Boundary Control Strategy Research Articles

An enhanced snow ablation optimizer for UAV swarm path planning and engineering design problems

The Snow Ablation Optimizer (SAO) is an advanced optimization algorithm. However, it suffers from slow convergence and a tendency to become trapped in local optima. To address these limitations, we propose an Enhanced Snow Ablation Optimization algorithm (ESAO). Initially, an adaptive T-distribution control strategy is employed to improve the algorithm's exploratory position adjustments, facilitating the identification of the global optimum. Furthermore, we introduce a Cauchy mutation strategy, endowing individuals with a robust capability to escape local extrema and steer the population towards more favorable directions. A leader-based boundary control strategy is also proposed to enhance the optimizer's search performance, significantly increasing the accuracy, speed, and stability of the algorithm in tackling complex problems. To validate the performance of ESAO, we utilize 29 CEC2017 benchmark functions for comparison against eight popular algorithms across various dimensions. Our algorithm ranked first in all comparisons, demonstrating ESAO's effectiveness. Additionally, to evaluate the practical applicability of the proposed method, we mathematically modeled the UAV swarm and solved the UAV swarm path planning problem using various competitor algorithms. Furthermore, we applied different competitor algorithms to two engineering design problems. The results demonstrate that ESAO performs the best. In general, ESAO outperforms its counterparts in terms of solution quality and stability, showcasing its superior application potential.

Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

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.

A multi-strategy improved rime optimization algorithm for three-dimensional USV path planning and global optimization

The RIME optimization algorithm (RIME) represents an advanced optimization technique. However, it suffers from issues such as slow convergence speed and susceptibility to falling into local optima. In response to these shortcomings, we propose a multi-strategy enhanced version known as the multi-strategy improved RIME optimization algorithm (MIRIME). Firstly, the Tent chaotic map is utilized to initialize the population, laying the groundwork for global optimization. Secondly, we introduce an adaptive update strategy based on leadership and the dynamic centroid, facilitating the swarm's exploitation in a more favorable direction. To address the problem of population scarcity in later iterations, the lens imaging opposition-based learning control strategy is introduced to enhance population diversity and ensure convergence accuracy. The proposed centroid boundary control strategy not only limits the search boundaries of individuals but also effectively enhances the algorithm's search focus and efficiency. Finally, to demonstrate the performance of MIRIME, we employ CEC 2017 and CEC 2022 test suites to compare it with 11 popular algorithms across different dimensions, verifying its effectiveness. Additionally, to assess the method's practical feasibility, we apply MIRIME to solve the three-dimensional path planning problem for unmanned surface vehicles. Experimental results indicate that MIRIME outperforms other competing algorithms in terms of solution quality and stability, highlighting its superior application potential.

Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying Coefficients via Event-Triggered Controller.

The aim of this article is to propose an observer-based event-triggered Robin boundary control strategy for the exponential stabilization of the coupled semilinear reaction-diffusion neural networks with spatially varying coefficients. Toward this aim, we design an observer to estimate the value of system states by using some of these system values as the available measurement. An observer-based event-triggered boundary stabilizer is then presented to exponentially stabilize the considered systems with the Zeno behavior being excluded. Throughout this article, the main used method is backstepping, which yields an explicit expression of the control formulae. Moreover, we see that the proposed event-triggered boundary control scheme can ensure the desired level of control performance with fewer control law updates. A numerical example is finally given to illustrate the effectiveness of our proposed method.

Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

Boundary Control Strategies for Consensus of Fractional-Order Multi-Agent Systems Based on Coupling PDE-ODEs

Multi-strategy improved artificial rabbit optimization algorithm based on fusion centroid and elite guidance mechanisms

The Artificial Rabbit Optimization (ARO) algorithm has been proposed as an effective metaheuristic optimization approach in recent years. However, the ARO algorithm exhibits shortcomings in certain cases, including inefficient search, slow convergence, and vulnerability to local optima. To address these issues, this paper introduces a multi-strategy improved Artificial Rabbit Optimization (IARO) algorithm. Firstly, in the enhanced search strategy, we propose integrating the centroid guidance mechanism and elite guidance mechanism with the greedy strategy to update the position during the exploration phase. Additionally, the Levy flight strategy integrated with self-learning, is employed to update the position during the development phase to improve convergence speed and prevent falling into local optima. Secondly, the algorithm incorporates a per-dimension mirror boundary control strategy to map individuals exceeding the boundary back within the boundary back inside the boundary. This boundary control strategy ensures the algorithm operates within bounds and enhances convergence speed. Finally, within the survival of the fittest strategy, an adaptive factor is introduced to gradually enhance the population's overall adaptability. This factor regulates the balance between exploration and exploitation, allowing the algorithm to fully explore the search space and improve its robustness. To substantiate the effectiveness of the proposed IARO algorithm, a rigorous and systematic verification analysis was undertaken. Comparative experiments for qualitative and quantitative analysis were conducted on three benchmark test sets, namely CEC2017, CEC2020, and CEC2022. The analysis results, including the Wilcoxon rank-sum test, consistently demonstrates that this improved algorithm outperforms ARO and other state-of-the-art optimization algorithms comprehensively. Finally, the feasibility of the IARO algorithm has been verified in seven classical constrained engineering problems.

