Boundary Control Research Articles

Prescribed-time and output feedback stabilization of heat equation with an intermediate-point heat source and boundary control

This paper addresses the problem of prescribed-time stabilization for the heat equation with an interior point heat source under output feedback. The study employs a two-step backstepping approach along with time-varying feedback techniques. A prescribed-time state observer and an observer-based boundary control law are developed. The proposed method extends the applicability of the prescribed time-stabilizing algorithm to heat equations with non-strict feedback terms. Numerical simulations validate its effectiveness.

Hierarchical exact controllability of a parabolic equation with boundary controls

This paper addresses the application of a multi-objective control problem to a parabolic equation. We present the Stackelberg-Nash strategy, which combines the concepts of controllability to trajectories with Nash equilibrium. Our assumption is that the system is influenced through a hierarchy of boundary controls, consisting of one main control (the leader) aiming to drive the solution to a specified target at a final time, and a pair of secondary controls (the followers) designed to minimize two prescribed cost functionals while adapting to the leader's objective. The main novelty of this work lies in the fact that all controls are located on the boundary. One of the primary challenges encountered is the derivation of suitable observability inequality of Carleman for an adjoint system with boundary coupling terms.

Secure consensus for PDEs-based multiagent systems under DoS attacks via boundary control approach

This paper focuses on secure consensus for leader-following multiagent systems (MASs) modeled by partial differential equations (PDEs) under denial of service (DoS) attacks. To mitigate the negative effects of DoS attacks, which can paralyze communication and cause agents to fail to receive valid control inputs, a buffer region is established in the communication channels among agents to temporarily store messages from neighbors. Additionally, since the states of the leader and followers are not always measurable, observers are used to estimate these states. To address these challenges, this paper proposes two boundary controllers to ensure leader-following consensus in both measurable and unmeasurable states. One controller is based on original boundary information, while the other utilizes observation information from both the leader and followers. To the best of our knowledge, this is the first attempt to use buffers to solve a class of PDEs-based MASs under DoS attacks. Furthermore, the boundary control approach has the potential to significantly reduce the number of actuators required, thereby lowering control costs. Finally, we present two numerical examples to validate the feasibility of the proposed methods.

Output feedback finite‐time boundary control for an unstable heat PDE with spatially varying coefficients

AbstractThis article studies the output feedback finite‐time boundary control for unstable heat systems with the spatially varying coefficient. First, a finite‐time observer with switched gains under a state‐dependent switching law is designed in order to estimate the states of the system in a finite‐time only exerting one displacement boundary measurement. Next, an observer‐based linear finite‐time control is planned. Namely, a linear switched control under a state‐dependent switching law is proposed to vanish every solution of an unstable heat partial differential equation with spatially varying coefficients in a finite time. We also present explicit forms for the proposed observer gains and output feedback finite‐time controller. Finally, some numerical simulations are provided to confirm the theoretical results.

Effect of learning culture and management control system on innovation performance: Evidence from startup companies in Indonesia

The startup must be able to innovate in response to the uncertainty of the business environment, which is changing rapidly along with advances in technology. This study aims to analyze the relationship between learning culture, belief, boundary control, dynamic capabilities, and innovation performance. Quantitative methods with AMOS and structural equation modeling were used to test 260 samples. Questionnaires were distributed among startup companies in Banten Province, Indonesia. The research results show that dynamic capabilities and the development of management control systems are influenced by learning culture. The findings inform that a strong learning culture attitude produces company confidence and a management boundary control system that can adapt to uncertain environmental changes. Startup companies should motivate their personnel to improve competence through a learning culture. The role of innovation performance is also indirectly influenced by beliefs and boundary control systems. Recognition of personnel abilities and contributions in collaboration with external sources opens up opportunities to compete in business. This finding is a key factor explaining that startup companies must face a rapidly changing environment by optimizing management’s ability to innovate, implementing management control systems routinely, and building a trust system to inspire and motivate employees.

