The high precision tracking is a fundamental objective for iterative learning control (ILC) systems, which may be challenging in the presence of the iteration-varying disturbances. This article aims to address the robust tracking control problem for ILC systems having the iteration-varying disturbances, where the accurate model information is unavailable. Based on the input and disturbed output data collected from the test iterations, the nominal model of the ILC system is first constructed, under which a disturbance observer (DOB) is established to estimate not only the iteration-varying disturbance but also the model uncertainty. Further, a DOB-based ILC updating law is developed to achieve the robust tracking objective through inserting the estimation of the iteration-varying disturbance and the model uncertainty such that the tracking error is dependent continuously on the bound of the second-order variation rate of the disturbance. Particularly, the perfect tracking objective can be realized under the iteration-varying disturbance subject to the convergent variation rate. As a result, the tracking performance of the ILC system is improved under the iteration-varying disturbance, where the design of the DOB and the DOB-based ILC updating law depends only on the input and output data from the test iterations in the absence of the accurate model information.

This article is dedicated to developing a robust data-based predictive iterative learning control (PILC) framework for linear time-varying (LTV) systems via a behavioral approach. By investigating the properties of the admissible behaviors of LTV systems, an input/output representation is constructed from data, based upon which a data-based trackability criterion is developed for iterative learning control (ILC) systems. Moreover, in the presence of measurement noises, a robust PILC framework is constructed from noisy data through adopting a slack-variable-based strategy. Consequently, even in the absence of model information, ILC systems can achieve robust tracking performance with a faster convergence speed of tracking errors. To validate the effectiveness of the proposed PILC framework, simulation tests are performed on a permanent magnet synchronous motor (PMSM).

This work presents a novel adaptive iterative learning control (AILC) approach for a class of nonlinear nonsquare systems with unknown control gain matrices. The proposed strategy avoids explicitly incorporating the control gain matrices into the control algorithms and does not require them to be invertible, thereby significantly broadening the applicability of AILC. In the proposed AILC method, a newly designed virtual control gain matrix is introduced, enabling the transformation of the unknown control gain matrix into a form of norm-bounded system uncertainty while accounting for input saturation. Building on this reformulation, a structurally simple AILC scheme is developed, incorporating an input-dependent auxiliary system to mitigate the effects of input constraints. Moreover, the proposed method is extended to nonaffine nonlinear systems by integrating neural network techniques. The convergence of the proposed AILC laws is rigorously analyzed within the composite energy function (CEF) framework, and its effectiveness is demonstrated through implementation on a permanent magnet synchronous motor (PMSM) and a numerical example of a nonaffine system.

This paper proposes a predictive learning controller for an omnidirectional wheeled mobile robot (OWMR) with the target of achieving high-precision tracking of the desired trajectory within repetitive tasks. A prediction mechanism, based on the concept of “learning from the future,” is presented to accelerate learning convergence. Moreover, a constrained mechanism is leveraged to guarantee learning safety by introducing constraints on the input difference. The stability of OWMR under the proposed predictive learning controller is realized by formulating an optimization problem that incorporates terminal costs and constraints, together with its performance across iterations being evaluated through an analysis method based on composite energy functions. Additionally, a reducing prediction horizon strategy is adopted to mitigate computational burden, which both enhances the suitability and ensures the initial feasibility of the predictive learning controller for real-world applications. Subsequently, our predictive learning controller is implemented on the OWMR, together with several practical discussions for its deployment. Comparative simulations and real-world experiments are conducted to validate the practicality and effectiveness, highlighting its advantages over existing approaches.

This paper deals with sideslip angle estimation problems of autonomous ground vehicles that repeatedly perform the specific tasks in the absence of model knowledge for their lateral dynamics. By designing appropriate estimators, the equivalence between estimator auxiliary input synthesis and output feedback stabilization along the iteration axis is established. Moreover, we propose an innovative data-based output feedback stabilization framework that leverages insufficient sampled data to formulate an output feedback controller without the need of identification. To be specific, with the application of some helpful linear matrix inequality (LMI) techniques, the data-based synthesis of required output feedback controller is transformed into solving the equivalent LMI conditions. By employing the proposed data-based estimation strategy and partial lateral dynamics information of ground vehicles, accurate estimation of sideslip angles over the entire estimation duration can be achieved even in the presence of disturbances. Experiments on an Ackermann steering intelligent vehicle are provided to demonstrate the effectiveness of the proposed estimation strategy.