Observer-based event-triggered boundary control of the one-phase Stefan problem

This paper presents an observer-based event-triggered boundary control strategy for the one-phase Stefan problem, utilising the position and velocity measurements of the moving interface. The design of the observer and controller is founded on the infinite-dimensional backstepping approach. To implement the continuous-time observer-based controller in an event-triggered framework, we propose a dynamic event triggering condition. This condition specifies the instances when the control input must be updated. Between events, the control input is maintained constant in a Zero-Order-Hold manner. We demonstrate that the dwell-time between successive triggering moments is uniformly bounded from below, thereby precluding Zeno behaviour. The proposed event-triggered boundary control strategy ensures the well-posedness of the closed-loop system and the satisfaction of certain model validity conditions. Additionally, the global exponential convergence of the closed-loop system to the setpoint is established using Lyapunov approach. A simulation example is provided to validate the theoretical findings.

Power Boundary Controlled Single-Stage LLC Power Factor Correction Converter and Its Optimal Parameter Design

The time-domain analysis on single-stage LLC power factor correction (PFC) converter is performed in this paper, which reveals that PON mode may occur around the peak point of instantaneous input power and cause instability issue. In order avoid PON mode, the power boundary between PO and PON mode is calculated. For the common design methods of LLC PFC converter with average mode control strategy, the power boundary requires to be higher than the instantaneous input power at its worst point. However, higher power boundary brings higher RMS value of resonant current, and causes higher reactive power loss. Therefore, it is a wasteful designing methodology, as the other points of instantaneous input power don't need such high power boundary. In order to improve the efficiency, a power boundary control strategy is proposed in this paper. By controlling the input current to make the instantaneous input power follow the power boundary, PON mode is eliminated. Consequently, the required power boundary is overall reduced, and the minimal RMS current of resonant tank can be achieved. Furthermore, the optimal parameter design is also presented. A 90∼240VAC input and 250W/48V output experimental prototype has been built to verify the analysis results.

Input-to-state stability analysis of heat equation with boundary finite-time control

This paper addresses the problem of input-to-state stabilization for heat equation with external input via boundary control strategy. Following Polyakov et al., 2017, based on the backstepping approach, a switching boundary control law depending on the system state is designed. By estimating the upper bound of kernel functions, switching levels are determined and commutation law is further constructed. For the chosen switched control, the well-posedness property is verified. It is proved that the resulting system is input-to-state stable, and the solutions of the system will not exceed the highest admissible level dependent on the disturbance amplitude. Meanwhile, a stronger result is also obtained, that is the finite-time stability for the disturbance-free system. The numerical example is provided to support the derived result.

Event-triggered boundary consensus control for multi-agent systems of fractional reaction–diffusion PDEs

The distributed consensus is considered for multi-agent systems (MASs), which characterized by fractional reaction–diffusion partial differential equations (RDPDEs) in this paper. Based on Lyapunov technique and linear matrix inequalities (LMIs) theory, the consensus can be realized via two novel event-triggered boundary control schemes. Firstly, a novel convergence principle subject to finite time is presented for the continuously differentiable function. Secondly, the cooling fin on surface of high-speed aerospace vehicle is remodeled by fractional RDPDEs system, and the well-posedness of presented system is discussed applying the monotone iterative approach. Thirdly, according to the presented static event-triggered boundary control strategy, the consensus criterion in finite time is addressed in the form of LMIs, in addition, the settling time is calculated accurately. Applying the dynamic event-triggered control protocol, the Mittag-Leffler (M-L) consensus condition is achieved. Moreover, the Zeno behaviors are ruled out for proposed event-triggered mechanisms. Finally, the high-speed aerospace vehicle model is presented to verify the effectiveness of the control performance.

