Wavelet Robust Control by Fuzzy Boundary Layer via Time-variant Sliding Surface

There are several techniques to control of an uncertain nonlinear system. A typical approach is sliding mode control technique [14]. In the sliding mode technique, the proper transformation of tracking errors to generalize errors is introduced, so that n order tracking problem can be transformed into an equivalent first order stabilization problem [16]. The sliding-mode control employs a discontinuous control to derive the system state to reach and maintain its motion on sliding surface. The discontinuity in the control action provides the chattering and the un-modeled frequencies may be activated, which are undesirable in application. To avoid these drawbacks, the boundary layer technique is exploited [14]. For achieving the better tracking performance a varying boundary layer is considered. In [9], the selftuning laws based on the bounded modeling error, for adjusting the boundary layer width and the other parameters have also been proposed. Furthermore, for calculating the control gain parameter, the difference functions f  and g  must be obtained, that is a drawback. The auto-tuning neurons computation for designing the sliding-mode control [3] and the fuzzy adjusting method for finding the suitable boundary layer width [12] are used. Most practical systems are non-linear and complex in nature with uncertain dynamics that may not be easily modeled mathematically. For this purpose, the identification methods are usually exploited [1], [2], [11], [17]. A direct adaptive fuzzy sliding mode control for uncertain nonlinear systems was presented in [13]. The GA-based fuzzy sliding mode controller with modified adaptive laws for robust control of an uncertain nonlinear plant has also been presented [4]. Recently, wavelets have led to advanced tools in many scientific and application research areas [5]. Multiscale analysis, synthesis properties and the learning abilities of neural wavelet networks, for approximation of nonlinear functions are well established [6], [15], [18]. In the literature only time-invariant sliding surface has been studied extensively. Here for the first time, a new case of time-variant sliding equation is presented. For this purpose, the rejection regulator based on a parameter that is called "rejection parameter" is defined. For objectively choosing the coefficients of error states in sliding equation rejection regulator is used. By tuning the rejection parameter, we can adjust the break frequency bandwidth and also the coefficients of error states in sliding equation. Such sliding equation, as a chain of ) 1 (  n adaptive first-order low-pass filters, rejects all un-modeled frequencies. The tracking precision is not guaranteed by using the saturation function. Therefore, instead of Wavelet Robust Control by Fuzzy Boundary Layer via Time-variant Sliding Surface