Chattering Free Optimal Sliding Mode Control Of Discrete Nonlinear Time-Delay Systems

As we all know, the most outstanding feature of variable structure control with sliding mode is the existence of sliding surface. Once the state trajectory reaches the sliding surface, it will maintain on the sliding surface or in the neighborhood of it. On the sliding surface, the main features of the system movement are: strong robustness, lower dimensions property, predefined system movement in the sliding mode, and so on. By selecting the sliding surfaces we can get the satisfying dynamic performance in the sliding mode. And the control algorithm is simple and easy to be realized. As a result, the variable structure control with sliding mode has been highly regarded and widely used in all kinds of control fields.In general, the sliding mode control design has two fundamental steps. The first step is to select the suitable equation of sliding surface such that the system exhibits the desired behavior in the sliding mode. The second step is to determine a switched control law to guarantee the reaching and sliding condition. Although there are many methods to design sliding surfaces, how to design optimal sliding surface has not been seen yet. If the optimal control and the designing of sliding surface can be combined together, the motion over the sliding surface can be optimized. However, control implementation by digital computers requires a certain sampling interval which may cause chattering along the sliding surface. The ideal sliding mode does not exist any more, even for the nominal systems. Consequently, the design of the sliding surface is very important as well as the eliminating of chattering.Nonlinear and time-delay exist in many systems such as industry, aerospace and ocean engineering. For example, the attitude and movement trajectory control systems for towed vehicles are nonlinear time-delay systems with six degree of freedom. And the vibration control systems for offshore platforms are nonlinear systems with time-delay. Therefore, the research of chattering free optimal sliding mode control for discrete nonlinear time-delay systems is significant both in theory and in practice. The...