Learning Control For Discrete-time Systems Research Articles

Robust iterative learning control for discrete-time systems with random initial state shifts

This paper presents the sufficient conditions of the stability for discrete-time systems with random initial state shifts when applying iterative learning control. Different sufficient conditions have been developed for systems with different characteristics to ensure boundedness of tracking errors and convergence of the learning process under random initial condition. First, the relationship between the initial shifts of two adjacent iterations is addressed with the help of the transition matrix. And the different analysis models are established for each type of systems: one-dimensional matrix analysis model and 2-D Roesser model. Second, the new and sufficient conditions are established for the proposed learning control law to ensure systems convergence by matrix theory and two-dimensional system theory. Third, solving the linear matrix inequality (LMI) yields the control gains. Finally, digital simulations illustrate the effectiveness and sufficiency of the presented conditions.

Reinforcement Learning Control for Discrete-time Systems over Fading Channels

This paper studies the average cost minimization problem for a class of discrete-time systems suffering from fading channels and additive noise. An approximate generalized policy iteration algorithm is proposed to search for the optimal control policy for the considered problem without resorting to the system matrices. The estimation errors of the kernel matrices are proven to be small and the proposed model-free reinforcement learning algorithm is proven to be convergent. Some numerical examples are provided to illustrate the obtained results.

Iterative Learning Control for Discrete-Time Systems With Full Learnability.

This article considers iterative learning control (ILC) for a class of discrete-time systems with full learnability and unknown system dynamics. First, we give a framework to analyze the learnability of the control system and build the relationship between the learnability of the control system and the input-output coupling matrix (IOCM). The control system has full learnability if and only if the IOCM is full-row rank and the control system has no learnability almost everywhere if and only if the rank of the IOCM is less than the dimension of system output. Second, by using the repetitiveness of the control system, some data-based learning schemes are developed. It is shown that we can obtain all the needed information on system dynamics through the developed learning schemes if the control system is controllable. Third, by the dynamic characteristics of system outputs of the ILC system along the iteration direction, we show how to use the available information of system dynamics to design the iterative learning gain matrix and the current state feedback gain matrix. And we strictly prove that the iterative learning scheme with the current state feedback mechanism can guarantee the monotone convergence of the ILC process if the IOCM is full-row rank. Finally, a numerical example is provided to validate the effectiveness of the proposed iterative learning scheme with the current state feedback mechanism.

Networked iterative learning control for discrete-time systems with stochastic packet dropouts in input and output channels

The paper develops a derivative-type (D-type) networked iterative learning control (NILC) scheme for repetitive discrete-time systems with packet dropouts stochastically occurred in input and output communication channels. The scheme generates the sequential recursive-mode control inputs by mending the dropped instant-wise output with the synchronous desired output, while it drives the plant by refreshing the dropped instant-wise control input with the used consensus-instant control input at the previous iteration. By adopting statistic technique, the convergences of the developed NILC scheme for linear and nonlinear systems are derived, respectively. The derivations present that under certain conditions the mathematical expectations of the stochastic tracking errors in the sense of 1-norm converge to zero. Numerical simulations exhibit the effectiveness and validity.

Iterative learning control for discrete-time systems with event-triggered transmission strategy and quantization

This paper investigates the iterative learning problem for discrete-time systems with event-triggered scheme and quantization. The event-triggered scheme is firstly considered in the iterative learning controllers to reduce the number of iteration steps to be updated. Here, the event-triggered scheme is designed depending on time t and iterative learning step k. Quantization is then introduced in the event-triggered controllers and some relaxed conditions are presented to guarantee the tracking problem by using some interval matrix properties. Finally, simulation results are given to illustrate the usefulness of the developed criteria.

Robust monotone inverse type iterative learning control for discrete-time systems

In this report the robustness of inverse type iterative learning control algorithm is examined. It is shown that an optimally chosen adaptive learning gain results in robust geometric convergnce provided any multiplicative plant uncertainty meets a positivity requirement.

Iterative learning control based on the gradient method for linear discrete-time systems

Methods of iterative learning control for discrete-time systems have already been proposed. However, the applicability of these schemes depends essentially on the structure of the system. There are systems to which these schemes cannot be applied, even if the system models are completely known. In this paper we present a scheme, based on the gradient method, of iterative learning control for linear discrete-time systems in order to overcome these difficulties. The applicability of this scheme depends only on the amount of uncertainty in the system parameters. Some convergence conditions expressed as ranges of parameters are also presented for practical application to systems with uncertainty.

Iterative learning control for discrete-time systems with exponential rate of convergence

An algorithm for iterative learning control is proposed based on an optimisation principle used by other authors to derive gradient-type algorithms. The new algorithm is a descent algorithm and has potential benefits which include realisation in terms of Riccati feedback and feedforward components. This realisation also has the advantage of implicitly ensuring automatic step-size selection and hence guaranteeing convergence without the need for empirical choice of parameters. The algorithm achieves a geometric rate of convergence for invertible plants. One important feature of the proposed algorithm is the dependence of the speed of convergence on weight parameters appearing in the norms of the signals chosen for the optimisation problem.