Study On Iterative Learning Control Algorithms Based On Optimization Scheme

Iterative learning control (ILC) is a new control scheme for improving the transient re-sponse and tracking performance of manipulated systems that operate repetitively. ILC seeks an ideal control input signal which can make the plant implement the perfect tracking of the desired output trajectory in given time interval, according to learning unknown signal from the repetition of task as an experience by trials. Due to simple construction of iterative learning law and less requirement for prior knowledge of systems, ILC is extensively applied into systems which are strong coupling or hard to model. Complexity and diversity of systems in engineering practice could also bring challenges to study ILC schemes.In this dissertation, some problems related to iterative learning control algorithms for di-verse systems are studied based on the analysis for iterative learning control process and the framework of optimization theory, such as the convergence of ILC algorithms, accelerating con-vergence speed, initial conditions of ILC scheme and so on. Here, ILC issues based on optimiza-tion schemes are considered by applying methods such as the vector rotation, Damped Newton method, the rank one update, the predictor-corrector method to improve performance of ILC algorithms. The main contributions of this dissertation are as follows.The issue of weakening convergence conditions of ILC scheme for discrete time systems with a rapid convergence speed is considered. An iterative learning control algorithm based on vector rotation is presented by utilizing geometrical analysis for the control task. Based on the nature of iterative learning control, the relationship between system outputs and plant errors is established in the form of the vector, and subsequently, rotation angle as a control parameter is employed to adjust the controller more convenient by using the vector rotation. The proposed ILC algorithm with geometrical convergence is composed of the second order iterative learning law which is the nonlinear construction, and the monotone convergence is obtained by the correction of error at current iteration. Finally, the weak convergence condition is given in terms of rotation angle and correction parameter. Simulations are demonstrated the effectiveness of the algorithm.The algorithm stability for non-minimum phase plants caused by singular values, which decelerate the convergence speed, is addressed. By introducing convex combination of future predicted errors and the incremental inputs of the next N trials into the cost criterion, where the weight parameters determine the importance of future errors and incremental inputs, the pre-dictive optimization of convex combination based ILC is proposed. According to solving the optimization problem of the cost criterion, and analyzing the convergence performance com-bined with the learning gain, ILC scheme with fast convergence speed for non-minimum phase plants is obtained. Then, it uses costate systems for a causal formulation of what is originally a non-causal algorithm. Numerical examples are given to illustrate the effectiveness of the pro-posed scheme.Quasi-Newton iterative learning control scheme based on rank-one update for nonlinear systems is proposed to solve the problem of tracking performance being low which is caused by the tremendous amount of calculation and the minor range of initial value. The tracking trajec-tory issue in ILC can be transformed into seeking the root of equation, in terms of disclosing the relationship between the optimization and general nonlinear ILC. Then, using the rank-one update to derive the recurrent formula to approximate the inverse of system Jacobian matrix, it proves that Quasi-Newton method based ILC can avoid the tremendous amount calculation of high-dimensional inverse matrix and converge rapidly. Convergence conditions proposed here extend the convergence domain and hence guarantee more choices for initial values. The simu-lations illustrate the theoretical results.The issue of low efficiency of ILC scheme for nonlinear systems caused by the difficulty in choosing initial value is investigated. In order to overcome this issue, an ILC scheme based on Damped Newton method for BIBO stable sampled nonlinear systems with global convergence is employed. In terms of a relax parameter different from ILC scheme based on Newton-type methods, iterative learning law and its convergence conditions are given, and under the condi-tions the ILC algorithm with global convergence is proposed to solve the issue of initial value derived from local convergence of existing Newton-type methods based ILC. Further, by explicit description for the choice of the parameter in the learning gain, the realization of algorithm is obtained in detail to guarantee the efficiency. With the aid of simulation, the proposed algorithm is demonstrated with global convergence.Iterative learning control scheme with global convergence based on predictor-corrector method for nonlinear systems is proposed to avoid the initial value issue of local convergence algorithms and weaken convergence conditions to extend the range of suitable systems. By intro-ducing homotopy continuation method into ILC context, and structuring the homotopy function in terms of a parameter, which is equivalent to increase one dimension for the control input, it makes tracking trajectory issue in ILC into tracing homotopy curve. As the change of parameter from0to1, the algorithm proposed here has advantage with global convergence. Firstly oper-ating the predictor to seek the trial point, and subsequently, implementing corrector by solving optimization sub-problem, new control input generated by the proposed algorithm based ILC is on the homotopy curve. Simulations show that ILC scheme based on predictor-corrector method can be convergent for different initial values.