Backstepping Control of Continuous Nonlinear Systems Using Chebyshev Neural Network

There are two types of system, one is linear and another one is nonlinear. For the control of linear systems there are several methods. Linear control theory is not directly applicable on nonlinear systems and there are so many approximations if linear control theory is directly applied on nonlinear systems. There is no unique method for analyzing nonlinear systems. A back stepping like design approach for reduced-order nonlinear observers is proposed. The basic idea of this approach is as follows. First, an appropriate function of the state variables to be estimated is constructed. The next function of the state variables to be estimated is then derived by designing the previous nonlinear function observer. Finally the procedure terminates, resulting in a partial differential equation to be solved. If the resultant differential equation is solvable, then the observer can be calculated. The connection between observers with linear error dynamics and this approach is discussed.