Robust Predictive Control For Fractional-order Descriptor Systems With Uncertainty

Fractional calculus is the extension of integer calculus,its differential order can be any real number or even complex number,compared with integer calculus,the use of fractional calculus for modeling,can improve the accuracy of the model and system performance.For the fractional-order descriptor system,it contains not only static information but also dynamic information,so it can more accurately reflect the physical process of the system.Uncertainty is always inevitable in real systems,and it is also true in fractional singular systems,its existence often leads to system performance degradation.With overlook to the uncertainty of the system,the robust predictive control can ameliorate the control property of the closed-loop system and elevate the robustness of the system by taking the uncertainty into consideration at the beginning of the design.Therefore,it is necessary to use robust predictive control method to deal with the uncertainty of fractional-order descriptor systems.In this paper,based on robust predictive control theory,LMI method and Lyapunov stability theory,robust predictive control for a class of uncertain fractional-order descriptor systems is studied.The continuous-time fractional-order descriptor systems of order 1??<2 and order 0<?<1 with uncertainty and the discrete-time fractional-order descriptor systems are studied respectively.The main work is as follows:Firstly,the issue of robust predictive control for a kind of continuous time fractional singular systems with uncertainty is studied,where the uncertainty is norm-bounded.When the system states are all measurable,the Lyapunov function is constructed based on the properties of fractional calculus.By using LMI toolbox and cone complement linearization algorithm,the sufficient conditions for the existence of state feedback control law when the fractional order is 1??<2 and 0<?<1 respectively are given,the displayed robust model predictive controller is obtained,and it is proved that the fractional order generalized closed-loop system is admissible under the feasible conditions.Secondly,the robust model predictive control problem for a class of discrete-time fractional-order descriptor systems with norm-bounded uncertainty is studied.Compared with the previous studies,the study of discrete-time fractional-order descriptor systems is more complicated because it contains not only the current moment state values but also the historical moment state values.Equivalent transformation is carried out for discrete-time fractional-order descriptor systems.By using the LMI method and Lyapunov stability theory,the sufficient conditions for the existence of robust predictive controllers are given by solving the min-max optimization problems in the infinite time domain,and the fractional-order descriptor closed-loop systems are guaranteed to be regular,causal and asymptotically stable.Finally,the simulation results show that the proposed control scheme is effective.