DIFFERENTIAL GEOMETRIC METHODS AND NONLINEAR CONTROL SYSTEMS

This paper introduces a new kind of methods—differential geometric methods (DGMs), which are effective in dealing with nonlinear control system. The relations between DGMs and nonlinear control system are discussed in section 2. The next section gives the definitions of (differentisble) manifold and differentiable map. In section 4, the concepts of vector field are given, and the relations between vector fields and dynamic systems are introduced. Lie algebra and Lie derivatives are briefly diacussed in section 5. Section 6 introduces the concepts of distribution and integral manifoid, and gives a very important theorem—Frobenius Theorem. In section 7, the linearization and input-output decoupling problems are investigated respectively. The structure of nonlinear control systems with symmetries are studied, and the properties of large-acale compsite systems with similarity are investigated in section 8.