A manifold deformation design scheme for the controls of nonlinear systems

A Manifold Deformation Design Scheme (MDDS) for the controls of nonlinear systems based on the topological analysis about system dynamics is proposed in this paper. Such a novel method can simplify the process of system dynamics analysis and controller design for nonlinear control systems, especially the problem of gain scheduling, so as to perform the desired specifications due to various applications in spite of losing system models or having uncertainties. The dynamics of a control system, linear or nonlinear, is a mathematical formalization based on some fixed rule which describes the time dependence of a point´s position in its ambient space. However, it is very hard to derive the differential equations out directly, but the I/O data can be obtained straightly for various kinds of physical systems, which can form a manifold in a topology space so that controller designs are looked as a process of manifold deformation until the specification (or desired manifold) is attained. MDDS can´t only provide an alternative deign method for control engineering but also solves the trouble of controller designs for practical applications. For validation, the designs and simulations of regulation and tracking controls for a nonlinear system with perturbation are performed further, and the results indicate that this design scheme is very efficient and has excellent characteristics of robustness.