Control design based on multi-index nonlinear control method

Abstract

Firstly, a nonlinear control system based on the Riemannian manifold is defined from the perspective of holism, and the expression of the system’s state equation in the local coordinate system of the Riemannian manifold is given. The geometric structure of the Riemannian manifold is discussed. The influence of nonlinear systems is studied. The controllability and observability of nonlinear systems is studied. Secondly, using the properties of involute distribution and fully geodesic submanifolds, the local parts of nonlinear systems based on Riemannian manifolds are given. Controllable structured decomposition, local observable structure decomposition and Kalman decomposition. Thirdly, using the properties of orthogonal involute distribution family, incremental involute distribution family and fully geodesic submanifold family, the research is based on Riemannian manifolds. The parallel decoupling problem and cascade decoupling problem of nonlinear control systems on the above, as well as the local disturbance decoupling problem of affine nonlinear control systems.