Distributed Feedback Control Research Articles

Research on high performance control strategy of slab thickness based on T-S fuzzy control

To address the difficulty of controlling the dynamic stability of the system after time-varying delay of the plate thickness detection at the final stand of the hot strip finishing mill. Firstly, a T-S fuzzy model based on rolling force and thickness state is established for the final stand of the hot strip finishing mill, and the maximum time delay for plate thickness detection is divided into several time delay intervals to establish a linear constant state space model of the time delay subintervals. Secondly, a distributed state feedback controller satisfying sufficient conditions for stability is solved by using the parallel distribution compensation (PDC) principle combined with Lyapunov stability theory and linear matrix inequality (LMI) methods. Simulation comparisons with current M-AGC and Smith prediction M-AGC system (Smith-AGC) show that our method can effectively reduce overshoot and oscillations in the dynamic response of the exit plate thickness when the operating conditions change and the system time delay parameters are mismatched, so that the system has better stability and dynamic performance.

Symplectic discrete-time Krasovskii passivity-based control for output consensus*

In this paper, we design a sampled-data distributed output feedback controller to achieve output consensus for linear continuous-time port-Hamiltonian systems in presence of unknown disturbances. The key idea is borrowed from Krasovskii passivity-based output consensus control for continuous-time dynamics. To conceptualise this rationale to sampled control systems, we deal with a discrete-time system arising from a symplectic discretization of a continuous-time linear port-Hamiltonian system, such as the implicit midpoint method. As a preliminary step, we introduce the concept of Krasovskii passivity for discrete-time systems and further show that a discretized linear port-Hamiltonian system is Krasovskii passive in the discrete-time sense. Then, based on the discrete-time version of Krasovskii passivity, we develop a sampled-data output feedback controller to achieve output consensus. The proposed sampled-data controller can be understood as a symplectic discretization of the continuous-time output consensus controller. Finally, we illustrate the effectiveness of the main result by achieving current sharing in a DC power network.

Emergent Dynamics of Asynchronous Multiagent Systems Under Signed Networks and Limited Communication Resources

Signed networks, usually used to describe cooperative and competitive coordination between agents, have potential applications in fields such as multi-robot formation and opinion dynamics, et al. Existing work on multi-agent dynamics on signed networks assumes that all agents communicate with their neighbors synchronously, which usually requires sufficient communication resources. However, due to the shortage of communication resources in practical applications, the synchronous communication manner is often not easy to achieve, especially on large scale networks. With that in mind, this paper proposes an asynchronous communication manner to investigate the dynamic behavior of multiagent systems on signed networks without structural restrictions, where only part of the communication links are allowed to transmit information each time instant. By designing a distributed feedback control law, the related properties of sub-stochastic matrices can be used to analyze the dynamic behavior of the agents. It turns out that the whole multi-agent system will evolve a variety of dynamic behaviors, including consensus, bipartite consensus and bipartite containment, which is influenced by the locations and roles of agents in the network. At last, computer simulations are provided to demonstrate the theoretical discovery.

Stability Analysis With LMI Based Distributed H ∞ Controller for Vehicle Platooning Under Random Multiple Packet Drops

This paper proposes a discrete time distributed state feedback controller design strategy for a homogenous vehicle platoon system with undirected network topology which is resilient to both external disturbances and random consecutive network packet drop. The system incorporates a distributed state feedback controller design by satisfying bounded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> norm using Lyapunov-Krasovskii based linear matrix inequality (LMI) approach that ensures internal stability and performance. The effect of packet drops on internal stability in terms of stability margin are studied for a homogenous vehicle platoon system with undirected network topology and external disturbance. The variation of stability margin, representing absolute value of least stable close-loop pole, is also studied for two common undirected network topologies for vehicle platooning, i.e., bidirectional predecessor following (BPF) and bidirectional predecessor leader following (BPLF) topologies by varying platoon members, packet drop rates with number of contiguous packets dropped. Results demonstrate that the control strategy best satisfies the requirement of maintaining a desired inter-vehicular distance with constant spacing policy and leader trajectory using two network topologies: BPF and BPLF. We show how these topologies are robust in terms of ensuring internal stability and performance to maintain cooperative motion of vehicle platoon system with different number of followers, random multiple consecutive packet drops and external disturbance.

