Control Of Dynamic System Research Articles

Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks

Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control.

The concept of creating a dynamic system control structure

The concept of creating a dynamic system control structure

Dynamic analysis and chaos control of spur gear transmission system with idler

This study aims to analyze the chaotic dynamics and present a chaos controller for spur gear transmission systems with idler. The chaotic dynamics of the spur gear mechanism has already been investigated. However, the presence of idler gears affects the chaotic behavior and the route to chaos for the nonlinear model of spur gears. This is investigated through the derivation of dimensionless dynamics, defining a Poincare’ section, and extracting the bifurcation diagrams of the system for variations of several parameter models. A nonlinear time-varying dynamic model of a spur gear transmission system with idler is established where backlash, time-varying stiffness, static transmission error, and external excitation are included and a region for the occurrence of chaos is found. The chaotic vibration suppression of the system is done by detecting the unstable periodic orbits embedded in the strange attractors and developing control law by employing sliding mode and adaptive sliding mode control strategy. The controller transmits a chaotic trajectory into the detected unstable periodic orbits. Numerical simulations including phase plane portrait, time histories diagrams, Poincare’ sections, and bifurcation diagrams demonstrate the behavior of the system and confirm the performance of the proposed controller.

Zero forcing number of graphs with a power law degree distribution.

The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbor color forcing rule. The zero forcing number provides topological information about linear algebra on graphs, with applications to the controllability of quantum dynamical systems. Here, I investigate the zero forcing number of undirected graphs with a power law degree distribution p_{k}∼k^{-γ} by means of numerical simulations. For graphs generated by the preferential attachment model, with a diameter scaling logarithmically with the graph size, the zero forcing number approaches the graph size when γ→2. In contrast, for graphs generated by the deactivation model, with a diameter scaling linearly with the graph size, the zero forcing number is smaller than the graph size independently of γ. Therefore the scaling of the graph diameter with the graph size is another factor determining the controllability of dynamical systems. These results have implications for the controllability of quantum dynamics on energy landscapes, often characterized by a complex network of couplings between energy basins.

Photodegradable Polyacrylamide Gels for Dynamic Control of Cell Functions.

Cross-linked polyacrylamide hydrogels are commonly used in biotechnology and cell culture applications due to advantageous properties, such as the precise control of material stiffness and the attachment of cell adhesive ligands. However, the chemical and physical properties of polyacrylamide gels cannot be altered once fabricated. Here, we develop a photodegradable polyacrylamide gel system that allows for a dynamic control of polyacrylamide gel stiffness with exposure to light. Photodegradable polyacrylamide hydrogel networks are produced by copolymerizing acrylamide and a photocleavable ortho-nitrobenzyl (o-NB) bis-acrylate cross-linker. When the hydrogels are exposed to light, the o-NB cross-links cleave and the stiffness of the photodegradable polyacrylamide gels decreases. Further examination of the effect of dynamic stiffness changes on cell behavior reveals that in situ softening of the culture substrate leads to changes in cell behavior that are not observed when cells are cultured on presoftened gels, indicating that both dynamic and static mechanical environments influence cell fate. Notably, we observe significant changes in nuclear localization of YAP and cytoskeletal organization after in situ softening; these changes further depend on the type and concentration of cell adhesive proteins attached to the gel surface. By incorporating the simplicity and well-established protocols of standard polyacrylamide gel fabrication with the dynamic control of photodegradable systems, we can enhance the capability of polyacrylamide gels, thereby enabling cell biologists and engineers to study more complex cellular behaviors that were previously inaccessible using regular polyacrylamide gels.

Fast finite-time dynamic surface tracking control of a single-joint manipulator system with prescribed performance

Based on Lyapunov finite-time stability theory and backstepping control strategy, we put forward a novel fast finite-time dynamic surface tracking control scheme for a single-joint manipulator system with prescribed performance. Compared with most of the traditional prescribed performance finite-time control methods, this work uses a new universal asymmetric barrier function and has a faster convergence speed. In addition, our proposed method eliminates the problem of explosion of complexity based on the dynamic surface. The proposed controller ensures that the closed-loop system is finite-time stable, and the output variable tracks the desired output signal at finite time. Meanwhile, the tracking error converges to the prescribed boundary constraints, and all the signals of the closed-loop system are bounded. In the end, a simulation example is presented to demonstrate the effectiveness of the proposed scheme.

Controllability implies mixing II. Convergence in the dual-Lipschitz metric

This paper continues our study of the interconnection between controllability and mixing properties of random dynamical systems. We begin with an abstract result showing that the approximate controllability to a point and a local stabilisation property imply the uniqueness of a stationary measure and exponential mixing in the dual-Lipschitz metric. This result is then applied to the 2D Navier–Stokes system driven by a random force acting through the boundary. A byproduct of our analysis is the local exponential stabilisation of the boundary-driven Navier–Stokes system by a regular boundary control.

