Adjacent-Agent Dynamic Linearization-Based Iterative Learning Formation Control

An Accelerated Adaptive Gain Design in Stochastic Learning Control

This study investigates the trajectory tracking problem for stochastic systems and proposes a novel adaptive gain design to enhance the transient convergence performance of the learning control scheme. Differing from the existing results that mainly focused on gain's transition from constant to decreasing ones to suppress noise influence, this study leverages the adaptive mechanisms based on noisy signals to achieve an acceleration capability by addressing diverse performance at different time instants throughout the operation interval. Specifically, an additional gain matrix is introduced into the adaptive gain design to further enhance transient convergence performance. An iterative learning control approach with such a gain design is proposed to realize high precision tracking and it is proven that the input error generated by the newly proposed learning control scheme converges almost surely to zero. The effectiveness of the proposed scheme and its improvement on the transient performance of the learning process are numerically validated.

Data-Driven Adaptive Iterative Learning Bipartite Consensus for Heterogeneous Nonlinear Cooperation-Antagonism Networks

Heterogeneous dynamics, strongly nonlinear and nonaffine structures, and cooperation-antagonism networks are considered together in this work, which have been considered as challenging problems in the output consensus of multiagent systems. A heterogeneous linear data model (LDM) is presented to accommodate the nonlinear nonaffine structure of the heterogeneous agent. It also builds an I/O dynamic relationship of the agents along the iteration-dimensional direction to make it possible to learn control experience from previous iterations to improve the transient consensus performance. Then, an adaptive update algorithm is developed for the estimation of the uncertain parameters of the LDM to compensate for the unknown heterogeneous dynamics and model structures. To address the problem of cooperation and antagonism, an adaptive learning consensus protocol is proposed considering two signed graphs, which are structurally balanced and unbalanced, respectively. The learning gain can be regulated using the proposed adaptive updating law to enhance the adaptability to the uncertainties. With rigorous analysis, the bipartite consensus is proven in the case that the graph is structurally balanced, and the convergence of the agent output to zero is also proven in the case that the graph is unbalanced in its structure. The presented bipartite consensus method is data-based without the use of any explicit model information. The theoretical results are demonstrated through simulations.

Robust Data-Driven Iterative Learning Control for Linear-Time-Invariant and Hammerstein-Wiener Systems

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.

Iterative Rectifying Methods for Nonrepetitive Continuous-Time Learning Control Systems

To implement iterative learning control (ILC), one of the most fundamental hypotheses is the strict repetitiveness (i.e., iteration-independence) of the controlled systems, especially of their plant models. This hypothesis, however, results in difficulties of developing theoretic analysis methods and promoting practical applications for ILC, especially in the presence of continuous-time systems, which is the motivation of the current paper to cope with robust tracking problems of continuous-time ILC systems subject to nonrepetitive (i.e., iteration-dependent) uncertainties. Based on integrating an iterative rectifying mechanism, continuous-time ILC can effectively address the ill effects of the multiple nonrepetitive uncertainties that arise from the system models, initial states, load and measurement disturbances, and desired references. Furthermore, a robust convergence analysis method is presented for continuous-time ILC by combining a contraction mapping-based method and a system equivalence transformation method. It is disclosed that regardless of continuous-time ILC systems with zero or nonzero system relative degrees, the robust tracking tasks in the presence of nonrepetitive uncertainties can be accomplished, together with the boundedness of all the system trajectories being ensured. Two examples are included to verify the validity of our robust tracking results for nonrepetitive continuous-time ILC systems.

Transient Bipartite Synchronization for Cooperative-Antagonistic Multiagent Systems With Switching Topologies

This article aims at addressing the transient bipartite synchronization problem for cooperative-antagonistic multiagent systems with switching topologies. A distributed iterative learning control protocol is presented for agents by resorting to the local information from their neighbor agents. Through learning from other agents, the control input of each agent is updated iteratively such that the transient bipartite synchronization can be achieved over the targeted finite horizon under the simultaneously structurally balanced signed digraph. To be specific, all agents finally have the same output moduli at each time instant over the desired finite-time interval, which overcomes the influences caused by the antagonisms among agents and topology nonrepetitiveness along the iteration axis. As a counterpart, it is revealed that the stability can be achieved over the targeted finite horizon in the presence of a constantly structurally unbalanced signed digraph. Simulation examples are carried out to demonstrate the effectiveness of the distributed learning results developed among multiple agents.

Event-Triggered ILC for Optimal Consensus at Specified Data Points of Heterogeneous Networked Agents With Switching Topologies

In this article, the optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.

Iterative Learning Control With Data-Driven-Based Compensation

The robust iterative learning control (RILC) can deal with the systems with unknown time-varying uncertainty to track a repeated reference signal. However, the existing robust designs consider all the possibilities of uncertainty, which makes the design conservative and causes the controlled process converging to the reference trajectory slowly. To eliminate this weakness, a data-driven method is proposed. The new design intends to employ more information from the past input-output data to compensate for the robust control law and then to improve performance. The proposed control law is proved to guarantee convergence and accelerate the convergence rate. Ultimately, the experiments on a robot manipulator have been conducted to verify the good convergence of the trajectory errors under the control of the proposed method.

