Novel iterative learning controls for linear discrete-time systems based on a performance index over iterations

An optimal iterative learning control (ILC) is proposed to optimize an accumulative quadratic performance index in the iteration domain for the nominal dynamics of linear discrete-time systems. Properties of stability, convergence, robustness, and optimality are investigated and demonstrated. In the case that the system under consideration contains uncertain dynamics, the proposed ILC design can be applied to yield a guaranteed-cost ILC whose solution can be found using the linear matrix inequality (LMI) technique. Simulation examples are included to demonstrate feasibility and effectiveness of the proposed learning controls.     

2D systems based robust iterative learning control using noncausal finite-time interval data

This paper uses a 2D system setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new 2D system based design algorithms provide a setting for the effective deployment of such information.     

Feedback iterative learning control for time-delay systems based on 2D analysis approach

This paper deals with the iterative learning control (ILC) design for multiple-input multiple-output (MIMO), time-delay systems (TDS). Two feedback ILC schemes are considered using the so-called two-dimensional (2D) analysis approach. It shows that continuous-discrete 2D Roesser systems can be developed to describe the entire learning dynamics of both ILC schemes, based on which necessary and sufficient conditions for their stability can be provided. A numerical example is included to validate the theoretical analysis.     

Adaptive iterative learning control for switched nonlinear continuous-time systems

In this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.     

Networked iterative learning control approach for nonlinear systems with random communication delay

This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.     

Observer-based distributed adaptive iterative learning control for linear multi-agent systems

This paper investigates the consensus problem for linear multi-agent systems from the viewpoint of two-dimensional systems when the state information of each agent is not available. Observer-based fully distributed adaptive iterative learning protocol is designed in this paper. A local observer is designed for each agent and it is shown that without using any global information about the communication graph, all agents achieve consensus perfectly for all undirected connected communication graph when the number of iterations tends to infinity. The Lyapunov-like energy function is employed to facilitate the learning protocol design and property analysis. Finally, simulation example is given to illustrate the theoretical analysis.     

A self‐tuning iterative learning controller for time variant systems

We consider the iterative learning control problem from an adaptive control viewpoint. The self‐tuning iterative learning control systems (STILCS) problem is formulated in a general case, where the underlying linear system is time‐variant and its parameters are all unknown and where its initial conditions are not constant and not determinable in various iterations. A procedure for solving this problem will be presented. The Lyapunov technique is employed to ensure the convergence of the presented STILCS. Computer simulation results are included to illustrate the effectiveness of the proposed STILCS. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Iterative learning control for a class of singular impulsive systems

In this paper, the iterative learning control problem for a class of nonlinear singular impulsive systems is discussed. Then, a D-type (derivative-type) iterative learning control algorithm is presented such that the output tracks the desired output trajectory as accurate as possible. Furthermore, the sufficient condition for the convergence of the proposed algorithm is established in detail. Finally, a numerical example is included to corroborate the theoretical analyses.     

Networked iterative learning control design for discrete-time systems with stochastic communication delay in input and output channels

This paper develops two kinds of derivative-type networked iterative learning control (NILC) schemes for repetitive discrete-time systems with stochastic communication delay occurred in input and output channels and modelled as 0-1 Bernoulli-type stochastic variable. In the two schemes, the delayed signal of the current control input is replaced by the synchronous input utilised at the previous iteration, whilst for the delayed signal of the system output the one scheme substitutes it by the synchronous predetermined desired trajectory and the other takes it by the synchronous output at the previous operation, respectively. In virtue of the mathematical expectation, the tracking performance is analysed which exhibits that for both the linear time-invariant and nonlinear affine systems the two kinds of NILCs are convergent under the assumptions that the probabilities of communication delays are adequately constrained and the product of the input–output coupling matrices is full-column rank. Last, two illustrative examples are presented to demonstrate the effectiveness and validity of the proposed NILC schemes.     

Convergence properties of two networked iterative learning control schemes for discrete-time systems with random packet dropout

This paper addresses convergence issue of two networked iterative learning control (NILC) schemes for a class of discrete-time nonlinear systems with random packet dropout occurred in input and output channels and modelled as 0–1 Bernoulli-type random variable. In the two NILC schemes, the dropped control input of the current iteration is substituted by the synchronous input used at the previous iteration, whilst for the dropped system output, the first replacement strategy is to replace it by the synchronous pre-given desired trajectory and the second one is to substitute it by the synchronous output used at the previous iteration. By the stochastic analysis technique, we analyse the convergence properties of two NILC schemes. It is shown that under appropriate constraints on learning gain and packet dropout probabilities, the tracking errors driven by the two schemes are convergent to zero in the expectation sense along iteration direction, respectively. Finally, illustrative simulations are carried out to manifest the validity and effectiveness of the results.     