Consensus of multi‐agent system with reaction‐diffusion terms and time delays via output‐feedback adaptive boundary control

SummaryMulti‐agent systems (MASs) are widely used in many necessary fields such as cybersecurity, precision agriculture, satellites, and smart grids. In many practical processes, a proportion of states cannot be obtained directly. Therefore, it is desired to design an observer. This article explores the utilization of output‐feedback adaptive control techniques to achieve consensus in MASs based on partial differential equations (PDEs) with reaction‐diffusion terms and time delays. First, in dealing with time‐invariant delays, an observer according to the Luenberger method is proposed to assess the state of agents. Convergence conditions of the estimated states are obtained by employing Lyapunov functions and Wirtinger inequality. Using the obtained estimated states, a boundary adaptive control strategy is proposed to make the error system consensus. The merit of this control method lies in the fact that communication between agents only occurs at the spatial boundary position, not throughout the entire spatial domain, and the parameters of the system can be constantly changed. Consensus criteria of MASs with time‐invariant delays are obtained by using the output‐feedback adaptive control, and the results are further generalized to the model with time‐varying delays. Lastly, two experimental scenarios are provided to show the practicality of the proposed theories.

Boundary controllability of a higher-order Boussinesq system

Boundary controllability of a higher-order Boussinesq system

A multi-strategy improved sparrow search algorithm for mobile robots path planning

Abstract Path planning for mobile robots plays a vital role in task execution, given the constraints imposed by environments and energy resources. It poses a significant challenge for mobile robots, requiring them to find a feasible path between the start point and target point that is obstacle-free and as short as possible. To address the challenge of path planning, a multi-strategy improved sparrow search algorithm with crazy operator (CMISSA) is proposed. Firstly, Tent chaos mapping and reverse learning are introduced into the population initialization of sparrow search algorithm (SSA) to enhance the uniformity and effectiveness of the initial population distribution. Secondly, adaptive parameters are applied in SSA to maintain a balance between exploitation and exploration. Thirdly, to prevent SSA from getting trapped in local optima, the crazy operator is used to perturb the population position. Finally, a novel adaptive boundary control strategy is introduced to handle the location of individuals that have crossed the boundary. In addition, the experimental results on 15 classical benchmark functions show that CMISSA has better optimization performance than other 10 comparison algorithms. Furthermore, in the path planning experimental results, the results of comparing CMISSA with 5 comparison algorithms on 5 different environments reveal CMISSA's average path shortening rates were 34.90%, 20.11%, 29.01%, 51.97%, 37.42%, respectively. It is further demonstrated that CMISSA has superior availability for solving mobile robots path planning.

New synchronization results for fractional neural networks with parameter uncertainty and reaction–diffusion terms

New synchronizations of fractional neural networks (FNNs) with uncertain parameters and reaction diffusion terms are investigated in this paper. Firstly, considering a system with mixed boundary conditions, a mixed boundary controller is designed. Sufficient criteria for the global exponential synchronization of the designed FNNs are given through Lyapunov function, inequality techniques and Razumikhin theorem. Furthermore, the exponential synchronization of the system can be explored under Neumann boundary conditions. An example is provided to verify the theoretical part and present the synchronization results for different fractional orders and diffusion coefficients.

The state and error-feedback regulator problems for a boundary control catalytic cracking process

This research work is devoted to boundary control of a catalytic cracking reactor using state and error feedback regulators. The process mathematical model is governed by a set of partial differential equations (PDEs), for which infinite-dimensional representation and spectral properties of the system generator are employed to solve the regulation problems. The primary objective is to track a desired output reference trajectory in the presence of disturbances that are generated by a distributed parameter exosystem. Initially, a state feedback stabilizing regulator is designed to drive the process output towards the reference trajectory. The second objective is to develop a dynamic controller that employs the tracking error as input. The closed-loop plant is shown to be exponentially stable and the tracking error asymptotically approaches zero. The performances of the designed regulators are shown through numerical simulations.