In this brief, we investigate the approximation theory (AT) of Bayesian recurrent neural network (BRNN) for stochastic time series forecasting (TSF) from a probabilistic standpoint. Due to the cumulative dependencies present in stochastic time series, which are incompatible with the recurrent structure of BRNN and further complicate the analysis of AT, we first perform marginalization and transform the time series into a probabilistically equivalent latent variable model (LVM). Subsequently, we analyze the AT by evaluating the approximation error between the output mean of BRNN and that of the LVM, which are derived through Taylor expansion-based uncertainty propagation and distribution parameterization, respectively. Finally, leveraging the Khinchin's law of large numbers, we study the convergence in probability of the sampling-based training algorithm, i.e., Bayes by Backprop (BBB), and prove that increasing the number of Monte Carlo samples in BBB leads to a convergence probability approaching one. Numerical simulations are conducted to demonstrate the validity of our results.

For learning control systems operating repetitively over a fixed time interval, the iterative methods are effective in accomplishing the perfect tracking task of a specified trajectory, resulting in the methodology of iterative learning control (ILC). In the classic ILC framework, three key steps are often involved: 1) making necessary hypotheses over ILC systems, 2) designing the ILC algorithms, and 3) establishing convergence conditions. However, a basic trackability problem is neglected: whether there exist some inputs that drive the ILC system such that the output is identical to the specified trajectory from beginning to end. This article is targeted at addressing the trackability problem and the related ILC design and analysis issues for continuous-time linear systems subject to vector relative degrees. The frequency-domain criteria are developed to determine the trackability of the given trajectory. In addition, the ILC design and analysis are proposed by utilizing a frequency-domain method, which establishes a close connection between the achievement of the perfect tracking tasks in ILC and the trackability of the given trajectory. Two examples are utilized to confirm the effectiveness of our trackability-based ILC results.

This paper deals with the problem of distributed estimation with consensus by utilizing a two-dimensional (2-D) system approach. The consensus protocol is employed as the information fusion strategy, enabling local communication among neighboring nodes to drive their estimates toward consensus, and the distributed dissipative filter is designed on each node. It is shown that the estimation error dynamics is asymptotically stable and meets the prescribed dissipativity performance. Moreover, by incorporating consensus updates in an additional time dimension, the estimator parameters are determined through a constructed 2-D system approach, thereby reducing the design complexity. Simulations demonstrate the validity of the proposed algorithm.

This article is aimed at developing novel safe iterative learning methods to deal with the high-precision attitude tracking problems of rigid bodies subjected to both nonconvex orientation constraints and iteration-dependent uncertainties. A “reactive exploration” strategy involving a dual-component mechanism is posed to realize safe iterative learning. The first component, named the learning mechanism, adeptly adjusts the learning intervals’ lengths and learns the information about the unmodeled dynamics and external disturbances. The second component, named the safety mechanism, handles the problem of multiple nonconvex orientation constraints. The two mechanisms operate independently, avoiding any potential coupling problems between them. Moreover, thanks to constructing two energy functions based on the auxiliary error information, the orientation constraint satisfaction and perfect tracking can be rigorously verified, regardless of the iteration-dependent learning intervals and the absence of the persistent full-learning assumption. In particular, the nonconvex orientation constraints can be time-iteration-dependent. Two simulation tests are provided to validate the effectiveness of the proposed safe iterative learning method for rigid spacecraft in a Sun-synchronous orbit.Note to Practitioners—Attitude tracking of rigid spacecraft or unmanned aerial/surface vehicles generally requires both safe operation and high precision for some specific periodical tasks, such as the repetitive sensing mission of satellites equipped with star sensors which are prevented from pointing to some undesired directions. With iterative learning control (ILC), it becomes possible to extract the useful information from previous operations and achieve perfect attitude tracking. However, conventional ILC is difficult to apply to the repetitive attitude tracking tasks when nonconvex orientation constraints exist. This work provides new insights into the “repetitive property”, leading to the development of safe ILC based on the “reactive exploration” strategy. This strategy resolves the coupling issue between the learning mechanism and the safety mechanism, which simplifies the controller design for practitioners. Moreover, perfect attitude tracking can be achieved despite the presence of time-iteration-dependent nonconvex constraints and iteration-dependent learning intervals. A novel composite energy function-based analytical method and numerical simulations are introduced to demonstrate the effectiveness of the proposed safe ILC method.