A Lyapunov Approach to Robust Cooperative Output Regulation of Multiagent Systems Under Infinite Communication Delays

This article investigates the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems with switching topologies and infinite distributed communication delays. A novel distributed observer is proposed for each agent to estimate the state of the so-called exosystem by taking consideration of both switching topologies and infinite distributed communication delays. A distributed output feedback controller is then developed based on the internal model principle and the estimated state without using the prior knowledge of communication delays. It is shown via the newly developed Lyapunov-like method that the robust cooperative output regulation problem can be solved under some mild assumptions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed controller.

Hybrid feedback and reinforcement learning-based control of machine cycle time for a multi-stage production system

With the increasing need of flexible manufacturing systems, machine flexibility has become one of the major impact factors. An important aspect of machine flexibility is the ability to change an individual machine’s capacity (or cycle time) to improve the overall system efficiency. In this paper, a novel control method is proposed for multi-stage production systems to dynamically change the individual machines’ cycle time to improve overall system efficiency. The proposed control method integrates distributed feedback control scheme and a Reinforcement Learning (RL) control scheme based on an extended actor-critic algorithm. The feedback control will determine whether a machine is turned on or off using real-time system status, while the RL control scheme will decide how to increase or decrease a machine’s cycle time when a machine is on. An improved actor-critic RL algorithm is developed to add an auxiliary model-based path to the standard model-free RL to enhance the learning performance. To demonstrate the effectiveness of the proposed method, numerical case studies have been performed that clearly show improvements in the overall profits and energy savings compared to other methods.

Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviation, and easy implementation is designed to stabilize SCKOs. With the help of the Lyapunov method and stochastic analysis skills, some novel sufficient conditions guaranteeing the stochastic stability for SCKOs are provided by constructing a new and suitable Lyapunov function for SCKOs. Finally, a numerical example is given to illustrate the effectiveness and applicability of the theoretical result.

Distributed robust output feedback control of uncertain fractional-order reaction-diffusion systems

This article focuses on the problem of distributed robust stabilization for a class of uncertain fractional-order reaction–diffusion systems (FRDS) by using two distributed output feedback control strategies: pointwise control based on collocated pointwise measurements and piecewise control based on collocated piecewise measurements. First, the corresponding distributed robust feedback controllers are designed based on the two measurement methods. Then, based on the Lyapunov direct method, Mittag-Leffler (M-L) function, and linear matrix inequality technique (LMI), sufficient conditions for the Mittag-Leffler stability of the closed-loop system are obtained in terms of linear matrix inequalities, respectively. Finally, numerical studies are given to verify the effectiveness of the robust distributed controllers designed in this article.

An Output Feedback Cascade Control Approach to Distributed Consensus of Nonlinear Multiagent Systems With Output Delays

This paper explores the distributed output feedback leader-following full state cascade consensus problem for nonlinear multiagent systems subject to output delays based on a fixed directed topology. Output delays caused by information transmission are considered herein. In this situation, a new distributed consensus strategy is developed by utilizing the output feedback control approach. By introducing delay state equations for all agents, a novel cascade compensator with delays is built for each follower to compensate the full state tracking error among the follower and leader, which is only dependent on the correlative outputs of its neighbor agents. Then, we propose a static gain-based distributed output feedback controller for the follower by means of the compensator. By constructing the Lyapunov-Krasovskii functional, it is demonstrated that the designed controllers can guarantee that all agents will acquire leader-following consensus under the directed topology. Moreover, this result can be easily expanded to solve the consensus problem considering communication delays. Finally, the validity of our given theoretical result is determined by executing a numerical simulation.