Evaluation of control accuracy for a boundary-coordinating device in a real-time hybrid test

Multi-axial real-time hybrid simulation (ma-RTHS) utilizes multiple loading devices to realize boundary control with multiple degrees of freedom (MDOF), thus being capable of handling complex dynamic scenarios and multi-dimensional problems. In this paper, a new control technique was developed by using a parallel configuration of double shaking tables to implement shear force and bending moment at the boundary between substructures. The dynamic forces are combined by inertia forces of controlled mass driven by electromagnetic shaking tables. The two shaking tables are packaged as a boundary-coordinating device (BCD). An enhanced three-variable control (ETVC) was proposed to consider the coupling effect between two shaking tables and incorporated with the adaptive time series (ATS) compensator to improve the synchronization of the two shaking tables. The proposed control method was verified by three rounds of hybrid tests on a four-story steel shear frame using different ground motions. Nine criteria were utilized to evaluate the performance of RTHS including both tracking performance and global performance indexes. It was proved that RTHS was successfully implemented, and the boundary forces were well-tracked by the proposed control strategy. Good tracking performance was achieved to prove the effectiveness of the strategy.

LMI-based boundary control of flexible manipulator with external disturbance

In this paper, we address the LMI-based boundary control issue of a flexible manipulator subject to external disturbance. First, the dynamics of the system is characterised by several partial differential equations (PDEs). Second, in order to realise the disturbance rejection, we propose two disturbance observers. Based on these observers, two boundary control protocols are designed via the linear matrix inequality (LMI) method for suppressing elastic vibration and regulating the angle of the joint. A significant feature of LMI is that the control gains can be efficiently solved. Finally, some simulation examples illustrate the effectiveness of the proposed theoretical results.

On the Exact Boundary Controllability of Semilinear Wave Equations

On the Exact Boundary Controllability of Semilinear Wave Equations

Boundary control problem for the reaction– advection– diffusion equation with a modulus discontinuity of advection

Boundary control problem for the reaction– advection– diffusion equation with a modulus discontinuity of advection

Existence and asymptotic behavior of a nonlinear axially moving string with variable tension and subject to disturbances

In this paper, we consider the stabilization question for a nonlinear model of an axially moving string. The model is assumed to undergo the variable tension and variable disturbances. The Hamilton principle is used to describe the dynamic of transverse vibrations. We establish the well-posedness by means of the Faedo-Galerkin method. A boundary control with a time-varying delay is designed to stabilize uniformly the string. Then, we derive a decay rate of the solution assuming that the retarded term be dominated by the damping one. Some examples are given to clarify when the rate is exponential or polynomial.

Boundary control problem for the reaction-advection-diffusion equation with a modulus discontinuity of advection

Рассмотрена периодическая задача для сингулярно возмущенного параболического уравнения реакция-диффузия-адвекция типа Бюргерса с модульной адвекцией, имеющая решение вида движущегося фронта. Сформулированы условия существования такого решения, построено его асимптотическое приближение. Поставлена задача управления, в которой требуемый закон движения фронта достигается за счет специальным образом подобранного краевого условия. Построено асимптотическое решение задачи граничного управления. При помощи асимптотического метода дифференциальных неравенств получены оценки точности решения задачи управления. Предложен оригинальный численный алгоритм решения сингулярно возмущенных задач с модульной адвекцией.

