the optimal one is nearby. Therefore the search algorithm should put more efforts in that area. LMS learning error is discarded in IBEDS as it does not represent the performance of the trained FLC either. This learning error can be reused when the training set is highly optimized and an exact approximation of the training set by an FLC is desired. To further speed up the optimization, in addition to suggesting the reuse of the LMS learning error, this paper also proposes to reuse the FLC parameter set during a search. A 4D inverted pendulum is studied, and the simulation results show that the search speed is improved.