This article focuses on exploring a class of Lyapunov analysis approaches to deal with the convergence problems on second-order signed networks (SOSNs) under arbitrary strongly connected directed topologies. A new class of Laplacian potentials is first proposed for SOSNs by exploiting the properties of Laplacian matrices. Then the relation between convergence behaviors of all agents and those of Laplacian potentials can be disclosed, which makes it possible to solve the convergence issues of SOSNs from the viewpoint of the Lyapunov stability theory even though the weight-balanced condition is not satisfied. Furthermore, the proposed Laplacian potential can be leveraged to deal with the convergence problems of distributed averaging for SOSNs. It is shown that the signed-average consensus objective is reached under the structurally balanced signed digraphs by designing a distributed control protocol according to the proposed Laplacian potential. Additionally, simulation examples are given to demonstrate the validity of our potential-based distributed control results.

In the realm of data-driven adaptive iterative learning control (AILC), the emphasis in designing and analyzing control schemes mainly concentrates on discrete-time systems, while fewer results are developed for the more common continuous-time plants. To overcome this limitation, a practical sampled-data AILC (SDAILC) is developed for continuous-time nonaffine nonlinear plants. A sampled-data iterative dynamic linearization (SDIDL) method is devised to build the dynamic connection between input and output (I/O) data throughout different iterations. On this basis, the SDAILC method, including a sampled-data parameter estimation algorithm and a learning control law, is proposed by utilizing optimization-based design. In SDAILC, the sampling period is treated as a parameter to compensate for its influence on the control performance, and an error feedback is naturally involved, improving the robustness against uncertainties and the closed-loop stability of the plant. Notably, SDAILC is a data-driven approach independent of model information. The validity of SDAILC is proved mathematically and demonstrated by simulations.

This article aims at exploring the dynamic behaviors of signed networks under the mixed static and dynamic control protocols, which reflect the existence of two classes of communication channels. An extended leader-follower framework admitting multiple dynamic leaders is established to identify the roles of all nodes in signed networks, depending on the union of two related signed digraphs. It is shown that bipartite containment tracking is achieved for signed networks despite any topology conditions. To be specific, every leader group realizes modulus consensus and the leaders dominate the dynamic evolutions of signed networks such that all followers converge within the bounded zone spanned by the leaders' converged states and their symmetric states. Furthermore, conditions on the zero convergence of dynamic control inputs are exploited, together with those on the (interval) bipartite consensus of signed networks. Simulation examples are given to demonstrate the convergence behaviors of signed networks with respect to the mixed static and dynamic control protocols.

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.

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called "iterative learning control (ILC)" emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.

In learning systems, high operation precision is often a desirable objective for the algorithm design. Though centralized algorithms are generally adopted, they are subjected to restrictive hypotheses on the learning systems. To overcome this challenging problem, we aim to propose some distributed learning algorithms that focus specifically on achieving the perfect tracking tasks for iterative learning control (ILC) systems. By noting the equivalent relation between the perfect tracking problem of ILC systems and the solving problem of linear algebraic equations (LAEs), we first present an observer-based distributed learning algorithm to solve LAEs, where a multiagent system is constructed with every agent being only required to access some partial information for LAEs. The distributed learning algorithm benefits from integrating both observer-based design and consensus-based design ideas such that for any solvable LAE, all agents can agree on a common solution of it under any initial conditions of agents, regardless of whether it has a unique solution or not. Then, with the distributed learning algorithm for LAEs, we further develop two classes of distributed learning control algorithms for ILC systems, which establish the perfect tracking objective in the presence of the trackable desired output even without using the basic relative degree condition that is generally imposed for conventional ILC.

