Nonlinear Distributed Control Research Articles

Temperature field optimization for distributed combined heat of multi-microwave sources based on group consistency under time-varying communication topology

Microwave heating is one of the commonly used methods for heat treatment of various materials. This paper proposes a consistent variable power heating strategy under multi microwave source cluster switching topology mode. Firstly, a distributed structure of microwave source cluster collaborative output with bidirectional ring communication topology was constructed using virtual structure method. On this basis, nonlinear distributed control with consistent output of microwave source clusters in different modes was achieved. Meanwhile, a microwave source clustering scheme is proposed, and the objective function of automatic power allocation for each subgroup and its constraint function are constructed to realize the formation of different clustering modes in different time periods, and the consistent output of self-allocation of power for each subgroup. Secondly, the feasibility and effectiveness of the proposed strategy are verified by the experiments of heating SiC materials in a high-power microwave reactor and analyzing the temperature uniformity and energy conversion efficiency during the heating process. Finally, the simulation results show that the temperature uniformity is improved by 35.7%–63.6% and the energy conversion efficiency is improved by 27.9%–41.1%, which can effectively optimize the temperature field distribution.

Exponential finite‐time couple‐group consensus for agents in cooperative‐competitive networks via pinning method

AbstractThis paper investigates the exponential finite‐time couple‐group consensus problem for multi‐agent systems via pinning control method. Considering the hybrid cooperative and competitive interactions among the agents, a new nonlinear distributed control protocol is proposed. Under the pinning control scheme, the criteria for guaranteeing the system with weakly connected communication topology achieve exponential couple‐group consensus in finite time are obtained, and the pinning control strategies are presented as well. Furthermore, the results show that the settling time for the system to reach consensus is independent of the initial states of the agents. Finally, the correctness of our results is verified by some simulations.

Modeling of a non-linear multi-agent distributed control system

The goal of our research aims to develop a mathematical model for consensus control system based on Lyapunov Theory and nonlinear dynamics functional equations. This paper describes a new solution that deals with the general-consensus problem and the leader-following consensus problem of non-linear multi-agent system (NMAS) in which the parameters of all follower agents can be different, and with an unforced agent as the leader in the multi-agent system (MAS). Different control rules were constructed for each different follower agent based on its own state variables and its communication with adjacent agents. Finally, numerical simulations are provided to demonstrate the feasibility of the developed mathematical model. The results have demonstrated the designed distributed control system satisfy the Lyapunov Theory since all the agents have converged to its steady state after a period of time.

Event-triggered control of interconnected nonlinear systems subjected to cyber-attacks and time-varying coupling

This paper addresses the problem of efficient control of nonlinear distributed networked control systems in the presence of stochastic deception attacks and time-varying coupling strength. A strategy combining model-based and event-triggered control to reduce the number of transmissions over a network thereby, saving network resources is proposed. In this strategy, a plant model at the controller end is used to estimate the state of each subsystem. Further, the control law between the two adjacent triggering instants changes in accordance with dynamics of the plant model. The nonlinearities present in each subsystem are approximated via neural network. The neural network weights and feedback signal are updated only when the event-triggering condition at the sensor end is violated. Also, a lower bound on the inter-event time is computed to avoid the occurrence of Zeno phenomena. Finally, the efficacy of the proposed methodology are verified through simulation examples.

Inverse Optimal Control of a Class of Nonlinear Multi-Agent Systems With Applications to Ship Slew Rate Control

Abstract This paper deals with the inverse optimal leader-following consensus problem of a class of high-order nonlinear multi-agent systems in strict-feedback form under directed communication topology. By employing the backstepping methodology and introducing an integral type Lyapunov function, a nonlinear distributed control law is constructed using the relative information between neighboring agents. The proposed control law solves the inverse optimal leader-following consensus problem under directed communication graph that contains a spanning tree with the root node being the leader agent. A practical example of ship slew rate control system is given to verify the effectiveness of the theoretical results.

Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion

In this paper, the quasi-synchronization problem of heterogeneous fractional-order coupled neural networks (HFCNNs) is studied. In addition, we also take the spatial diffusion effect into consideration, and design an adaptive controller to attenuate the interference of heterogeneous terms. On the one hand, for quasi-synchronization, we propose a nonlinear distributed control law based on local information exchange between neighboring nodes, so that the synchronization error converges to a regulable bounded domain with a certain decay rate. On the other hand, leader-following quasi-synchronization, the reference trajectory is designed in advance and the corresponding distributed controller is developed to make the synchronization errors still tending to the bounded set. Finally, the simulation results show that the theoretical results are correct.

