Iterative Learning Control Of The Non-repetitive Continuous-time System

Traditional iterative learning control requires the controlled system to be strictly repeated,that is,the initial state,tracking task and operating environment of the controlled system are strictly repeated.However,the system's initial state shift,disturbances and measurement noise in the actual environment may make the system not fully repeatable.Therefore,the study of iterative learning control of non-repetitive systems has important theoretical and practical significance.At present,the research on iterative learning control of non-repetitive(related to iterations)systems has achieved some results,but it is mainly for discrete-time systems.This paper considers the iterative learning control problem of continuous-time non-repetitive(related to iterations)systems.The main contents include:(1)Consider the iterative learning control of the continuous-time regular linear system in which the system matrices,states and output disturbances,initial states,and desired trajectory change with iterations.Using the P-type learning algorithm in which the learning gain matrix changes with iterations and the principle of compression mapping.Through rigorous mathematical analysis and theoretical proof,the convergence of the output error of the controlled system is obtained,that is,the actual output of the system can completely track the desired output in a finite time.Through numerical simulation,the effectiveness of the learning algorithm is verified.(2)Discussed iterative learning control of continuous-time non-repetitive non-regular linear systems.Design a D-type learning algorithm in which the learning gain matrix changes with iterations.Using the relationship between the state error(the difference between the desired state and the actual state of the system)and the output error,the tracking error of the non-repetitive non-regular system can reduce to zero with increasing iterations.And numerical simulation illustrates the effectiveness of the D-type learning algorithm.(3)Consider the iterative learning control of the non-repetitive parabolic distributed parameter system with time and space variables.Design a P-type learning algorithm in which the learning gain matrix changes with iterations.Based on the norm,compression mapping principle and Gronwall-Bellman inequality,it is obtained that the actual output of the controlled system can fully track the desired output when the number of iterations intend to infinite.Through numerical simulation,the validity of the learning law is verified.