An adaptive support vector regressor controller for nonlinear systems

Generalized self-tuning regulator based on online support vector regression

“…Thus, the feasible increment directions for the bias and the Lagrange multipliers of the samples in S can be obtained for a given Dk c using (23)- (25). The derivation and calculation of the Lagrange multiplier of current sample (Dk c ) is detailed in [38]. The variation in margin values as a result of increment Dk c for non-support samples can be calculated as follows using (18), (20),…”

“…. ; z m are the indices of non-support samples, c are margin sensitivities and c ¼ 0 for samples in S. The alternation of the matrix H for learning and forgetting stages and detailed information related to recursive algorithm can be attained via [18,38,40,41]. Fig.…”

“…Fig. 1 E, S and R subsets before (a) and after (b) training [13,18,38,40] Neural Comput & Applic 3 Contruction of optimization problem for self-tuning regulator 3…”

“…This situation causes a significant dilemma to train SVR structures without the explicit information of desired output data. However, a similar problem which hampers to utilize SVR directly as a controller in control block was managed to overcome in [38]. For this purpose, Uçak and Ö ke Günel proposed ''closed-loop system margin'' notion to solve this situation.…”

“…The main contribution of the paper is utilizing an online SVR to approximate the optimal parameter values of a self-tuning regulator. For this purpose, the ''closed-loop margin'' notion proposed in [38] has been expanded to design STRs and online SVR update equations are derived. The proposed mechanism is used to optimize the parameters of two different type of controllers, namely PID and fuzzy PID controllers.…”