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This paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

Summary: This study proposes a novel iterative learning control scheme for discrete‐time linear systems based on the Broyden‐class optimization method. To overcome the difficulty of lacking system information, a cost function is introduced for the performance index by constructing a positive‐definite matrix with little system information. An optimization‐based learning control algorithm is proposed using a Hessian matrix approximation and the generated input sequence is demonstrated to exhibit a superlinear convergence rate. The proposed scheme is extended to address the point‐to‐point tracking problem. Numerical simulations are provided to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article develops a novel framework for iterative learning control (ILC) design of discrete‐time systems with non‐uniform trial lengths by using the method of alternating projections. In contrast to existing results for the non‐uniform trial length problem, this article uses the Hilbert space setting and hence the linear discrete‐time system dynamics with non‐uniform trial lengths can be represented by multiple affine subspaces (or linear varieties). Motivated by the successive projection design between two closed convex sets, the considered ILC problem can be transformed into alternating projections between multiple sets, then the Hilbert space setting is used to establish key systems theoretic properties. Moreover, an optimal ILC design is developed for systems with non‐uniform trial lengths, which is also extended to the case of input constraints. A numerical case study is given to illustrate the applicability of the new design. [ABSTRACT FROM AUTHOR]

In this work, a novel adaptive event‐trigered iterative learning control (ILC) scheme is designed for discrete‐time nonlinear systems with time‐varying parameters and random initial states. The reference trajectory can be iteration‐invariant or iteration‐varying. The control input is updated when the event‐triggering condition is satisfied, which reduces the action time of controller and consequently the unnecessary waste of communication resource. An adaptive event‐triggering condition parameter is designed to improve the efficiency of the event generator. Moreover, the parameter updating law of adaptive iterative learning controller is designed based on the recursive least squares algorithm. With the proposed adaptive ILC with event‐triggered mechanism, the learning convergence along the iteration axis is guaranteed and communication burden is reduced. Finally, rigorous theoretical analysis under Lyapunov theory and illustrative examples are given to demonstrate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

In this work, the problems of predictive compensation, unknown nonlinearity, and nonaffine structure are considered simultaneously for a quantized iterative learning control (QILC) design and analysis under a data‐driven framework. The compensation strategy can avoid deteriorated data transmission quality owing to limited channel capacities. First, a dynamic linearization methodology is employed to transform the nonlinear plant into a virtual iterative linear data model (iLDM) which includes all the input signals over a time‐window from the initial time instant to the current one. The iLDM is also used as a predictive model to estimate the unavailable information caused by the encoding–decoding mechanism. Then, a predictive compensation‐based QILC is proposed by optimizing quadratic functions, which includes an output prediction mechanism, a quantized iterative learning updating law, a quantized iterative parameter estimation law, and a resetting algorithm. The result is also extended to a class of MIMO nonlinear nonaffine discrete‐time systems. The developed control laws are data‐driven and independent of any system information. The theoretical results are proved by the use of contraction mapping principle and induction method. Examples are provided to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article proposes a dynamic time warping (DTW)‐based iterative learning control (ILC) scheme for discrete‐time nonlinear systems to tackle the path learning problem with varying trial lengths and terminus constraint. By incorporating the improved DTW algorithm, the varying trial lengths are aligned as a desired length. Meanwhile, this algorithm can find the most similar waypoints between the output and the desired paths, which can be used to design an updating law and facilitate the convergence of path learning. Different from the existing ILC methods based on the probability distribution function for learning trajectory in the time domain, the method in this article can be applied to learn the spatial path corresponding to the desired trajectory. Furthermore, the learning property in the presence of variable initial states is discussed under the proposed method. Several illustrative examples manifest the validity of the proposed DTW‐based ILC algorithm. [ABSTRACT FROM AUTHOR]

In this article, an iterative learning approach is proposed for the formation control of discrete‐time multi‐agent systems, where the trial length of each learning iteration is randomly varying. In particular, a modified state error related to the prescribed formation is defined by taking into account the nonuniform actual trial length that could be different from the desired one. Then, a P‐type iterative learning protocol is established for switching networks of agents subject to nonuniform trial lengths, and the convergence analyses are given for the fixed and the iteration‐varying initial conditions respectively. It shows that through iterative learning, the given formation will be maintained among multiple agents in the entire time interval of one trial. In the end, simulations are done to demonstrate the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this article, an output‐feedback Q‐learning algorithm is proposed for the discrete‐time linear system to deal with the H∞$$ {H}_{\infty } $$ tracking control problem. The problem is formulated as a zero‐sum game in the Stackelberg game framework with a discount factor to make the value function bounded. According to the principle of optimality, the game algebraic Riccati equation (GARE) is derived and solved by the Q‐learning algorithm to get the optimal solution of the Stackelberg game without requiring the knowledge of system dynamics and state. It is proved that the solution of the algorithm converges to the optimal control input and the worst‐case disturbance with excitation noises during training, and the Stackelberg strategy can achieve a lower L2$$ {L}_2 $$ disturbance attenuation level than the Nash one. Moreover, the impacts of the discount factor on the stability of the closed‐loop system and solvability of the GARE are analyzed to provide some criteria for the choice of the discount factor. Simulation examples are provided to validate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this work, based on the robust iterative learning control (ILC) scheme, the finite‐iteration tracking control is investigated for discrete‐time linear systems in repetitive process setting with external disturbances. First, the concept of finite‐iteration tracking is defined. Then by utilizing the lifted‐vector‐matrix technique, the discrete‐time linear system can be reformulated as an input–output transmission equation. Moreover, a P‐type ILC scheme is employed, and then the finite‐iteration tracking of the resultant system is guaranteed with the designed iterative learning controller. Meanwhile, the settling iteration can be explicitly obtained. Particularly, the case of data loss occurred during information transmission is also studied, and sufficient conditions are presented such that the finite‐iteration tracking can be achieved in a finite interval. Lastly, the effectiveness and applicability of the presented method are validated via a numerical simulation. [ABSTRACT FROM AUTHOR]