Pole assignment and distributed output feedback control via graph-based decomposition

ABSTRACT A new distributed observer-based output feedback control design with an arbitrary control structure is proposed. Assuming that the linear time-invariant (LTI) system does not have any fixed-modes with respect to the control structure, the pole placement at the desired locations becomes theoretically feasible. In this paper, the structural output feedback controller design is transformed into equivalent problems based on a graph-theoretic approach. Two augmented structures are established and formulated as the solution of a set of binary linear programs (BLP). The first one facilitates the incorporation of the maximum number of edges in the principal bipartite graph and the second one results in the least order of dynamic control for the principal block. Next, the distributed design problem is segmented into two stages: (i) design of a set of static control loops based on convex optimisation, to maximise the controllability/observability radius and (ii) design of the control loops corresponding to the principal bipartite graph based on the reduced-order observer-based control. The performance of the proposed approach is investigated in terms of the pole-placement accuracy, control effort, robustness to perturbations in system dynamics, and effect of controller order reduction.

Containment control of discrete‐time multi‐agent systems with application to escort control of multiple vehicles

AbstractThis article investigates the escort control problem for heterogeneous discrete‐time multi‐agent systems with multiple leaders. We develop a distributed output feedback control law such that the followers are secured within the convex hull spanned by the output of the leaders. First, the followers estimate the target convex hull and the system matrices of the leaders via a distributed observer. We then devise a distributed dynamic output feedback control protocol based on this observer to achieve the escort control by using only neighboring relative output information of leaders. The security of the followers is guaranteed by seeing that the output tracking errors converge to zero exponentially. In the numerical simulations, we discuss the potential deployment of the proposed method to a brand‐new escort control of mixed traffic consist of connected automated vehicles and partially automated vehicles. This vehicular escort control formulation can be regarded as a generalization of the conventional vehicular platoon control problem into both longitudinal and lateral dimensions. The numerical results validate the effectiveness and the computational feasibility of the proposed control protocols.

Event-triggered controller design for LTI systems: A distributed interval observer-based approach

This paper investigates the distributed event-triggered control design problem for networked linear time-invariant (LTI) systems with partially measurable states, in the presence of bounded external disturbances. A distributed interval observer-based event-triggered control scheme has been proposed, the main features of this scheme lie in a) designing a novel distributed interval observer to deal with the unknown states and bound disturbances problem; b) proposing a distributed feedback control method using interval estimation information, the partially measurable limitation has been solved; c) introducing a decreased time-varying function with dead-zone modification to avoid the Zeno behavior. Moreover, sufficient conditions for the stability of closed-loop systems are given in the Lyapunov sense by using matrix inequalities and transmission strategy. Finally, the uniformly ultimately bounded stability and Zeno behavior avoidance of the proposed approach have been numerically demonstrated.

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders' measurable output was designed to estimate a convex combination of the leaders' states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders' convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.

Mathematical analysis of tumor-free equilibrium in BCG treatment with effective IL-2 infusion for bladder cancer model

&lt;abstract&gt;&lt;p&gt;We present a theoretical study of bladder cancer treatment with Bacillus Calmette-Guerin (BCG) and interleukin 2 (IL-2) using a system biology approach to translate the treatment process into a mathematical model. We investigated the influence of IL-2 on effector cell proliferation, presented as a distributed feedback control in integral form. The variables in the system of Ordinary Differential Equations (ODE) are the main participants in the immune response after BCG instillations: BCG, immune cells, tumor cells infected with BCG, and non-infected with BCG. IL-2 was involved in the tumor-immune response without adding a new equation. We use the idea of reducing the system of integro-differential equations (IDE) to a system of ODE and examine the local stability analysis of the tumor-free equilibrium state of the model. A significant result of the model analysis is the requirements for the IL-2 dose and duration, depending on the treatment regimen and tumor growth. We proved that the BCG+IL-2 treatment protocol is more effective in this model, using the spectral radius method. Moreover, we introduced a parameter for individual control of IL-2 in each injection using the Cauchy matrix for the IDE system, and we obtained conditions under which this system would be exponentially stable in a tumor-free equilibrium.&lt;/p&gt;&lt;/abstract&gt;

Distributed control of linear partial integro-differential equations based on the input-output linearisation approach

