| Non-instantaneous impulsive differential system combines physical principles and s-tatistical regression into two modeling methods,using differential equations and algebraic equations modeling,and has a wide range of applications in pest control,pharmacoki-netics and engineering control.Based on the study of the controllability and optimal control of non-instantaneous impulsive differential systems,it is also expected to design an effective learning control strategy so that the output of the controlled system running repeatedly in a finite time interval can track the predetermined trajectory.Therefore,it is necessary to study the finite-time complete tracking control of non-instantaneous impulsive differential systems.In this dissertation,we use operator semi-group theory,set-valued mapping theory,non-compactness measure theory,fractional-order calculus theory,nonlinear functional analysis theory and iterative learning control technology to systematically study the con-trollability,the existence of optimal control and the finite time complete tracking control of the integer-order non-instantaneous impulsive differential equations,the fractional-order non-instantaneous impulsive differential evolution equation and the differential inclusion system.The main contents of this dissertation are as follows:Firstly,the integer-order non-instantaneous non-autonomous impulsive differential equations are studied,and the appropriate definition of the mild solution is given.The existence and uniqueness of the mild solution and the sufficient conditions for the con-trollability system are given by using the contraction mapping principle and Schauder fixed point method and other fixed methods.Furthermore,the~2norm of the tracking error function is used as the performance index to obtain a new result of the existence of optimal control.On this basis,the Caputo type fractional evolution equation is studied on Hilbert space,and the appropriate definition of the mild solution is given by using the fractional calculus theory.By constructing the compound operator,the existence and approximate controllability of mild solution are obtained by using the techniques of nonlinear functional analysis,operator semi-group theory and fixed point method such as Krasnoselskii’s fixed theorem,Schauder fixed theorem and Arzela-Ascoli lemma and Balder theory,and then the existence result of the more general Lagrange type optimal control problem are obtained.Secondly,the finite-time complete tracking control of integer-order and fractional-order non-instantaneous impulsive differential systems is studied by means of iterative learning control technology.In the case of fixed batch length,the classic-type learning law is designed.In the variation case of batch length,the improved-type learning law,the-type learning law with local average operator and without redundant information,the nonlinear learning law based on the concept of the domain alignment operator and Schmidt orthogonalization method are designed respectively.Combining the Lipschitz condition,the H¨older inequality,the fractional-order Gronwall inequality and compres-sion mapping principle,some sufficient conditions are given in the sense of-norm to ensure that the tracking error of the system with initial state offset converges to zero as the number of repetitions increases.The effectiveness of the theoretical results is verified by several numerical examples.The comparison of the convergence speed also shows that the nonlinear learning law has a good acceleration convergence effect.Thirdly,the orbital approximate controllability,the existence and the stability of optimal control for integer-order non-instantaneous impulse evolution inclusions are stud-ied.In the case that the nonlinear set-valued mapping satisfies the upper semi-continuity and the almost lower semi-continuity,the orbital controllability of inclusion problem is transformed into the fixed point problem of operator equation corresponding to single-valued mapping,and the approximate controllability result of orbital is obtained by using the theory of the non-compactness measure and the corresponding fixed point theorem.By means of the compactness relation between the compactness of the set-valued map-ping and the compactness of the fixed point set,the existence results of optimal control are obtained,and the general stability of optimal control in the sense of Baire class is studied by using the Fort lemma.Finally,the finite-time complete tracking control of impulsive differential inclusion is studied.Assuming that the right-end set-valued mapping satisfies the Lipschitz con-tinuous condition on a particular finite-dimensional convex closed set,the classicaland-type learning laws are designed.With the help of Steiner selection result,the convergence analysis results of the iterative learning control problem of the first-order nonlinear differential inclusion controlled system are given,and the theoretical results are applied to the speed control of the robotic fish.On this basis,the above theoretical results are extended to the controlled system which is a non-instantaneous impulsive heat conduction differential inclusion system,and the sufficient conditions for convergence of system tracking errors are obtained in the appropriate Sobolev space. |