Signed networks admitting antagonistic interactions among agents may polarize, cluster, or fluctuate in the presence of time-varying communication topologies. Whether and how signed networks can be stabilized regardless of their sign patterns is one of the fundamental problems in the network system control areas. To address this problem, this paper targets at presenting a self-appraisal mechanism in the protocol of each agent, for which a notion of diagonal dominance degree is proposed to represent the dominant role of agent's self-appraisal over external impacts from all other agents. Selection conditions on diagonal dominance degrees are explored such that signed networks in the presence of directed time-varying topologies can be ensured to achieve the uniform asymptotic stability despite any sign patterns. Further, the established stability results can be applied to achieve bipartite consensus tracking of time-varying signed networks and realize state-feedback stabilization of time-varying systems. Simulations are implemented to verify our uniform asymptotic stability results for directed time-varying signed networks.

Mode information is of great significance when investigating the Markov jump systems (MJSs). However, it is common in practical scenarios that the mode information is not completely accessible, which probably induces nonsynchronization problems. Taking this into consideration, in this article, we study nonsynchronous$\mathcal H_{\infty }$model order reduction for 2-D MJSs with model uncertainty. The considered 2-D system and reduced-order model are characterized by the Roesser model. The nonsynchronization phenomenon between the original system and the reduced-order model is dealt with under the framework of the hidden Markov model. By appropriately selecting the Lyapunov function, the asymptotic mean-square stability and the$\mathcal H_{\infty }$performance of the error system are analyzed, and sufficient conditions are proposed. Based on this, an efficient design method for nonsynchronous model order reduction is further proposed with the help of a projection lemma. Finally, the correctness and effectiveness of the designed reduced-order model are verified through some simulations.

This article considers the fully distributed leaderless synchronization in a complex network by only utilizing local neighboring information to design and tune the coupling strength of each node such that the synchronization problem can be solved without involving any global information of the network. For an undirected network, a fully distributed synchronization algorithm is presented to adjust the coupling strength of each node based on a simple adaptive law. When the topology of a network is directed, two different types of adaptive algorithms are developed to achieve synchronization in a fully distributed manner, where the coupling strength of each node is designed to be either the sum or product of two non-negative scalar functions. The fully distributed leaderless synchronization of a directed network is investigated in a leader-follower framework, where the leader subnetwork is analyzed by using the techniques from constrained Rayleigh quotients and the follower subnetwork is addressed by employing the properties of nonsingular M -matrices. Simulations are given to illustrate the theoretical results.

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.

Learning to perform perfect tracking tasks based on measurement data is desirable in the controller design of systems operating repetitively. This motivates this article to seek an optimization-based design and analysis approach for data-driven learning control systems by focusing on iterative learning control (ILC) of repetitive systems with unknown nonlinear time-varying dynamics. It is shown that perfect output tracking can be realized with updating inputs, where no explicit model knowledge but only measured input-output data are leveraged. In particular, adaptive updating strategies are proposed to obtain parameter estimations of nonlinearities. A double-dynamics analysis approach is applied to establish ILC convergence, together with boundedness of input, output, and estimated parameters, which benefits from employing properties of nonnegative matrices. Simulations are implemented to verify the validity of our optimization-based adaptive ILC.

This article is concerned with how the effect of time-varying topologies is overcome and the behaviors of cooperative–antagonistic networks (CANs) are identified. An extended leader–follower (ELF) framework is established for CANs, in which each leader is allowed to evolve dynamically due to the communication with its neighbor leaders. It is shown that a new class of bipartite containment fluctuation behaviors emerges in the presence of the ELF framework, regardless of any structure conditions for CANs. In particular, the leaders are clustered into separate groups, each of which can realize the modulus consensus, whereas the followers may not be enabled to converge but fluctuate within the bounded region spanned by all leaders’ states and their symmetric states. A simulation example is provided to demonstrate the effectiveness of the behavior analysis results developed for CANs.