In this paper, the input-output linearisation control approach is extended to distributed parameter systems whose dynamical behaviour is described by a partial integro-differential equation. The design of the infinite dimensional state feedback controller is achieved using the late lumping approach, i.e., using the partial integro-differential equation model without any prior reduction or approximation. Thus, based on the notion of the characteristic index as a generalisation of the relative degree, a distributed state feedback controller is designed by evaluating the successive time derivatives of the controlled output. The designed controller yields in closed loop a first order lumped parameter system where the time constant is a design parameter that fixes the desired dynamical behaviour. The stability of the closed loop system is investigated, based on semi-group theory, by employing the perturbation theorem of the bounded linear operators, and the sufficient condition for exponential stability in L2-norm is derived. This condition yields the upper bound for the design parameter, i.e., the time constant. Both output tracking and stabilisation capabilities of the developed state feedback are demonstrated through numerical simulation by considering three application examples: Volterra, Fredholm and Fredholm-Volterra PIDEs. The effectiveness of the developed controller is shown by simulation.

Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights

&lt;p style='text-indent:20px;'&gt;This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller with a time-varying delay. Under appropriate assumptions on the time-varying delay term and time-dependent weights, we obtain exponential stability estimates by using the multiplicative technique, and prove the equivalence between stabilization and observability.&lt;/p&gt;

Leader-Following Cluster Consensus as a Graphical Differential Game With a Nash Equilibrium Solution

This paper formulates the leader-following cluster consensus problem of a homogeneous linear time-invariant multi-agent system over a directed graph as an N-player graphical differential game. The agents utilize distributed state feedback control laws based on the available information to calculate their best response. In general, the absence of centralized information prevents the best responses of agents from constituting a Nash equilibrium solution. We show that the best responses depending on the unique solution of an algebraic Riccati equation constitute a Nash equilibrium for the proposed graphical differential game with a modified cost function. A numerical example illustrates the Nash equilibrium solution by showing that the agents can not improve their performance by altering their responses while solving the leader-following cluster consensus problem.

Regional Eigenvalue Assignment in Cooperative Linear Output Regulation

The contribution of this paper is a regional eigenvalue assignment method for cooperative output regulation of heterogeneous linear multiagent systems with an internal model-based distributed dynamic state feedback control law. The proposed method offers an agent-wise local approach to synthesize distributed control gains while assigning, for example, the minimal decay rate and the minimal damping ratio of the overall closed-loop system as desired. Numerical examples demonstrate the efficacy of the proposed method by assigning the eigenvalues of a large-scale system to different regions, specifically, disks, shifted half-planes, and conic sectors.

An intelligent hybridized distributed feedback control approach for the JIT open-shop scheduling problem

An intelligent hybridized distributed feedback control approach for the JIT open-shop scheduling problem

Behavioral Harmonization of a Cyclic Vehicular Platoon in a Closed Road Network

This paper presents a method to dynamically harmonize the behaviors of cyclic vehicular platoons in a closed road network. Different from the open-chain counterpart, a cyclic platoon formulates a traffic flow ring constrained by interconnection coupling feature and finite-length geometry, which brings challenges for platoon control design and analysis. First, by exploiting the circulant structure of homogeneous cyclic platoons, the closed-loop dynamics is decomposed into a set of decoupled systems with the same low dimension as a single vehicle. Based on this decomposition, an analytical necessary and sufficient stability condition is derived for the design of distributed feedback controllers. This necessary and sufficient condition is further relaxed into sufficient conditions to remove the dependence on the platoon size. Next, the string stability is proved with the sufficient conditions derived above based on frequency-domain analysis. Then, based on integral sliding mode control, we prove that heterogeneous vehicles can behave like homogeneous ones so that the results on homogeneous cyclic platoons can be extended to heterogeneous cyclic platoons. Finally, the equilibrium velocity and spacing errors are derived to explain the effect of geometry conditions on the steady-state behavior. Numerical simulations using both linear and nonlinear vehicle models are conducted to validate our findings.