Networked control systems (NCS) are spatially distributed systems where communication among plants, sensors, actuators and controllers occurs in a shared communication network. NCS have been studied for the last ten years and important research results have been obtained. These results are in the area of stability and stabilizability. However, while important, these results must be complemented in different areas to be able to design effective NCS. In this paper we approach the control design of NCS using symbolic (finite) models. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an "aggregate" of continuous states. We consider a fairly general multiple-loop network architecture where plants communicate with digital controllers through a shared, non-ideal, communication network characterized by variable sampling and transmission intervals, variable communication delays, quantization errors, packet losses and limited bandwidth. We first derive a procedure to obtain symbolic models that are proven to approximate NCS in the sense of alternating approximate bisimulation. We then use these symbolic models to design symbolic controllers that realize specifications expressed in terms of automata on infinite strings. An example is provided where we address the control design of a pair of nonlinear control systems sharing a common communication network. The closed-loop NCS obtained is validated through the OMNeT++ network simulation framework.
Integrated Symbolic Design of Unstable Nonlinear Networked Control Systems
Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche（信息与系统分析研究所，意大利国家研究委员会）；Department of Information Engineering, Computer Science and Mathematics, Center of Excellence DEWS, University of L’Aquila（拉奎拉大学信息工程、计算机科学与数学系，DEWS卓越中心）
This paper provides a protocol to address the robust output feedback consensus problem for networked heterogeneous nonlinear negative-imaginary (NI) systems with free body dynamics. We extend the definition of nonlinear NI systems to allow for systems with free body motion. A new stability result is developed for the interconnection of a nonlinear NI system and a nonlinear output strictly negative-imaginary (OSNI) system. Also, a class of networked nonlinear OSNI controllers is proposed to achieve output feedback consensus for heterogeneous networked nonlinear NI systems. We show that in this …
A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI) controllers to all the nonlinear NI plants in positive feedback through the network topology. First, we extend the definition of nonlinear NI systems from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and also extend the definition of OSNI systems to nonlinear scenarios. Asymptotic stability is proved for the clos…
We introduce a versatile framework to model and study networked control systems (NCSs). An NCS is described as a feedback interconnection of a plant and a controller communicating through a bidirectional channel modelled by cascaded nonlinear two-port networks. This model is sufficiently rich to capture various properties of a real-world communication channel, such as distortion, interference, and nonlinearity. Uncertainties in the plant, controller and communication channels can be handled simultaneously in the framework. We provide a necessary and sufficient condition for the robust finite-g…
Structural accessibility and structural observability of nonlinear networked systems
CONACyT - Institute of Mathematics, Universidad Nacional Autonoma de Mexico（墨西哥国立自治大学数学研究所）；Institute of Mathematics, Universidad Nacional Autonoma de Mexico（墨西哥国立自治大学数学研究所）；Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004（南特数字科学实验室）
Most approaches for self-triggered control (STC) of nonlinear networked control systems (NCS) require measurements of the full system state to determine transmission times. However, for most control systems only a lower dimensional output is available. To bridge this gap, we present in this paper an output-feedback STC approach for nonlinear NCS. An asymptotically stable observer is used to reconstruct the plant state and transmission times are determined based on the observer state. The approach employs hybrid Lyapunov functions and a dynamic variable to encode past state information and to m…
This paper provides a control protocol for the robust output feedback consensus of networked heterogeneous nonlinear negative-imaginary (NI) systems. Heterogeneous nonlinear output strictly negative-imaginary (OSNI) controllers are applied in positive feedback according to the network topology to achieve output feedback consensus. The main contribution of this paper is extending the previous studies of the robust output feedback consensus problem for networked heterogeneous linear NI systems to nonlinear NI systems. Output feedback consensus is proved by investigating the internal stability of…
This paper studies the tracking control problem of nonlinear networked and quantized control systems (NQCSs) with communication delays. The desired trajectory is generated by a reference system. The communication network is to guarantee the information transmission among the plant, the reference system and the controller. The communication network also brings about some undesired issues like time-varying transmission intervals, time-varying transmission delays, packet dropouts, scheduling and quantization effects, which lead to non-vanishing network-induced errors and affect the tracking perfo…
This paper studies the construction of dynamic symbolic abstractions for nonlinear control systems via dynamic quantization. Since computational complexity is a fundamental problem in the use of discrete abstractions, a dynamic quantizer with a time-varying quantization parameter is first applied to deal with this problem. Due to the dynamic quantizer, a dynamic approximation approach is proposed for the state and input sets. Based on the dynamic approximation, dynamic symbolic abstractions are constructed for nonlinear control systems, and an approximate bisimulation relation is guaranteed fo…
