Stability Analysis And Fractional-order Control For Nonlinear Switched Systems

With the development of industry, it was discovered that many practical systems are fractional order, using fractional order differential equations can more accurately describe the characteristics of the system. The fractional order calculus has significant advantages on its control strategy, such as extensive regulation on parameter range, flexible phase change, stable control robustness, long-term memory and so on. The robustness of control law could be improved directly by utilizing the fractional order calculus. Switched system is hybrid system which is composed of a series of continuous time or discrete subsystems and the switching rules on them. Recently, researches about the switched system are mainly focused on its dynamic property which include the stability, controllability and observability. The main purpose is to design a controller that could stabilize the system and optimize performance. The stability of fractional nonlinear switched system and the design about fractional order controller are discussed based on the theory of fractional order calculus in this paper.The main contents could be obtained as:1) The research background and significant of switched system is introduced, as well as some existing problems. The theory of fractional order control and its relevant merits are studied.The introduction about the fundamental theory of fractional order calculus that used in this paper is also given.2) This paper deals with the stabilization for a class of fractional order nonlinear switched system. Based on the Caputo definition, the stability of switched system is researched through the fractional order Lyapunov function and muliti-Lyapunov functions technique. The numerical calculus in Matlab/Simulink software shows that the system is asymptotical stable and the advance of fractional order calculus is also be probed.3) The fractional order control of nonlinear switched system is discussed. Apply the fractional order theory to the backstepping approach, a fractional order controller for a class of nonlinear switched system is designed through the fractional order backstepping technique. The switching law is then established through the muliti-Lyapunov functions technique. Through the Matlab/Simulink platform, simulationes to numerical example verifies the stability of control effects.4) Apply the fractional order backstepping approach to the trajectory tracking problem of a two degree freedom wheel robot and create a fractional order contrail tracker. The control effect of trajectory tracking for robot would be improved significantly with the controller owns the‘memory' property. Several sets of parameters with different fractional orders are selected to compare the robot posture error and a novel control strategy with variable fractional orders is proposed. The superiority and effectiveness of fractional order control is verified by thesimulation to the robot trajectory tracking in Matlab environment.