Disturbance Decoupling for a Class of Nonlinear Control Systems Based on Lie Symmetry Method

To fully explore the inherent structural properties of symmetric nonlinear control systems, this paper introduces the Lie symmetry method to the disturbance decoupling problem for a class of SISO nonlinear control systems. Firstly, the state-space equations and the disturbance decoupling model for a class of SISO nonlinear control systems are defined; Secondly, the key technologies and algorithm approaches of Lie symmetry theory for differential equations are introduced, and the conditions and the properties of Lie symmetry for nonlinear control systems under group action are given in detail; Finally, the derived distribution of Lie symmetric infinitesimal generators is used to prove the sufficient conditions for local disturbance decoupling in the system, and the closed-loop state feedback analytical law of the system is constructed. Numerical simulations demonstrate the effectiveness of Lie symmetry method. The research has shown that nonlinear control systems with Lie symmetry have good internal structure and properties, and their disturbance decoupling conditions are relatively not strict. At the same time, using Lie symmetry, the cascade decoupling standard form and the static state feedback law of nonlinear control systems can be constructed.