Sliding Mode Control Of Fractional-Order Nonlinear Systems

In recent years, the theory of sliding mode control has formed a relatively independent branch. This theory has been applied in continuous and discrete systems, linear and nonlinear systems, lumped parameter and distributed parameter systems,certainty and uncertainty systems, centralized control and decentralized control, etc. The research of sliding mode control has a great development on the theory and application.The thesis is divided into six chapters.In Chapter 1, we introduce the background, the domestic and foreign research situation about fractional calculus,control and chaos of fractional order, and we also present the main work of this thesis.In Chapter 2, we recall the necessary preliminaries for the study of this thesis, including definitions and properties of fractional calculus,definitions of chaos, definitions of sliding mode control and the stability theorem.In Chapter 3, we briefly introduce the relevant knowledge of discrete fractional order.We first investigate the Lotka Volterra chaos maps by the difference theory. By using Matlab software, we plot the bifurcation diagram of chaos.After observing the image,we will analyze those factors that associate with chaos.At the same time, we consider that there is the delay time in the real world. So, we investigate the Lotka-Volterra chaos maps of fractional order with the delay time.In Chapter 4, we analyse the problem about synchronization of fractional order chaotic systems with parameter uncertainties based on adaptive sliding mode control. On the one hand, we design fractional integral sliding model control law, and we replace sign function with hyperbolic tangent function so that we deal with the problem of chatter in sliding mode control with effectively. On the other hand, we modify the sliding surface, which are constructed with fractional derivative and fractional integral. We can show that the system tracking errors convergence is deduced from fractional order stability theorems. Finally, we estimate the uncertain parameter with Matlab.In Chapter 5, we investigate the terminal sliding mode control of fractional order nonlinear system. In the first step, we establish the suitable sliding surface and control law for SISO systems of fractional order nonlinear. And we show that the system trajectories will converge to the sliding manifold in a finite time. In the next step, we consider fractional order large scale nonlinear systems, which is more complex.In addition, a fully decentralised fractional order sliding model control with a integral sliding surface is developed. Besides, an adaptive fuzzy structure is applied to approximate the interactions and uncertainties.Finally,numerical simulations are presented to validate the effectiveness of the system.In Chapter 6,we propose some new ideas for our future work based on the research at present.