Abstract—Sliding mode control (SMC) has a strong capability in controlling nonlinear systems with uncertainties. However, SMC requires thorough knowledge of the controlled plant parameters and dynamics that is difficult to be obtained or may be unknown, which causes difficulties in calculating the equivalent control law of SMC. To overcome this problem, this paper proposes an adaptive SMC using simple adaptive control (SAC) developed for a class of single-input single-output (SISO) nonlinear systems with unknown parameters and dynamics, bounded-input bounded-output (BIBO), and bounded nonlinearity. The role of SAC is to construct an equivalent control input of adaptive SMC. To construct a corrective control input, this paper applies the sign function with a modified sliding surface. Finally, the stability analysis of the proposed method is carried out, and the effectiveness of this method is confirmed through computer simulations. I. INTRODUCTION ARIABLE structure control with sliding mode, which is commonly known as sliding mode control (SMC), is a nonlinear control strategy that is well known for its robust characteristics [1]. The main feature of SMC is that it can switch the control law very fast to drive the system states from any initial states onto a user-specified sliding surface, and to maintain the states on the surface for all subsequent time [1], [2]. This results in a system that is insensitive to parametric uncertainties and external disturbances [3], [4]. The conventional SMC has two disadvantages [3]. The first disadvantage is the difficulty in calculating equivalent control law of SMC where it requires thorough knowledge of the controlled plant parameters and dynamics [3], [4]. Since those parameters and dynamics are difficult to obtain or may be unknown, the calculation of the equivalent control law of SMC may be very difficult. The second disadvantage is the chattering phenomenon [4]. Recently, intelligent techniques based on fuzzy logic and neural networks have been applied to SMC to overcome those disadvantages [3], [5]—[7]. However, by those methods, it still requires a complex and time consuming process to calculate the control law of SMC. On the other hand, adaptive control methods were All authors are with the Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan (phone: +81-43-290-3280; e-mail: yasser@graduate.chiba-u.jp). developed to overcome difficulties connected with the ignorance of plant structure and critical parameter values as well as control regimes [8]. Among the adaptive control methods, simple adaptive control (SAC) procedure, which was developed by Sobel et al. [9], is considered as an attempt to simplify the adaptive controllers, since no observers or identifiers are needed in the feedback loop [10]. For linear plants with unknown structures, SAC is an important class of adaptive control scheme [10]. However, for nonlinear plants with unknown structures, it may not be possible to ensure that the plant output will follow the output of the reference model perfectly by using conventional SAC [11], [12]. In this paper, we attempt to improve the method proposed in [13] by providing the stability analysis and defining the class of nonlinear systems which it can control. This paper proposes an adaptive SMC strategy using SAC for a class of single-input single-output (SISO) nonlinear systems with unknown parameters and dynamics, bounded-input bounded-output (BIBO), and bounded nonlinearity. This method is designed to overcome the difficulties in the standard SMC caused by the requirement of thorough knowledge of the controlled plant parameters and dynamics, while keeping the chattering phenomenon minimal. The role of SAC is to construct an equivalent control input of adaptive SMC. To construct a corrective control input, this paper applies the sign function with a modified sliding surface. Hence, no any prior knowledge of the plant is required for calculating the equivalent control law. Furthermore, the proposed control method will keep the chattering phenomenon minimal. Finally, the stability analysis of the proposed method is carried out and computer simulations are executed, and the effectiveness of our method is confirmed. II. SLIDING MODE CONTROL In designing a standard sliding mode controller, first we are required to construct a sliding surface that represents a desired system dynamics, and then to develop a switching control law such that a sliding mode exists on every point of the sliding surface. Any state outside the surface is driven to reach the surface in a finite time. First let us consider an SISO nonlinear plant with BIBO to An Adaptive Sliding Mode Control Using Simple Adaptive Control for A Class of SISO Nonlinear Systems with Bounded-Input Bounded-Output and Bounded Nonlinearity Muhammad Yasser, Student Member, IEEE, Agus Trisanto, Student Member, IEEE, Ayman Haggag, Non Member, IEEE, Jianming Lu, Member, IEEE, Hiroo Sekiya, Member, IEEE, and Takashi Yahagi, Member, IEEE V Proceedings of the 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 13-15, 2006 WeIP4.2 1-4244-0171-2/06/$20.00 ©2006 IEEE. 1599