Learning Identification Strategies And Learning Control For Some Classes Of Systems

The repetitive systems undertaken perform tasks over a pre-specified finite-time inter-val or track periodically trajectory. Learning control scheme is applied to deal with these systems. The amount to be learned is acquired to be a const, while variables are allowed to be learned under the learning control mechanism. In this paper, the identification and control problems of repetitive systems are discussed, and learning identification methods are presented, furthermore, learning controller is designed. Iterative learning control for system with initial error are discussed, and the specific algorithm is addressed. The main work is summarized in the following:1. Learning identification method, based on "repetitive invariants principle", is pre-sented for stochastic systems with time-varying parametric uncertainties. The systems undertaken perform tasks repetitively over a pre-specified finite-time interval, and a least squares learning algorithm is derived on the basis of the repetitive operations. The learning identification method applies for periodically time-varying systems. It is shown that the es-timates converge to the time-varying values of the parameters, and the complete estimation can be achieved under repetitive persistent excitation condition, a sufficient condition for establishing repetitive consistency of the learning algorithms. For accelerated convergence speed, several multi-innovation gradient learning algorithms are derived on the basis of the repetitive operations. Numerical results are presented to demonstrate the effectiveness of the proposed learning algorithms.2. The problem of adaptive backstepping repetitive learning control is addressed for a class of periodically time-varying discrete-time strict-feedback systems. A repetitive learn-ing least squares algorithm is applied for parameter estimation, where the lower bound for the control gain is introduced to avoid the potential singularity. An iteration-domain key technical lemma is given for the purpose of performance analysis, which is a slight mod- ification of the key technical lemma used for analysis of discrete adaptive systems. It is shown that the zero-error convergence can be achieved as the iteration increases, while the variables of the closed-loop system undertaken are bounded.3. A characteristic modeling method for continuous-time and discrete-time nonlinear time-varying systems is presented, with a unified model described by a first-order time-varying difference equation. Learning identification algorithms, the least squares/gradient learning algorithms with a forgetting factor, are suggested for the purpose of parameter es-timation. On the basis of the parameter estimation, an adaptive iterative learning control strategy is proposed to achieve perfect tracking over a pre-specified finite-time interval. Nu-merical simulation and experiment on a permanent-magnet synchronous motor are carried out to demonstrate the effectiveness of the modeling and control method.4. The problem of iterative learning control for systems in the presence of a fixed initial shift is addressed. A feedback-aided PD-type learning algorithm is proposed, and the convergence analysis indicates that such a learning algorithm ensures that the tracking error achieves the asymptotic convergence with respect to time, as iteration approaches infinity. Furthermore, the initial rectifying PD-type and PID-type strategies are adopted, respectively, to form learning algorithms for eliminating the effect of the fixed initial shift. It is shown that the system output converges to the desired trajectory over a pre-specified time interval, whatever value the fixed initial shift takes. Numerical results are presented to demonstrate effectiveness of the proposed learning algorithms.