Cooperative distributed nonlinear model predictive control of a formation of differentially-driven mobile robots

Due to the increasing complexity of today’s tasks and the demand for higher performance and robustness, using a single robot is not always expedient in robotics applications. Therefore, having multiple autonomous robotic agents collaborate utilizing explicit communication is gaining more attention. The goal of this article is to develop a distributed algorithm that allows the formation control of multiple differentially-driven mobile robots. The formation control goal is formulated in a novel manner by leveraging results on the control of a single differentially-driven mobile robot, which is sophisticated due to the present non-holonomic constraint. This results in a nonlinear distributed control problem. The fundamental functionality of the developed algorithm is analyzed in simulation scenarios. The applicability to real-life scenarios is demonstrated through experiments with custom hardware. To the best of the authors’ knowledge, this is the first time that nonlinear distributed model predictive control is applied to a formation of differentially-driven mobile robots using a theoretically-founded cost function and, moreover, that the results are verified with hardware experiments.

Distributed Control of Networked Nonlinear Systems via Interconnected Takagi–Sugeno Fuzzy Systems With Nonlinear Consequent

This article deals with the problem of designing nonlinear distributed control laws for continuous-time networked nonlinear heterogeneous systems with bounded sector nonlinear interconnections. The networked system is a combination of interconnected Takagi–Sugeno (TS) fuzzy systems with nonlinear consequent subject to state and control input constraints. The new sufficient conditions, taking into account state constraints and actuators saturation, are derived in terms of linear matrix inequalities. Further, it is shown that the closed-loop system can be made asymptotically stable while reducing the conservatism over decentralized and linear distributed control laws derived following the same method. At the same time, the maximization of the estimate of the domain of attraction (DoA) for the closed-loop system is pursued. Finally, two cases are presented to illustrate the effectiveness of the proposed design approach: 1) an electrical power system composed of two-machine subsystems and 2) a network of multiple inverted pendulums connected by nonlinear springs.

Constrained H∞ Consensus of Second-Order Discrete-Time Multi-Agent Networks With Nonconvex Velocity Constraints

This paper addresses the constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus of second-order discrete-time multi-agent systems with nonconvex velocity constraints and external disturbances over a directed network. A novel nonlinear distributed control law is proposed to enable all agents converge to an agreement cooperatively while their velocities remain in different nonconvex constraint sets. To measure the effect of external disturbances on consensus, a nonlinear H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> output function is introduced via maximum and minimum functions. By a model transformation, the original closed-loop system is changed into an equivalent one. And then, the convergence analysis and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance analysis are completed by utilizing Lyapunov stability theory and robust control theory. In addition, the sufficient constrained H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus conditions are deduced in the form of matrix inequalities under the assumption of strong connectivity of directed network. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

High Quality of Service in Future Electrical Energy Systems: A New Time-Domain Approach

In this paper we study dynamical distortion problems in future electrical energy systems with high renewable penetration. We introduce a new time-domain modeling of electrical energy systems comprising inverter-controlled distributed energy resources (DERs). This modeling is first used to quantify the relations between distortions and real/reactive power dynamics. Next, to ensure acceptable Quality of Service (QoS), a novel nonlinear distributed inverter control is introduced. Sufficient conditions are established for the guaranteed performance of the proposed control. These conditions further support the practical implementation of the derived controller. The effectiveness of this enhanced control is illustrated using simulations for the case of avoiding system instability during sudden grid reconfigurations. Simulations also show that distortions can be suppressed in systems with parallel-connected solar photovoltaics (PVs).

Distributed Finite-time Bipartite Consensus of Multi-agent Systems via Event-triggered Control

This paper investigates a distributed finite-time event-triggered bipartite consensus control for multi-agent systems. Under scenarios of energy limitation, an event-triggered strategy coupled with a nonlinear distributed control protocol is proposed only relying on local information, where the controller only updates at triggered instants. We proved that when the antagonistic network contains a spanning tree, the event-triggered controller can drive all agents to reach consensus value with an identical magnitude but opposite signs. Moreover, both the convergence time depending on the initial state and the positive lower bound of inter-event times are achieved. Simulation results show that the proposed controller has better disturbance rejection properties and can achieve bipartite consensus faster compared to an asymptotic controller.

Finite-time consensus tracking control for multi-agent systems with nonlinear dynamics under Euler digraph and switching topology

In this paper, the finite-time consensus tracking control for multi-agent systems under Euler digraph and switching topology are discussed. The new nonlinear distributed control protocol is proposed under which the systems can reach finite-time consensus tracking. Furthermore, the leader needs to connect with only one follower and which agent is connected will have no effect on finite-time consensus under Euler digraph. It is found that adding edges or increasing feedback gains will be an effective way to reduce the settling time. Two sufficient conditions are proposed to achieve finite-time consensus tracking for multi-agent systems under Euler digraph and switching topology. Finally, numerical simulations are presented to verify the effectiveness of obtained theoretical results.