We present a novel indirect adaptive fuzzy-regulated optimal control scheme for continuous-time nonlinear systems with unknown dynamics, mismatches, and disturbances. Initially, the Hamilton-Jacobi-Bellman (HJB) equation associated with its performance function is derived for the original nonlinear systems. Unlike existing adaptive dynamic programming (ADP) approaches, this scheme uses a special non-quadratic variable performance function as the reinforcement medium in the actor-critic architecture. An adaptive fuzzy-regulated critic structure is correspondingly constructed to configure the weighting matrix of the performance function for the purpose of approximating and balancing the HJB equation. A concurrent self-organizing learning technique is designed to adaptively update the critic weights. Based on this particular critic, an adaptive optimal feedback controller is developed as the actor with a new form of augmented Riccati equation to optimize the fuzzy-regulated variable performance function in real time. The result is an online indirect adaptive optimal control mechanism implemented as an actor-critic structure, which involves continuous-time adaptation of both the optimal cost and the optimal control policy. The convergence and closed-loop stability of the proposed system are proved and guaranteed. Simulation examples and comparisons show the effectiveness and advantages of the proposed method.

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.

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.

This article is concerned with the robust convergence analysis of iterative learning control (ILC) against nonrepetitive uncertainties, where the contradiction between convergence conditions for the output tracking error and the input signal (or error) is addressed. A system equivalence transformation (SET) is proposed for robust ILC such that given any desired reference trajectories, the output tracking problems for general nonsquare multi-input, multi-output (MIMO) systems can be equivalently transformed into those for the specific class of square MIMO systems with the same input and output numbers. As a benefit of SET, a unified condition is only needed to guarantee both the uniform boundedness of all system signals and the robust convergence of the output tracking error, which avoids causing the condition contradiction problem in implementing the double-dynamics analysis approach to ILC. Simulation examples are included to demonstrate the validity of our established robust ILC results.

The precise tracking control of high-speed train is an essential prerequisite to ensure the safety and comfort of the train. In this paper, an adaptive iterative learning control (ILC) scheme for the velocity and displacement tracking of high-speed train is proposed to handle the unknown time-varying parameters and lumped uncertainties. The composite energy function (CEF) method is used to analyze the stability of closed-loop system. Since the train usually runs on the same railway periodically, such as the same tunnels, slopes, bridges, etc., ILC is an inherent method for designing the tracking controller that is able to improve the operation performance of train iteratively. To the best of our knowledge, it is the first time that the multi-agent framework and ILC methodology are considered simultaneously in a single train, which can better reveal the coupled characteristic of adjacent cars and impose the repetitive operation pattern of train. The results of numerical simulations show that the tracking performance of the train toward the reference trajectory is significantly improved along with the increase of the number of operations.

In signed networks, the cooperation and antagonism cause great difficulties for their behavior analysis, especially, when they are subject to time-varying topologies. This is different from unsigned networks involving only cooperations, of which behavior analysis can be feasibly achieved based on the nonnegative matrix theory. With these facts, this article first bridges a relation between signed and unsigned networks and then takes advantage of the relation for the behavior analysis of signed networks under directed switching topologies. In particular, a solution is provided for the connection of signed and unsigned networks via solving a class of linear dynamic systems, which is obtained by separating antagonisms from cooperations. The solution makes it possible to employ the convergence results for unsigned networks to address the convergence issues for signed networks. If the joint spanning tree condition is met, then switching signed networks can achieve the quasi-interval bipartite consensus. Moreover, the established results can be applied to signed networks with both continuous-time and discrete-time dynamics.

Typically, iterative learning control (ILC) is applied based on a core hypothesis that the strict repetitiveness of control environment, task, and model should be satisfied by the controlled system. The problem of interest in this paper is: whether and how can ILC robustly work for controlled systems subject to iteration-dependent environments, tasks and models? To successfully solve this problem, an ILC algorithm using a high-order internal model (HOIM) is proposed and convergence conditions are developed. It is shown that HOIM-based ILC both possesses robustness against iteration-dependent uncertainties from initial states, disturbances, and plant models and tracks iteration-dependent references. Also, simulation tests validate the effectiveness of HOIM-based ILC.

In this article, the robust trajectory tracking problem of iterative learning control (ILC) for uncertain nonlinear systems is considered, and the effects from locally Lipschitz nonlinearities, input saturations, and nonzero system relative degrees are treated. A saturated ILC algorithm is given, with the convergence analysis exploited using a composite energy function-based approach. It is shown that the tracking error can be guaranteed to converge both pointwisely and uniformly. Furthermore, the input updating signal can be ensured to eventually satisfy the input saturation requirements with increasing iterations. Two examples are given to demonstrate the validity of saturated ILC for systems with the relative degree of one, input saturation, and locally Lipschitz nonlinearity.