Resilient Observer-Based H ∞ Control of Uncertain Nonlinear Networked Control Systems

This paper considers the resilient H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic control of nonlinear uncertain systems over a network assuming random communication packet dropouts, a subject which is seldom considered in the current literature for such uncertain systems. The uncertainties in the system and the controller are real, time-varying and norm bounded. Bernoulli distribution with white sequence is used to model the random packet losses with assumed conditions on the probability distribution. The resilient controller designed is an observer-based dynamic. The resulted closed-loop system is exponentially mean square stable and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is less than a prescribed level γ for all admissible uncertainties. New sufficient conditions for the existence of such a controller are presented and proved based on the linear matrix inequalities (LMIs) approach. A numerical example is presented to demonstrate and show the effectiveness of the developed theory.

Dynamic Analysis and Robust Control of a Chaotic System with Hidden Attractor

In this paper, a 3D jerk chaotic system with hidden attractor was explored, and the dissipativity, equilibrium, and stability of this system were investigated. The attractor types, Lyapunov exponents, and Poincare section of the system under different parameters were analyzed. Additionally, a circuit was carried out, and a good similarity between the circuit experimental results and the theoretical analysis testifies the feasibility and practicality of the original system. Furthermore, a robust feedback controller was designed based on the finite‐time stability theory, which guarantees the synchronization of 3D jerk master‐slave system in finite time and asymptotically converges to the origin. Finally, we also give verification for the discussion in this paper by numerical simulation.

Detailed Dynamic Modeling, Control, and Analysis of a Grid-Connected Variable Speed SCIG Wind Energy Conversion System

Wind energy as a renewable energy source continues to be a better alternative to fossil-fuel based generation due to its low cost and environmental benefits. While considerable research efforts have been focused on modeling and control of grid connected variable speed squirrel cage induction generator (SCIG) wind energy conversion systems (WECS), comprehensive models for grid integration studies have been almost non-existent. This paper presents the detail modeling, control and analysis of a grid-connected 2.25-MW variable speed SCIG based WECS that can be utilized for grid integration studies. The presented WECS model consists of a pitch regulated wind turbine connected to a SCIG through a gear box. Then, a full-capacity power electronic converter with maximum power point tracking (MPPT), dc bus voltage regulation and power factor correction, connects the SCIG to the grid. The power converter system comprises of back to back two-level voltage source converters linked through a dc-link capacitor. The generator and grid-side converters are controlled using indirect rotor field-oriented control (IR-FOC) and voltage-oriented control (VOC) respectively. The overall system is simulated in MATLAB/Simulink for a varying wind speed. Results show that the presented model is adequate and efficient in the representation of a variable speed SCIG WECS. In addition, the model meets all of the system performance objectives while simultaneously meeting all of the control objectives.

Dynamic Event-triggered Consensus Control of Discrete-time Linear Multi-agent Systems

Abstract We consider the distributed event-triggered consensus control problem of linear multi-agent systems in the discrete-time domain. The agents interact locally and exchange their state information with each other to reach a group decision value. We develop event-triggering protocols to facilitate opportunistic inter-agent communication and control updates for saving energy expenses. Continuous communication is avoided in triggering the conditions for monitoring and controller updates. Our general approach is to employ event-triggering laws with threshold mechanisms that depend on the states of the agents. We start with a static version and then generalize it so that it entails an internal auxiliary variable to regulate the threshold dynamically for each agent. Lyapunov-based design methods dictate when agents should communicate and update their control so that the network achieves consensus. A numerical example is provided to illustrate the efficacy of theoretical analysis.

A cyber-physical system approach for enabling ventilation on-demand in an underground mining site

Creating awareness on the gas concentration along with the timely provision of fresh air is of major importance for preserving the normal operating condition of mining equipment as well as for the well-being of people working underground. However, the deployment and application of a data acquisition and control system in underground sites remain challenging.In order to safeguard the mining personnel, a cyber-physical system for monitoring the concentration of gases enabling adaptive control of the ventilation system is discussed in this study. Long-range communication modules are used to collect field data that are processed to enable awareness over underground conditions. A ventilation on-demand module and an energy consumption evaluation component enable dynamic control of the ventilation system based on the measured gases concentration. A prototype implementation has been tested on a simulated use case with real-world sensor data.

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The paper is focused on an information and telecommunication robot (ITR) that is a cluster of precision mobile mechanical objects (sensors or multisensors) that perform a common mission concerning either monitoring or protection of the territory or the coordinates of the search ob-jects location.ITRs are equipped with wireless telecommunication systems and high-performance small-sized on-board computers that allow the use of cloud technologies and fog computing. A group of unmanned aerial vehicles (UAVs) that perform a common mission (such as searching for victims of natural disasters) and are equipped with interoperable wireless tele-communications systems can be considered as a flying ITR. Mobile sensor networks (robotic sensor networks and systems) are also considered as a possible technical implementation of ITR. From a theoretical point of view, these control objects can be classified as composite dy-namic systems (CDS). The article also analyzes the notion of trajectories of composite dynam-ical systems that are called branched trajectories in the scientific literature. These trajectories consist of several sections of joint movement of CDS subsystems and some sections of their individual movement to the targets along separate branches of the trajectory. Analysis of the physical content of the phenomena that accompany the process of ITR (and especially of mobile ITR) functioning has shown that such clusters are under accidental influence. Therefore, sto-chastic CDS should be considered as a model of ITR functioning. To solve the problem of opti-mizing the process of stochastic CDS control, there arises a task of developing a method of sto-chastic dynamic programming with complete information about the vector of the ITR state. The article describes a solution to the problem of stochastic composite dynamic system control op-timization, with an arbitrary branching scheme provided that complete information about the state vector is available.