A Consensus-based Nonlinear and Lipchitz-continuous Distributed Cooperative Secondary Control Method for Islanded AC Microgrids

In this paper, a consensus-based, nonlinear, and Lipchitz-continuous distributed secondary control (DSC) method is proposed to coordinate all the distributed generators (DGs) in an islanded AC microgrids (MGs). This proposed DSC strategy can not only guarantee the restoration control for frequency and voltage, but also realize an accurate active power sharing control for the whole microgrid system. Through introducing a nonlinear, Lipchitz-continuous dynamic from Beta Probability Distribution Function (Beta PDF), the convergence speed of DSC is accelerated, the finite-time convergence of DSC is ensured, and the transient overshoot of DSC is diminished comparing with traditional DSC. Moreover, the common chattering phenomenon in non-Lipchitz DSC scheme is eliminated. The stability and performance of the proposed DSC are also analysed in this paper. An islanded AC microgrid test system with four inverter-based DGs is built in MATLAB/SIMULINK to further validate the effeteness of the proposed DSC strategy.

Optimality condition analysis of macro-hybrid mixed variational inclusions

Optimality conditions of stationary macro-hybrid mixed variational inclusions governing constrained optimal control problems, are analyzed in a setting of reflexive Banach functional spaces. Primal and dual macro-hybrid mixed variational resolvent fixed-point methods are applied to establish solvability results for the state systems. Optimal control macro-hybrid mixed optimality conditions are determined via a perturbation conjugate duality analysis, on the basis of mixed variational evolutionary results recently published by the author. Mechanical applications to dual nonlinear distributed control steady diffusion processes as well as to primal boundary constrained static elastoviscoplastic deformation systems illustrate the theory.

Controller design for nonlinear time delay distributed control systems subjected to input saturation nonlinearity and disturbances

This article proposes a state feedback controller synthesis for nonlinear time-delay distributed control systems subjected to input saturation nonlinearity and disturbances. Nonlinear time-delay distributed control system individual states are without time-delay and the states coming from other subsystems have the communication link time-delay. The coupling states time-delay is presumed to be time-varying within a predefined bound. First, we suggest global state feedback controller design and then, we extend the proposed global design technique to more general local state feedback controller scheme by using an auxiliary region of attraction. Linear matrix inequality (LMI)-based solution is anticipated to synthesis global and local state feedback controller by using global and local sector bounded condition, Lyapunov–Krasovskii function, and Lipschitz condition. Which guarantee global and local asymptotic stability of the complete closed-loop system and $$ L_{2} $$ gain reduction of the mapping from $$ d_{p} (t) $$ to $$ z_{p} (t) $$ . Application results are presented to validate the benefits and effectiveness of the anticipated controller design schemes.

Distributed leader-following consensus of nonlinear multi-agent systems with nonlinear input dynamics

Abstract This paper addresses the problem of distributed leader-following consensus for a multi-agent system with an affine nonlinear term. The communication topology we adopt is an undirected connected graph and the leader sends its information to one or more followers. To make each follower asymptotically synchronize with the leader, a nonlinear distributed control protocol is proposed. Using a Lyapunov function and a matrix theory, we establish sufficient conditions which ensure the consensus of these nonlinear multi-agent systems. Finally, a numerical simulation is provided to verify the effectiveness and usefulness of the developed method.

On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are exponentially stable, can have that property verified by a separable metric. Making use of recent results in the theory of positive linear systems and separable Lyapunov functions, we prove several new results showing when this is possible, and discuss the application of to nonlinear distributed control design via convex optimization.

On the Design of Nonlinear Distributed Control Protocols for Platooning Systems

In this letter, we introduce a novel sufficient condition for the stability of acyclic directed networks subject to time- and state-dependent disturbances. Such a condition, which essentially characterizes the behavior of the network in terms of the solutions of its unperturbed dynamics, is applied to address the problem of designing distributed control protocols for vehicle platooning. Specifically, we show how it can be used to design both linear and nonlinear distributed control protocols for the stable platooning of a network of automated vehicles. We illustrate the effectiveness of our approach via a representative example.

Stabilization of a non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls

This paper considers the stabilization of non-homogeneous rotating body-beam system with the torque and nonlinear distributed controls. To stabilize the system, the authors propose the torque and nonlinear distributed controls applied on the disk and flexible beam respectively. As long as the angular velocity of the disk does not exceed the square root of the first eigenvalue of the related self-adjoint positive definite operator, the authors show that the torque and nonlinear distributed control laws suppress the system vibrations, in the sense that the beam vibrations are forced to decay exponentially to zero and the body rotates with a desired angular velocity.

Leader-Follower Fixed-Time Group Consensus Control of Multiagent Systems under Directed Topology

This paper investigates the fixed-time group consensus problem for a leader-follower network of integrators with directed topology. A nonlinear distributed control protocol, based on local information, is proposed such that the follower agents in each subgroup are able to track their corresponding leaders in a prescribed convergence time regardless of the initial conditions. Simulation examples are presented to demonstrate the availability of our theoretical results.