Data-Driven Adaptive Consensus Learning From Network Topologies

The problem of consensus learning from network topologies is studied for strongly connected nonlinear nonaffine multiagent systems (MASs). A linear spatial dynamic relationship (LSDR) is built at first to formulate the dynamic I/O relationship between an agent and all the other agents that are communicated through the networked topology. The LSDR consists of a linear parametric uncertain term and a residual nonlinear uncertain term. Utilizing the LSDR, a data-driven adaptive learning consensus protocol (DDALCP) is proposed to learn from both time dynamics of agent itself and spatial dynamics of the whole MAS. The parametric uncertainty and nonlinear uncertainty are estimated through an estimator and an observer respectively to improve robustness. The proposed DDALCP has a strong learning ability to improve the consensus performance because time dynamics and network topology information are both considered. The proposed consensus learning method is data-driven and has no dependence on the system model. The theoretical results are demonstrated by simulations.

A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

Event-Triggered Distributed Data-Driven Iterative Learning Bipartite Formation Control for Unknown Nonlinear Multiagent Systems

In this study, we investigate the event-triggering time-varying trajectory bipartite formation tracking problem for a class of unknown nonaffine nonlinear discrete-time multiagent systems (MASs). We first obtain an equivalent linear data model with a dynamic parameter of each agent by employing the pseudo-partial-derivative technique. Then, we propose an event-triggered distributed model-free adaptive iterative learning bipartite formation control scheme by using the input/output data of MASs without employing either the plant structure or any knowledge of the dynamics. To improve the flexibility and network communication resource utilization, we construct an observer-based event-triggering mechanism with a dead-zone operator. Furthermore, we rigorously prove the convergence of the proposed algorithm, where each agent's time-varying trajectory bipartite formation tracking error is reduced to a small range around zero. Finally, four simulation studies further validate the designed control approach's effectiveness, demonstrating that the proposed scheme is also suitable for the homogeneous MASs to achieve time-varying trajectory bipartite formation tracking.

Spatial Linear Dynamic Relationship of Strongly Connected Multiagent Systems and Adaptive Learning Control for Different Formations

This article addresses an important problem of how to improve the learnability of an intelligent agent in a strongly connected multiagent network. A novel spatial-dimensional linear dynamic relationship (SLDR) is developed to formulate the spatial dynamic relationship of an agent with respect to all the related agents. The obtained SLDR virtually exists in the computer to describe the input-output (I/O) relationship in the spatial domain and an iterative adaptation mechanism is developed to update the SLDR using I/O information to show real-time dynamical behavior of multiagent systems with nonrepetitive initial states. Subsequently, an SLDR-based adaptive iterative learning control (SLDR-AILC) is presented with rigorous analysis for iteration-variant formation control targets. Not only the 3-D dynamic behavior of the multiagent network but also the control protocols of the communicated agents are incorporated in the learning mechanism and thus strong learnability of the proposed SLDR-AILC is achieved to improve control performance. The proposed SLDR-AILC is a data-driven scheme where no explicit model structure is needed. Simulations with strongly connected topologies verify the theoretical results.

Further Results for Edge Convergence of Directed Signed Networks

The edge convergence problems have been explored for directed signed networks recently in 2019 by Du, Ma, and Meng, of which the analysis results, however, depend heavily on the strong connectivity of the network topologies. The question asked in this article is: whether and how can the edge convergence be achieved when the strong connectivity is not satisfied? The answer for the case of spanning tree is given. It is shown that if a signed network is either structurally balanced or r-structurally unbalanced, then the edge state can be ensured to converge to a constant vector. In contrast, if a signed network is both structurally unbalanced and r-structurally balanced, then its edge state does not converge to a constant vector any longer, but to a time-varying vector trajectory with a constant speed. Further, the dynamic behavior results of edges can be derived to address the node convergence problems of signed networks. The simulation examples are provided to illustrate the validity of the established edge convergence results.

Distributed Controller Design and Analysis of Second-Order Signed Networks With Communication Delays

This article concentrates on dealing with distributed control problems for second-order signed networks subject to not only cooperative but also antagonistic interactions. A distributed control protocol is proposed based on the nearest neighbor rules, with which necessary and sufficient conditions are developed for consensus of second-order signed networks whose communication topologies are described by strongly connected signed digraphs. Besides, another distributed control protocol in the presence of a communication delay is designed, for which a time margin of the delay can be determined simultaneously. It is shown that under the delay margin condition, necessary and sufficient consensus results can be derived even though second-order signed networks with a communication delay are considered. Simulation examples are included to illustrate the validity of our established consensus results of second-order signed networks.