Repetitive control of Hamiltonian systems based on variational symmetry

This paper is concerned with repetitive control of Hamiltonian systems, which is based on iterative learning control utilizing the variational symmetry of those systems. Variational symmetry allows us to obtain an algorithm to solve a certain class of optimal control problems in a repetitive control framework. Therefore, the proposed method can deal with not only trajectory tracking control problems but also optimal trajectory generation problems, never before considered in a repetitive control framework. A convergence analysis of this algorithm is also discussed. Furthermore, some numerical simulations demonstrate the effectiveness of the proposed method.     

即时学习算法在非线性系统迭代学习控制中的应用

运用即时学习算法来解决一类非线性系统的迭代学习控制初值问题。对于任何类型的迭代学习控制算法，即时学习算法都能有效地估计初始控制量，减小了初始输出误差，加快了算法的收敛速度，使得经过有限次迭代后系统输出能严格跟踪理想信号。对机器人系统的仿真结果表明了该方法的有效性。     

Iterative learning approaches to design finite-time consensus protocols for multi-agent systems

In this paper, the finite-time output consensus problem of multi-agent systems is considered by using the iterative learning control (ILC) approach. Two classes of distributed protocols are constructed from the two-dimensional system point of view (with time step and iteration number as independent variables), and are termed as iterative learning protocols. If learning gains are chosen appropriately, then all agents in a directed graph can be enabled to achieve finite-time consensus with the iterative learning protocols. Moreover, all agents in a directed graph can be guaranteed to reach finite-time consensus at any desired terminal output if the iterative learning protocols are improved by introducing the desired terminal output to some (not necessarily all) of the agents. Simulation results are finally presented to illustrate the performance and effectiveness of our iterative learning protocols.     

Necessary and sufficient condition for convergence of iterative learning algorithm

This correspondence is concerned with an iterative learning algorithm for MIMO linear time-varying systems. We provide a necessary and sufficient condition for the existence of a convergent algorithm. The result extends the main result in Saab (IEEE Trans. Automat. Control 40(6) (1995) 1138).     

Iterative learning control for linear discrete time nonminimum phase systems

This paper investigates iterative learning control for linear discrete time nonminimum phase systems. First, iterative learning control with advanced output data is considered for maximum phase systems. Next, the results are extended to nonminimum phase systems. The stability of the inverse mapping from the desired output to the input is proven based on the results for maximum phase systems. The input should be updated with the output which is more advanced than the input by the sum of the relative degree of the system and the number of nonminimum phase zeros. An example is given to indicate the importance of proper advances of output in the input update law.     

Performance limitations in the robust servomechanism problem for discrete time periodic systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for discrete time periodic systems. In studying this problem, the RSP for a multi-input/multi-output discrete time system is considered; application of these results is then made to the “periodic system robust servomechanism problem”, and explicit expressions for the limiting costs for error tracking regulation are obtained. These limitations can be characterized completely by the number and location of the non-minimum phase transmission zeros of the system's associated lifted system, together with a term which depends on the order of the system, the number of inputs, the number of transmission zeros and the system's period.     

线性广义系统的迭代学习控制

针对线性时不变广义系统的迭代学习控制问题．利用时间加权范数性质．通过Frobenius范数给出广义系统在D型和PD型闭环学习律作用下系统的实际输出轨迹逐渐逼近理想输出轨迹的充分条件．并指出在D型闭环学习律的基础上加上P型闭环学习律不影响控制系统的收敛性．但可以改变系统的性能．仿真算例说明了该方法的有效性．     

Virtual control strategy and conditioning technique for tracking and learning controls under input restrictions

The virtual control strategy for mechanical systems has been recently proposed (Gnucci and Marino, 2021) in the context of under-actuated mechanical systems. Such a strategy views and represents an under-actuated mechanical system as a fully actuated system with virtually added inputs and outputs having to satisfy, through a suitable choice of the virtual output reference signals, the virtual input zero-equality constraint: the related adaptive tracking control problem is then solved through standard design techniques. This paper exhibits a twofold aim. The first one is: to enlarge the concept of zero-input constraint and thus naturally adapt the virtual control approach to the case in which an actuator fault can occur. The second aim is: to show how the application and transposition of such an adaptation to two well-known classes of nonlinear systems (special systems in multi-variable tracking form with two inputs and outputs under actuator faults; one-relative-degree, single-input, single-output systems in output feedback form under input saturation) not only own strong connections with the conditioning technique, originally conceived in the context of anti-windup problems under input constraints, but they also gain original results.