This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the time-delay case, both static and dynamic quantizers are combined to approximate the state and input sets. …
In this paper, we propose a design of a model-free networked controller for a nonlinear plant whose mathematical model is unknown. In a networked control system, the controller and plant are located away from each other and exchange data over a network, which causes network delays that may fluctuate randomly due to network routing. So, in this paper, we assume that the current network delay is not known but the maximum value of fluctuating network delays is known beforehand. Moreover, we also assume that the sensor cannot observe all state variables of the plant. Under these assumption, we app…
Nonlinear-Gain Distributed Zeroth-Order Optimization for Networked Black-Box Control
School of Artificial Intelligence, Hubei University（湖北大学人工智能学院）；School of Economics and Management, Wuhan University（武汉大学经济与管理学院）；School of Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电气工程学院）；Baidu（百度）
This paper studies symbolic abstractions for nonlinear control systems using logarithmic quantization. With a logarithmic quantizer, we approximate the state and input sets, and then construct a novel discrete abstraction for nonlinear control systems. A feedback refinement relation between the constructed discrete abstraction and the original system is established. Using the constructed discrete abstraction, the safety controller synthesis problem is studied. With the discrete abstraction and the abstract specification, the existence of a safety controller is investigated, and the algorithm i…
Symbolic models or abstractions are known to be powerful tools for the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach to the construction of symbolic models for nonlinear control systems. In particular, the symbolic model is constructed based on learning the un-modeled part of the dynamics from training data based on state-space exploration, and the concept of an alternating simulation relation that represents behavioral relationships with respect to the original control system. Moreover, we aim at achiev…
Payame Noor University（帕亚梅努尔大学）；University of Virginia（弗吉尼亚大学）
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior…
A Physics-Informed Dynamic Graph Neural Network (PIDGeuN) is presented to accurately, efficiently and robustly predict the nonlinear transient dynamics of microgrids in the presence of disturbances. The graph-based architecture of PIDGeuN provides a natural representation of the microgrid topology. Using only the state information that is practically measurable, PIDGeuN employs a time delay embedding formulation to fully reproduce the system dynamics, avoiding the dependency of conventional methods on internal dynamic states such as controllers. Based on a judiciously designed message passing …
In bipartite consensus tracking (BCT) tasks for nonlinear multiagent systems, stochastic disturbances and actuator faults are regarded as essential factors that hamper effective controller formulation and tracking precision improvement. To address these difficulties, we design an improved finitetime performance function (FTPF) for a fuzzy fault-tolerant distributed cooperative control scheme to achieve finite-time robust precision BCT tasks for nonlinear multiagent systems. The parameter selection range of the improved FTPF is relaxed, which renders systems to achieve better transient performa…
Exact Robust Instability Analysis for Networked Dynamical Systems with Biological Application
Institute of Integrated Research, Institute of Science Tokyo（综合研究研究所，东京科学大学）；Applied Physics and Physico-Informatics, Keio University（应用物理与物理信息学，庆应义塾大学）；Mechanical and Aerospace Engineering, University of California Los Angels（机械与航空航天工程，加州大学洛杉矶分校）；Department of Electrical Engineering, National Sun Yat-sen University（电气工程系，国立中山大学）
This paper addresses the problem of modeling and scheduling the transmissions generated by multiple event-triggered control (ETC) loops sharing a network. We present a method to build a symbolic traffic model of periodic ETC (PETC), which by construction provides an exact simulation of such traffic. The model is made in such a way as to avoid the combinatorial explosion that is typical of symbolic models in many applications. It is augmented with early triggering actions that can be used by a scheduler to mitigate communication conflicts. The complete networked control system is then modeled a…
Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of a discrete abstraction for a continuous-time system require time-space discretization of the concrete system, which constitutes property satisfaction for the continuous-time system non-trivial. In this work, we aim at relaxing this requirement by introducing a control interface. Firstly, we connect the continuous-time uncertain concrete system with its discrete deterministic state-space abstraction with a control interface. Then, a novel stabil…
Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is limited. Recent research in predicting the network level resilience pattern has advanced our understanding of the coupling relationship between global network topology and local nonlinear component dynamics. However, when there is uncertainty in the model parameters, our understanding of how this translates to uncertainty in resilience is unclear for a larg…
This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics. The presented method is based on the framework of Symbolic Control. In this way, our method returns a provably correct state-feedback controller for the underlying coverage specification, which is the TSP leaving out the requirement for optimality on the route. In addition, we utilize the Lin-Kernighan-Helsgaun TSP solver to heuristically optimize the cost for…