This article considers the equivalence and convergence of two iterative learning control (ILC) schemes with state feedback for a class of multi‐input‐multi‐output discrete‐time nonlinear systems in which each desired trajectory corresponds to a unique desired input or an infinite number of desired inputs. First, we strictly prove that the two ILC schemes are equivalent if they have the identical initial system inputs. Moreover, by the input space transformation method and mathematical induction we establish the necessary and sufficient criterion for the convergence of system output, input and state sequences. It is shown that the (locally Lipschitz) continuity is enough to guarantee the (exponential) convergence. Generally, the learned desired input depends on the values of the initial signals, the learning gain matrix and the state feedback item. By designing them with appropriate structures, the dependence is disappeared. Third, we show how to leverage the available information of system dynamics to design the learning gain matrix and state feedback for better tracking performance. Finally, we provide an example to illustrate the usefulness of our findings, in which we introduce the energy of learnable desired input to evaluate the learning performance. [ABSTRACT FROM AUTHOR]

In this work, an adaptive iterative learning control (AILC) method is designed for a class of parametric discrete‐time nonlinear systems with random initial condition, unknown time‐varying input gain and multiple time‐iteration‐varying factors including multiple unknown time‐iteration‐varying parameters and unknown time‐iteration‐varying external disturbance. The iteration‐varying factors can be generated by virtue of multiple iteration‐varying high‐order internal models, respectively, where iteration‐varying high‐order internal model means it has iteration‐varying order or coefficients. Moreover, the parameter updating law is designed based on the recursive least squares algorithm. Using the designed AILC based on iteration‐varying high‐order internal model, the learning convergence in the iteration domain is guaranteed through rigorous theoretical analysis under Lyapunov theory. Finally, two simulation examples are given to demonstrate that the proposed scheme is effective. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we consider a novel iterative DMPC (distributed model predictive control) scheme for linear discrete‐time systems which are connected by network. Every system is dynamically coupled to neighbors. The proposed method can reduce the communication load without degrading performance compared to cooperative DMPC by sensitivity and information topology analysis. The proposed algorithms are applied in a four‐water‐tanks numerical example, and the simulation results show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we explore how to get the information of input‐output coupling parameters (IOCPs) for a class of uncertain discrete‐time systems by using iterative learning technique. Firstly, by taking advantage of repetitiveness of control system and informative input and output data, we design an iterative learning scheme for unknown IOCPs. It is shown that we can get the exact values of IOCPs one by one through running the repetitive system T+1 times if the control system is with identical initial state and noise free. Secondly, we give the iterative learning scheme for unknown IOCPs in the presence of measurement noise, system noise, or initial state drift and analyze the influence factors on the performance of developed iterative learning scheme. Meanwhile, we introduce the maximum allowable control deviation into the iterative learning mechanism to minimize the negative impact of noise on the performance of learning scheme and to enhance the robust of iterative learning scheme. Thirdly, for a class of multiple‐input–multiple‐output systems, we also develop iterative learning mechanism for unknown input‐output coupling matrices. Finally, an illustrative example is given to demonstrate the effectiveness of proposed iterative learning scheme. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a model‐free algorithm for global stabilization of linear systems subject to actuator saturation. The idea of gain‐scheduled low gain feedback is applied to develop control laws that avoid saturation and achieve global stabilization. To design these control laws, we employ the framework of parameterized algebraic Riccati equations (AREs). Reinforcement learning techniques are developed to find the solution of the parameterized ARE without requiring any knowledge of the system dynamics. In particular, we present an iterative Q‐learning scheme that searches for a low gain parameter and iteratively solves the parameterized ARE using the Bellman equation. Both state feedback and output feedback algorithms are developed. It is shown that the proposed scheme achieves model‐free global stabilization under bounded controls and convergence to the optimal solution of the ARE is achieved. Simulation results are presented that confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel high-order optimal terminal iterative learning control (high-order OTILC) is proposed via a data-driven approach for nonlinear discrete-time systems with unknown orders in the input and output. The objective is to track the desired values at the endpoint of the operation cycle. The terminal tracking errors over more than one previous iterations are used to enhance the high-order OTILC's performance with faster convergence. From rigor of the analysis, the monotonic convergence of the terminal tracking error is proved along the iteration direction. More importantly, the condition for a high-order OTILC to outperform the low-order ones is first established by this work. The learning gain is not fixed but iteratively updated by using the input and output (I/O) data, which enhances the flexibility of the proposed controller for modifications and expansions. The proposed method is data-driven in which no explicit models are used except for the input and output data. The applications to a highly nonlinear continuous stirred tank reactor and a highly nonlinear fed-batch fermentater demonstrate the effectiveness of the proposed high-order OTILC design. [ABSTRACT FROM AUTHOR]

In this paper, a high-order internal model (HOIM)-based iterative learning control (ILC) scheme is proposed for discrete-time nonlinear systems to tackle the tracking problem under iteration-varying desired trajectories. By incorporating the HOIM that is utilized to describe the variation of desired trajectories in the iteration domain into the ILC design, it is shown that the system output can converge to the desired trajectory along the iteration axis within arbitrarily small error. Furthermore, the learning property in the presence of state disturbances and output noise is discussed under HOIM-based ILC with an integrator in the iteration axis. Two simulation examples are given to demonstrate the effectiveness of the proposed control method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]