Dynamic Modeling and Control of a Single-Phase Grid-Connected photovoltaic System

Designing control strategies to connect a photovoltaic (PV) system to the grid has been significantly challenging. This paper focuses on developing a controller for a single-phase PV system connected to the grid and its implementation to modify the power factor in the distribution power system. To design a grid-connected PV system, its components are modeled, such as PV panels, Maximum Power Point tracking (MPPT) algorithm, the grid interface inverter with the appropriate filter, and the DC link capacitor. SIMULINK / MATLAB is used for simulation in this study. The proposed control strategy is designed to track the maximum power point of The PV panels and control the PV active and reactive output power. In this paper, the presented reactive power control provides the PV system with power factor correction (PFC) capability. The proposed technique for checking controller validity is tested, and the results prove that the proposed controller is good and provides the required performance.

Dynamic characteristics and control of supercritical compressed air energy storage systems

Compressed air energy storage systems are often in off-design and unsteady operation under the influence of external factors. A comprehensive dynamic model of supercritical compressed air energy storage system is established and studied for the first time. In this model, important factors, including volume effect and thermal inertia, are considered for system dynamic simulation which used to be ignored in the past. The transient characteristics and control methodology are mainly focused in this work. The exergy efficiency of transient processes is detected to better understand the dynamic process. Specifically, firstly the response characteristics of system power, mass flow rate, thermal storage temperature/outlet water temperature, and exergy efficiency under the step of key regulation parameters are studied in depth. And then a control framework is well built and studied. The result shows that the influence of the volume effect on the system dynamic characteristics is concentrated in the early time, and mainly affecting the mass flow rate and then the power. The influence of thermal inertia on the system dynamic characteristics takes a long time, mainly affecting thermal storage temperature and the outlet temperature. With the new-built controller, during energy charging, under 10% step-down command of load, the power can quickly reach equilibrium for about 10 s, while thermal storage temperature can be controlled in about 8 s. During the energy discharging period, the combination control mode can achieve shorter load equilibrium time and smaller load overshoot.

Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.

Control of a non-stationary dynamic system with estimating a strategy of human resources management by the integral indicators method

A general idea research is a lack of articles to estimate system indicator of the effectiveness of the strategy of human resources management (HR) at an economic object (enterprise). We are use the method of integral indicators for a comprehensive assessment of the activities of an economic object (enterprise). The economic object is formalized as a non-stationary dynamic system. The system has a dimension of 1.2 million parameters. The parameters of the object under research (business processes) are compared with staff responsibilities. The sanctions mode is set by blocking staff responsibilities in the interval in each time period t. The integral indicator is calculated according to the standard mode (Strategy 1) of the economic object (enterprise) and without blocking the staff responsibilities. Also, the integral indicator is calculated according to the non-standard operating mode of the enterprise (Strategy 2) with the blocking of staff responsibilities. The difference between the integral indicator of Strategy 2 and Strategy 1 is an estimation of the impact of the imposed sanctions. The resource consumption for the restoration of the normal operation of an economic object after the imposed sanctions is give (61.63 million rubles). Example 2 introduces equipment sanctions from America for a new project. An analysis of the indicators of a new project is carried out with the search and use of analog equipment

Supplemental Material for A Test of Synergy in Dynamic System Control Tasks

Supplemental Material for A Test of Synergy in Dynamic System Control Tasks

Graphon Control of Large-Scale Networks of Linear Systems

To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of graphon theory and the theory of infinite dimensional systems. First, graphon dynamical system models are formulated in an appropriate infinite dimensional space in order to represent arbitrary-size networks of linear dynamical systems, and to define the convergence of sequences of network systems with limits in the space. Exact controllability and approximate controllability of graphon dynamical systems are then investigated. Second, the minimum energy state-to-state control problem and the linear quadratic regulator problem for systems on complex networks are considered. The control problem for graphon limit systems is solved in each case and approximations are defined which yield control laws for the original control problems. Furthermore, convergence properties of the approximation schemes are established. A systematic control design methodology is developed within this framework. Finally, numerical examples of networks with randomly sampled weightings are presented to illustrate the effectiveness of the graphon control methodology.

Analyzing control properties of multi-agent linear systems

The networked multi-agent systems that they are interconnected via communication channels have great applicability in multiple areas, such as power grids, bioinformatics, sensor networks, vehicles, robotics and neuroscience, for example. Consequently, they have been widely studied by scientists in different fields in particular in the field of control theory. Recently an interest has grown to analyze the control properties as consensus controllability and observability of multi-agent dynamical systems motivated by the fact that the architecture of communication network in engineering multi-agent systems is usually adjustable. In this paper, we analyze how to improve the control properties in the case of multiagent linear time-invariant dynamical systems.