This paper studies the output tracking control problems for multiple-input, multiple-output (MIMO) locally Lipschitz nonlinear (LLNL) systems subject to iterative operation and uncertain, iteration-varying external disturbances and initial conditions. Under the assumption of a linear, P-type iterative learning control (ILC) update law, a double-dynamics analysis (DDA) approach is proposed to show the convergence of the ILC process in the presence of the locally Lipschitz nonlinearities and iteration-varying uncertainties. The DDA approach results in a contraction mapping-based convergence condition that guarantees both: 1) the boundedness of all system trajectories and 2) the robust convergence of the output tracking error. Further, a basic system relative degree condition is given that provides a necessary and sufficient (NAS) guarantee of the convergence of the ILC process. As a corollary, it is noted that in the absence of iteration-varying uncertainties, the results likewise provide an NAS convergence guarantee for MIMO LLNL systems. The simulations are presented to illustrate the ideas.

This paper addresses a class of network-to-network control problems in the presence of heterogeneous topologies. To achieve the coordination of nodes in a controlled network, a networked controller with a heterogeneous topology is presented in an observer form based on the nearest neighbor rule. It is shown that the network-to-network control problem can be transformed into a coordination problem on a network subject to hybrid static and dynamic interactions. Furthermore, these hybrid interactions among nodes can be represented by appropriately constructing a dynamic graph, of which the connectivity provides a necessary and sufficient guarantee for all nodes to reach agreement on the average quantity of their initial conditions. Simulations are given to illustrate the effectiveness of our results obtained through the dynamic graph approach.

This paper focuses on characterizing edge dynamics of signed networks subject to both cooperative and antagonistic interactions and copes with the state convergence problems of the resulting edge systems. To represent the two competitive classes of interactions that emerge in signed networks, signed digraphs are adopted and the relevant edge Laplacian matrices are introduced, with which an edge-based distributed protocol is presented. The relation between the edge Laplacian matrix and the structural balance (or unbalance) of a signed digraph is disclosed by taking advantage of properties of undirected cycles. Further, it is shown that for a signed network, the state of its edge system converges to a constant vector, regardless of whether its associated signed digraph is structurally balanced or unbalanced. This result does not need to impose the assumption upon the digon sign-symmetry of the signed digraph that is generally required by the node-based distributed protocols. In particular, the state convergence results of edges can be exploited to handle traditional bipartite consensus problems for the nodes of signed networks. Simulation examples are given to illustrate the effectiveness of the edge-based analysis method proposed for signed networks.

Learning from saved measurement and control data to refine the performance of output tracking is the core feature of iterative learning control (ILC). Even though this implementation process of ILC does not need any model knowledge, ILC typically requires the strict repetitiveness of the control systems, especially on the plant models of them. The questions of interest in this paper are: 1) whether and how can robust ILC problems be solved with respect to the nonrepetitive (or iteration-dependent) model uncertainties and 2) can convergence conditions be developed with the effective contraction mapping (CM)-based approach to ILC? The answers to these questions are affirmative, and the CM-based approach is applicable to robust ILC that accommodates certain nonrepetitive uncertainties, especially in the plant models. In particular, an H∞-norm condition is proposed to ensure the robust ILC convergence, which can be solved to determine learning gain matrices. Simulation tests are performed to illustrate the validity of our presented H∞-based analysis results.

This paper deals with the problems of cancer classification and grouped gene selection. The weighted gene co-expression network on cancer microarray data is employed to identify modules corresponding to biological pathways, based on which a strategy of dividing genes into groups is presented. Using the conditional mutual information within each divided group, an integrated criterion is proposed and the data-driven weights are constructed. They are shown with the ability to evaluate both the individual gene significance and the influence to improve correlation of all the other pairwise genes in each group. Furthermore, an adaptive sparse group lasso is proposed, by which an improved blockwise descent algorithm is developed. The results on four cancer data sets demonstrate that the proposed adaptive sparse group lasso can effectively perform classification and grouped gene selection.

