Tracking Control For Singularly Perturbed Systems With Uncertainty

Singularly perturbed systems are dynamic systems with small perturbed parameters,which are widely used in robotics,electric power,aerospace and so on.The characteristics of singularly perturbed systems are multiple time scales.In recent years,new research achievements have been made on singularly perturbed systems.Furthermore,tracking control as an important area of research attracts more attention.For tracking control,performance of the system not only meets certain requirements,but the actual output can track the expected output appropriately.In practical control problems,the output tracking of the system appears a certain degree of deviation,due to the parameter perturbation,external signal interference and time-delay.Therefore,in this paper,robust predictive tracking control for uncertain singularly perturbed systems is studied by using the method of robust predictive control.The main contents are as follows:(1)The problem of robust predictive control for a class of uncertain singularly perturbed systems is studied.Combined with linear matrix inequality and Lyapunov stability theory,the linear quadratic performance index optimization problem is solved online.Based on the method of linear matrix inequality,the sufficient conditions for the existence of robust predictive state feedback controller are given.It is verified that the uncertain singularly perturbed closed-loop system is admissible(regular,stable and impulse free).Finally,the correctness and effectiveness of the proposed method are proved by numerical simulation.(2)The problem of robust predictive tracking control for singularly perturbed systems with external disturbances and parameter uncertainties is researched.The augmented system is obtained by combining the perturbed uncertain singularly perturbed system with the perturbed external tracking system.Firstly,based on Lyapunov stability theory and linear matrix inequality method,the optimization problem under linear quadratic performance index is solved online,and the sufficient conditions for the existence of robust predictive state feedback tracking controller and a set of piecewise continuous state feedback control sequences are obtained.It is proved that there is a feasible solution to the optimization problem at the initial time,and the perturbed uncertain singular perturbation system is allowed.Finally,the correctness and feasibility of the proposed method are verified by simulation comparison diagram.(3)The problem of robust predictive tracking control for uncertain singularly perturbed systems with time delay is studied.Firstly,when the system has state delay,the original time-delay system is combined with the tracking system to obtain the augmented matrix.Using Lyapunov stability theory,state feedback tracking controller with memory and linear matrix inequality method,the optimization problem under infinite time-domain quadratic performance index is solved online.The design method of state feedback tracking controller with memory and the solution method of system matrix with memory are given,and it is proved that the original system is admissible.Finally,a numerical example is given to demonstrate the effectiveness and feasibility of the proposed method.