Regional traffic congestion coordination control based on critical links

Critical links have the characteristics of carrying large traffic flow and quickly affecting the operational performance of the road network. Existing regional traffic congestion coordination control methods do not consider the impact of critical links. To solve this issue, this paper proposes a regional traffic congestion coordination control method based on critical links. First, the median, gravitational index, and traffic sharing ratio are selected as the identification indexes of critical links in urban networks. Second, the road network vulnerability is assessed, and road link criticality is calculated based on joint entropy theory and multi-scale factor synthesis of multi-metric identification results. Then, the regional signal control range is determined, and a multi-stage signal control optimization model is developed. Finally, the optimal traffic signals for intersections are obtained by minimizing the pressure at the maximum phase of the road link and maximizing the capacity of critical links. To demonstrate the effectiveness of the proposed methods, two benchmarks (i.e., the MAXBAND method and existing traffic signals) are compared. The results show that (1) in terms of boundary control, the average vehicle delay at the boundary intersection of the road network is 34.62 s, an increase of 7.49 s and 5.03 s compared to the benchmark methods, respectively. (2) In terms of internal control, the average delay of the road network based on the proposed method is 87.54 s, which is reduced by 16.38 % and 28.73 % compared with the benchmark methods, and the queue lengths of the critical links are reduced by 21.47 % and 34.15 %, respectively. (3) The control process of the proposed method enables the number of vehicles within the road network to be maintained near the optimal carrying capacity, which gives the road network an efficient operating efficiency.

Boundary controllability for a 1D degenerate parabolic equation with drift, a singular potential, and a Neumann boundary condition

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and a singular potential. Here, we consider a weighted Neumann boundary control at the left endpoint, where the potential arises. We use a spectral decomposition of a suitable operator, defined in a weighted Sobolev space, and the moment method by Fattorini and Russell to obtain an upper estimate of the cost of controllability. We also obtain a lower estimate of the cost of controllability using a representation theorem for analytic functions of exponential type.

New ways of working and psychological well-being: work intensity as a target variable of job resources

PurposeDigitalization and flexibility of workplaces as aspects of new ways of working are associated both positively and negatively with employees’ well-being. However, the mechanisms behind this relationship are not clear yet. We present work intensity as a link between new ways of working and psychological well-being. Furthermore, we address two job resources to alter this association: autonomy and boundary control.Design/methodology/approachOverall, 1,099 employees of a public administration organization participated in the survey and answered a web-based questionnaire. The organization was in the transition to new ways of working including the introduction of a digital filing system and remote work.FindingsThe results of regression analyses provided evidence that flexibility and dissolution of boundaries were positively related to work intensity, which in turn was associated with emotional exhaustion and work engagement. Thus, new ways of working were negatively associated with psychological well-being, mediated by work intensity. Further analyses revealed that the job resources of autonomy and boundary control moderated the relationship between flexibility respectively dissolution of boundaries with work intensity. Thus, these job resources acted as buffering factors and mitigated the association of new ways of working with work intensity.Originality/valueThe results indicated that work intensity could be perceived as a conceptual bridge between new ways of working and psychological well-being providing a promising target variable for the deployment of job resources to preserve employees’ well-being.

Reducing Electric Vehicles Charging Costs Utilizing Optimal Control Method Based on Diverse Charging Patterns

Plug-in electric vehicles (PEVs) present a promising solution for decreasing greenhouse gas emissions and conserving natural oil reserves. However, the growing number of PEVs connected to the electric grid raises concerns regarding the reliable and safe operation of the network. This concern stems from the fact that the charging operation of electric vehicles (EVs) involves a significantly high level of electricity consumption due to the size of EVs' battery charging period. Unscheduled charging activities can lead to increased electricity consumption, increase in PEV charging costs and overload on the distribution grid. To address this issue, this paper proposes a coordinated charging schedule for PEVs, utilizing an optimized EV battery charging model with an optimal control method that deals with finding the best possible control signal for a dynamic system over period of time aiming to optimize a particular performance index, while satisfying various constraints such as boundary condition, state, and control path. The results demonstrate that the proposed optimized charging schedule reduces charging costs by up to 21% compared to an unscheduled charging pattern. Index Terms— Charging cost, coordinated charging, optimal control, plug-in electric vehicle, penetration level, unscheduled charging.