This brief addresses the iterative learning control (ILC) problems for discrete-time systems subject to iteration-dependent tracking time intervals. A modified class of P-type ILC algorithms is proposed by properly defining an available modified output, for which robust convergence analysis is performed with an inductive approach. It is shown that if a persistent full-learning property is ensured, then a necessary and sufficient convergence condition of ILC can be derived to reach the perfect output tracking objective though the tracking time interval is iteration-dependent. That is, the tracking of ILC for iteration-dependent time intervals can be guaranteed in the same deterministic (not stochastic) convergence way as that of traditional ILC over a fixed time interval. Furthermore, the developed tracking results can be extended to admit iteration-dependent uncertainties in initial state and external disturbances. Simulation tests are also included to demonstrate the effectiveness of the modified P-type ILC.

Robots are widely used to help post-stoke patients conduct rehabilitation training for the motor function recovery. Because of the existence of repetitiveness in the rehabilitation training, a high-order iterative learning controller (ILC) is proposed for one hand rehabilitation robot in this paper. A series of tracking experiments are conducted to verify the effectiveness and superiority of the proposed controller by comparing to the PID controller, the P-type ILC, and the PD-type ILC. Experimental results show that: (1) the average tracking errors of the P-type ILC and the PD-type ILC are smaller than that of the PID controller, and the steady-state performance of the PD-type ILC is better than that of the P-type ILC; and (2) compared to the PD-type ILC, the average transient performance index of the high-order ILC is decreased by 33.9%. The mean value and variance of the tracking error are decreased by 21.1% and 14.4%, respectively.

A control algorithm for a 3-RPS parallel platform driven by pneumatic cylinders is discussed. All cylinders are controlled by proportional directional valves while the kinematic and dynamic properties of the system are modeled. The method of adaptive robust control is applied to the controller using a back-stepping approach and online parameter estimation. To compensate for the uncertainty and the influence caused by estimations, a fast dynamic compensator is integrated in the controller design. To prevent any influence caused by the load applied to the moving platform changing in a practical working situation, the identification of parameters is taken as the initialization of unknown parameters in the controller, which can improve the adaptability of the algorithm. Using these methods, the response rate of the parameter estimation and control performance were improved significantly. The adverse effects of load and restriction forces were eliminated by the initialization and online estimation. Experiments under different situations illustrated the effectiveness of the adaptive robust controller with parameter initialization, approaching average tracking errors of less than 1%.

This paper addresses adaptive synchronization control problem of networked robot systems characterized by Lagrangian function, where exact dynamic models are unknown and velocity measurements are unavailable. A class of distributed observers, comprised of multiple dynamic variables and static variables, are established based on not imposing a priori restriction on the boundness of the observer states. The observer is compatible for different control schemes with or without structure uncertainties. Using the estimated states given by the observer, adaptive distributed control input is developed, and then closed-loop dynamic models for filtered vectors are established. It is proven that our proposed control scheme permits global exact state estimation and global asymptotic synchronization while compensating for structure uncertainties.

This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols.

This paper deals with the consensus tracking control issues of multiagent systems and aims to solve them as accurately as possible over a finite time interval through an iterative learning approach. Based on the iterative rule, distributed algorithms are proposed for every agent using its nearest neighbor knowledge, for which the robustness problem is addressed against initial state shifts, disturbances, and switching topologies. These uncertainties are dynamically changing not only along the time axis but also the iteration axis. It is shown that the matrix norm conditions can be developed to achieve the convergence of the considered consensus tracking objectives, for which necessary and sufficient conditions are presented in terms of linear matrix inequalities to guarantee their feasibility in the sense of the spectral norm. Furthermore, simulation examples are given to illustrate the effectiveness and robustness of the obtained consensus tracking results.

We investigate motion synchronization of dual-cylinder pneumatic servo systems and develop an adaptive robust synchronization controller. The proposed controller incorporates the cross-coupling technology into the integrated direct/indirect adaptive robust control (DIARC) architecture by feeding back the coupled position errors, which are formed by the trajectory tracking errors of two cylinders and the synchronization error between them. The controller employs an online recursive least squares estimation algorithm to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, and uses a robust control law to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. Therefore, asymptotic convergence to zero of both trajectory tracking and synchronization errors can be guaranteed. Experimental results verify the effectiveness of the proposed controller.

