Iterative learning control for nonlinear heterogeneous multi-agent systems with multiple leaders

ABSTRACTIn this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.

Formation control for nonlinear multi-agent systems by robust output regulation

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.

The consensus problem under a single leader forms the foundation of coordination control in multi-agent systems (MASs). Nonetheless, the issue of containment control, which involves multiple leaders, represents a critical aspect that demands further investigation. This paper addresses the containment control of nonlinear heterogeneous partial difference multi-agent systems (HPDMASs) characterized by state time delays and governed by hyperbolic or parabolic partial difference equations. This study proposes a D-type distributed iterative containment control protocol incorporating initial state learning, which leverages local state information from neighboring agents. Using the contraction mapping principle, this research examines the convergence conditions for the containment error within a finite time interval. The results demonstrate that, under the proposed containment control protocol, the containment error in the HPDMASs can gradually converge to zero as the number of iterations increases. Simulation results are provided to validate the effectiveness of the proposed control protocol.

This paper investigates the distributed containment control problem for multi-agent systems with general linear dynamics under a directed graph. A new observer based on the relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid designing the observer for the leaders in the existing literature. A matrix transformation is introduced to eliminate the coupling terms resulting from the simultaneous design of the observer and the controller gains. Then a sufficient condition on the existence of the observer-based controllers is presented in terms of strict linear matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design method.

In this paper, the bipartite containment control problem of multi-agent systems (MASs) with unknown disturbances is studied. At first, a signed undirected graph is used to describe the Cooperative-Antagonistic interaction among the agents. Different from some conventional results of convergence in the infinite time domain, the control protocol proposed in this paper achieves the fixed-time convergence, and applies the fixed-time control and bipartite consensus to the containment control, making the proposed control protocol more practical. In addition, this paper also considers the existence of external disturbances and a novel fixed-time bipartite containment control protocol is proposed to eliminate them. Then, the stability analysis under the control protocol is completed by using the Lyapunov theory and mathematical theorem. Finally, the effectiveness of the proposed control scheme is verified by some simulation examples.

Collective point-to-point iterative learning control of multi-agent system with switched reference

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

This article investigates the practical time-varying output formation tracking (TVOFT) problem for heterogeneous nonlinear multiagent systems (MASs) having multiple leaders, where agents herein could have heterogeneous dynamics and interact with each other under event-triggered communications. It is required that the outputs of followers not only track the predefined convex combination of multiple leaders but also achieve the desired time-varying formation simultaneously. The existing works on formation tracking problems for MASs with multiple leaders depend on the assumption that each follower is a well-informed or uninformed follower, where the well-informed follower is required to have all the leaders as its neighbor. To remove the limitation, a fully distributed observer-based formation tracking control protocol is developed and employed. First, an adaptive state observer with an edge-based event-triggered mechanism for estimating the states of multiple leaders is proposed based on the neighboring interactions, which eliminates the unexpected Zeno behavior. Second, a novel observer is constructed for each follower by exploiting the output information of the follower, in which the adaptive neural network (NN)-based approximation is exploited to compensate for the unknown nonlinearity. A practical TVOFT control protocol is then generated by the proposed observers, where the parameters are determined by an algorithm including five steps. With the help of Lyapunov stability theory and output regulation method, a practical TVOFT criterion for the considered closed-loop system is derived. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example.

Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements

Containment control of singular heterogeneous multi-agent systems

In this paper, an adaptive iterative learning control (AILC) law is developed for two-link rigid-flexible coupled manipulator system in three-dimensional (3D) space with time-varying disturbances and input constraints. Based on the Hamilton’s principle, a dynamic model of a manipulator system is established. The conditional equation that is coupled by ordinary differential equations and partial differential equations is derived. In order to achieve high-precision tracking of the revolving angles and vibration suppression of the elastic part, the iterative learning control law based on the disturbance observer is considered in the process of the design controller. The composite Lyapunov energy function is proposed to prove that the angle errors and elastic deformation can eventually converge to zero with the increase of the number of iterations. Ultimately, the simulation results to rigid-flexible coupled manipulator system are given to prove the convergence of the control objectives under the adaptive iterative learning control law.

The 2D state space system model is established with state delay and actuator faults, and what is more, the iterative learning control (ILC) law required by the batch process model is designed. Using the knowledge of 2D system theory and an iterative learning control law, the 2D state space model can be changed into an equivalent 2D-Roesser closed-loop system model. According to the optimized cost function and Lyapunov stability theory, sufficient conditions for the solvability of model predictive control (MPC) problems in the form of linear matrix inequalities (LMIs) are given. A new solution is proposed which depends on the bound of the state delay. At last, the effectiveness of the method is proved through simulation experiments.

In this article, the containment control problem of multiagent systems (MASs) with active leaders under a directed communication graph is addressed. A novel pull-based event-triggered protocol combined with aperiodic sampled-data mechanism is first presented, where each agent merely updates controller at its own triggering instants. Under the proposed control protocols, the information is only exchanged and calculated at the aperiodic sampling instants, therefore, it can reduce communication congestion and save computing resources. Furthermore, the Zeno behavior is naturally excluded because the trigger instants are in the set of aperiodic sampled instants. By virtue of the algebraic graph theory and Lyapunov stability analysis, it is shown that the active leaders can reach their desired states predefined arbitrarily and all followers are driven to the convex hull formed by the leaders. Finally, an illustrative example is given to validate the theoretical results and emphasize the advantages of the proposed protocols.

Since they were first introduced by Arimoto, iterative learning control (ILC) methods have received lots of attention because of their effectiveness and briefness. In this paper, an open-closed-loop PID-type ILC scheme with bounded learning matrixes for the control of nonlinear time-varying systems are studied. Under a few reasonable restrictions that are very common, as in other ILC research papers on the convergence problem, sufficient conditions for guaranteeing the convergence of ILC systems are given and then proved with linear operator theory. Both the system and the ILC scheme described have very general forms. It is shown that the convergence condition is weaker than some known results for a similar ILC scheme.