Robust Hybrid Sliding Mode Control for Uncertain Nonlinear Systems Using Output Recurrent CMAC

In recent years, the sliding-mode control (SMC) theory has been widely and successfully applied in different systems such as control systems, power systems, and biped robotics, among others [12, 13]. For control systems the salient features of SMC techniques are fast convergence, external disturbance rejection, and strong robustness [12]. However, the uncertainty bound in SMC may not be easily obtained; a large switching control gain is always chosen in order to guarantee system stability. Unfortunately, this causes high-frequency control chattering which may result in unforeseen instability and deteriorates system performance. The uncertainty bound can be estimated via an adaptive algorithm or intelligent approximation tool, for example, neural networks or fuzzy systems. A number of works that proposed an uncertainty bound estimator to reduce control chattering in SMC have been reported in [8, 15, 17].

The advantages of using CMAC over NN in many practical applications have been presented in recent literature [4-6, 14]. However, the conventional CMAC uses local constant binary receptive-field basis functions. The disadvantage is that its output is constant within each quantized state and the derivative information is not preserved. For acquiring the derivative information of input and output variables, Chiang and Lin developed a CMAC network with a nonconstant differentiable Gaussian receptive-field basis function, and provided the convergence analyses of this network [3]. Based on this concept, some researchers have utilized the CMACs with a Gaussian receptive-field basis function to control nonlinear systems [9, 10]. However, the major drawback of these CMACs is that their application domain is limited to static problems due to their inherent network structure.

This study is organized as follows. Problem formulation is described in Sect. 3.2. The proposed RHSMC scheme is constructed in Sect. 3.3. In Sect. 3.4, the simulation results of the proposed RHSMC for a nonlinear biped robot system are presented. Conclusions are drawn in Sect. 3.5.