In this study, we developed and tested a high-precision motion trajectory tracking controller of a pneumatic cylinder driven by four costless on/off solenoid valves rather than by a proportional directional control valve. The relationship between the pulse width modulation (PWM) of a signal’s duty cycle and control law was determined experimentally, and a mathematical model of the whole system established. Owing to unknown disturbances and unmodeled dynamics, there are considerable uncertain nonlinearities and parametric uncertainties in this pneumatic system. A modified direct adaptive robust controller (DARC) was constructed to cope with these issues. The controller employs a gradient type adaptation law based on discontinuous projection mapping to guarantee that estimated unknown model parameters stay within a known bounded region, and uses a deterministic robust control strategy to weaken the effects of unmodeled dynamics, disturbances, and parameter estimation errors. By using discontinuous projection mapping, the parameter adaptation law and the robust control law can be synthesized separately. A recursive backstepping technology is applied to account for unmatched model uncertainties. Kalman filters were designed separately to estimate the motion states and the derivative of the intermediate control law in synthesizing the deterministic robust control law. Experimental results illustrate the effectiveness of the proposed controller.

Resiliency is one of the most critical objectives found in complex industrial applications today and designing control systems to provide resiliency is an open problem. This paper proposes resilient control design guidelines for industrial systems that can be modeled as networked multiagent consensus systems subject to disturbances or noise. We give a general analysis of multiagent consensus networks in the presence of different disturbances from the input-to-output stability point of view. Using a nonsingular linear transformation, some necessary and sufficient results are established for disturbed multiagent consensus networks by taking advantage of the input-to-state stability theory, based on which the disturbance rejection performance is analyzed in three cases separated by the spaces of disturbances and state disagreements between agents. It is shown that the linear matrix inequality technique can be adopted to determine the optimal disturbance rejection indexes for all the three cases. In addition, two illustrative numerical examples are given to demonstrate the derived consensus results for different types of directed graphs and subject to different classes of disturbances.

This paper is devoted to the consensus tracking issue on multiagent systems. Instead of enabling the networked agents to reach an agreement asymptotically as the time tends to infinity, the consensus tracking between agents is considered to be derived on a finite time interval as accurately as possible. We thus propose a learning algorithm with a gain operator to be determined. If the gain operator is designed in the form of a polynomial expression, a necessary and sufficient condition is obtained for the networked agents to accomplish the consensus tracking objective, regardless of the relative degree of the system model of agents. Moreover, the H∞ analysis approach is introduced to help establish conditions in terms of linear matrix inequalities (LMIs) such that the resulting processes of the presented learning algorithm can be guaranteed to monotonically converge in an iterative manner. The established LMI conditions can also enable the iterative learning processes to converge with an exponentially fast speed. In addition, we extend the learning algorithm to address the relative formation problem for multiagent systems. Numerical simulations are performed to demonstrate the effectiveness of learning algorithms in achieving both consensus tracking and relative formation objectives for the networked agents.

This paper is devoted to solving formation problems of multi-agent systems with higher-order dynamics. By using the iterative learning control (ILC) approaches, effective distributed algorithms are developed to enable all agents in directed graphs to achieve the desired relative formations perfectly over a finite-time interval. It is shown that the graph theory can be combined to develop conditions for both asymptotic stability and monotonic convergence of multi-agent formation ILC. Simulation results are finally given to verify our theoretical study.

Iterative learning control (ILC) is a kind of effective data-driven method that is developed based on online and/or offline input/output data. The main purpose of this paper is to supply a unified 2-D analysis approach for both continuous-time and discrete-time ILC systems with relative degree. It is shown that the 2-D Roesser system framework can be established for general ILC systems regardless of relative degree, under which convergence conditions can be provided to guarantee both asymptotic stability and monotonic convergence of the ILC processes. In particular, conditions for the monotonic convergence of ILC can be given in terms of linear matrix inequalities, and formulas for the updating law can be derived simultaneously. Simulation results are presented to illustrate the effectiveness of ILC determined through the 2-D design approach in dealing with the higher order relative degree problem of ILC systems, as well as the robustness of such ILC against uncertainties.