Nonlinear Feedforward Systems Improve Footwork And Solve The Control Law, Relaxation

Nonlinear feedforward systems is one kind of nonlinear cascade systems whose composite Lyapunov function is difficult to be constructed,But,it is convenient to establish the Lyapunov function with cross-term,however,it is too complicated to solve the cross-term by the conventional Method.The design method fairly rely on the accurate knowledge of the system as well,and has to use the general form of the solution of the system and to meet an complicated integral computation.This paper mainly give us two way to simplify the solve methods of Lyapunov function.One method is use the basic recursive step of forwarding to make the method of relaxed forwarding adapt to a larger area of nonlinear forwarding system,and make the system achieve global asymptotic stability and local Exponential stabihty; The other method is make a little change on relaxed forwarding,achieve system's global asymptotic stability and local quadratic stability.First:Use the method of recursive relaxed forwarding to solve the Lyapunov function and controller for the nonlinear feedforward systemsDuring the construction of the Lyapunov function,using relaxed forwarding to construct the composite Lyapunov function can avoid calculate both the integrate of theψ(z,ξ) and the form of the solution of the system.On the contrary,only through calculate a set of linear algebraic equations can obtain the explicit composite Lyapunov function.This paper on the basic of the construction of the Lyapunov function with relaxed cross-term,using the basic reeursive step of forwarding,extend the relaxed forwarding from use once to use several times in the construction of the Lyapunov function with relaxed cross-term in one system.Thereby the construction of Lyapunov function with relaxed cross-term can be use widely in the feedforward system.In the end we give a simulation example to prove the effectiveness of this method.Second:Make improve to the relaxed forwarding method to solve the Lyapunov function and controller for nonlinear feedforward systems,and also extend it to the High-order systemsThis part on the base of the first part of the relaxed forwarding method,uses some of the hypothesis and Proposition,and adding a hypothesis that Quadratic stability for the Local linear model of the system.We make use of a transform as in 3.1 the third section was given,change the general system into the form of system(1.2.3).Use a new way to solve the Lyapunov function and controllers for a class of nonlinear systems,which involve a base system with a control input and a forwarding structure.Both part of the system are allowed to be nonlinear,multidimensional.We present a new approach to design stabilizing controllers which assure both global asymptotic stability and local quadratic stability.The main assumptions required for such a stabilizing linearized model of the system,global asymptotic stability for the base system and some mild conditions on the forwarding structure and the nonlinearity of the system.In the end we also give a simulation example to prove the effectiveness of this method.