Optimal Iterative Learning Control Algorithms And Convergence Analysis

Iterative learning control (ILC), which is firstly proposed in the movement control of manipulator, is a technique for improving the tracking performance of systems or processes that operate repetitively over a fixed time. ILC utilizes the deviation between actual output and desired output to modify current control input signal by learning, this control method has brought ILC widely acceptance and highly attention in the field of control engineering. The ILC algorithm does not rely on the repeatable system model very much and has good tracking accuracy in practice. Due to these characteristics, ILC has become an important control method of modern intelligent control technology.Traditional parameter iterative learning control algorithm ensures the tracking error converge monotonically to zero only when the original plant is positive. In order to solving this limitation, a high-order parameter optimal iterative learning control algorithm is introduced in this paper. The proposed algorithm is established by a quadratic performance index with the tracking errors from earlier trials to construct optimal learning law. The proposed algorithm can guarantee the tracking error converge monotonically to zero even the relaxation system is non-positive.A PID parameter optimal iterative learning control algorithm based on singular value decomposition is also given in this paper. The proposed algorithm establishes the norm performance index and obtains learning gain matrix by applying singular value decomposition to the original plant, and ensure the closed-loop tracking errors of this algorithm converge monotonously to zero even the original plant is non-positive. Furthermore, a PID controller is added to the design of ILC algorithm to improve learning efficiency.Focuses on the tracking problems of dynamic nonlinear system, a novel parameter optimal Broyden-like method based iterative learning control scheme is proposed in this paper. The Broyden-like method is used to iteratively calculate the approximation of the Jacobian matrix, and the parameter-optimal method is used to optimize the learning gain of the algorithm. Compared with traditional Newton-method, the proposed algorithm can avoid the calculation of the inverse of the Jacobian matrix of system. Furthermore, the algorithm has the properties of global and monotonic convergence.A class of specific target tracking problems for non-linear systems with the reference trajectory sampled only in some specific times is discussed. Accordingly, a modified Newton-method-based iterative learning control scheme is suggested to solve this problem. It is proved theoretically that the algorithm can ensure the closed loop system to have global and monotonic convergence. A case study of final product tracking problem of a mixed, liquid-phase batch reactor is given to demonstrate the effectiveness and tracking accuracy of the proposed algorithm.In order to solve robust iterative learning control problem of a class of discrete-time nonlinear systems with initial state errors, external disturbances and output noises, a novel norm-optimal based robust iterative learning control algorithm is proposed in this paper. It is proven theoretically that in the absence of these disturbances, the algorithm can guarantee the tracking error of the closed-loop system uniformly converging to zero geometrically. In the presence of these disturbances and uncertainties, the sufficient condition of robust BIBO stability for the proposed algorithm is given.Finally, this paper discus the robust stability condition of P-type iterative learning control algorithm for a class of nonlinear dynamic discrete system. It is proved that in the presence of state, output disturbances and initial uncertainties, the system output can converge to the neighbor domain of desired trajectories. In the absence of these disturbances and uncertainties, the system output can converge to the desired trajectories uniformly.