Fault-compensation-based boundary control for hyperbolic PDEs: An adaptive iterative learning scheme

In this paper, a fault-compensation-based boundary control strategy is developed for a class of distributed parameter systems expressed by second-order hyperbolic Partial Differential Equations (PDEs), in the case of actuator faults. Considering multiplicative actuator faults and additive actuator faults simultaneously, we put forward a hierarchical fault compensation scheme, i.e., an adaptive iterative learning boundary control technique. Lyapunov-Like analysis method and a variation of Wirtinger’s inequality are used to design a boundary control scheme with an adaptive law, guaranteeing the asymptotical stability of the closed-loop hyperbolic PDE system with multiplicative faults. An iterative learning term is proposed to boost the performance of the system under both multiplicative faults and additive faults, and a composite energy function is used in analysis. With the proposed fault-compensation-based adaptive iterative learning boundary control technique, multiplicative faults are redeemed towards the time horizon and additive faults are compensated towards the iteration horizon. An active acoustic noise reduction process is presented to illustrate the merit and effectiveness of the designed adaptive iterative learning boundary control technique.

Nussbaum function‐based adaptive boundary control for flexible manipulator with unknown control directions and nonlinear time‐varying actuator faults

AbstractThis study proposes a novel boundary control strategy for a vibrating single‐link flexible manipulator system modeled by partial differential equations. The system has uncertain control directions and actuator faults. Existing research studies model fault‐tolerant control systems with fixed fault coefficients; in this study, the actuator faults are nonlinear and time‐varying, and the control directions are unknown. To circumvent the obstacles introduced by the unknown control directions and nonlinear varying actuator failures, an adaptive boundary controller is designed by using Nussbaum functions with fast growth rates and the bound estimation method. In the developed control scheme, all closed‐loop signals are shown to be uniformly bounded. Additionally, the angle tracking error and vibration asymptotically converge to zero. Finally, numerical simulations for five cases demonstrate the effectiveness of the modeled boundary controller.

Anti-Disturbance Boundary Control for a Wave Equation With Input Disturbance

In this article, we investigate the exponential stabilization issue of a wave equation with the external input disturbance, which is described by a nonlinear exogenous system. A novel disturbance observer is constructed to estimate the unknown input disturbance. Then, based on the proposed disturbance observer, a boundary control strategy is developed to cancel the effect of disturbance and stabilize the system. The exponential stability is proven by employing the Lyapunov’s direct method. This method can be extended to a class of flexible systems described by the hyperbolic partial differential equation met in the practical engineer area. The example of a nonuniform flexible string system is given, where the effectiveness of the proposed strategy is evaluated based on simulations.

Observer-based Periodic Event-triggered Boundary Control of the One-phase Stefan Problem

The Stefan problem models the phenomenon of phase transition between a liquid and a solid as the time evolution of the temperature profile of a liquid-solid material and its moving interface. This paper provides a novel observer-based periodic event-triggered boundary control (PETBC) strategy for the one-phase Stefan problem using the position and velocity measurements of the moving interface. We propose a method to convert a specific class of continuous-time dynamic event-triggers that require continuous monitoring to periodic event-triggers that only require periodic evaluation. We achieve this result by finding an upper bound on the underlying continuous-time event-trigger between two successive periodic evaluations. We provide an explicit criterion for choosing a sampling period for periodically evaluating the event-trigger. The control input is updated only at events indicated by the periodic event-trigger and is applied in a zero-order hold fashion between two events. We establish the closed-loop system well-posedness along with certain model validity conditions under the proposed PETBC. Further, we prove that the exponential convergence to the setpoint under continuous-time event-triggered boundary control (CETBC) is preserved under the proposed PETBC. We provide simulation results to validate the theoretical developments.

Construction and management of smart campus: Anti-disturbance control of flexible manipulator based on PDE modeling.

With the rapid development of smart campus, this paper studies the attitude tracking control of flexible manipulator (FM) in colleges and universities under elastic vibration and external disturbances. First, different from the traditional modeling based on ordinary differential equations (ODEs), the partial differential equations (PDEs) dynamic model of a manipulator system is established based on the Hamilton principle (HP). Second, the boundary control condition of the end system of the manipulator is introduced to adjust the vibration of the manipulator. Furthermore, a Proportional-Derivative (PD) boundary control (PDBC) strategy is proposed by the Lyapunov function to suppress the vibration of the manipulator. Finally, a numerical comparison simulation based on MATLAB/SIMULINK further verifies the robustness and anti-disturbance performance of the control method proposed in this paper.

An improved sparrow search algorithm based on quantum computations and multi-strategy enhancement

Aiming at the defects of the sparrow search algorithm (SSA), such as a deficient optimization accuracy and low search efficiency, the sparrow search algorithm based on quantum computations and multi-strategy enhancement (QMESSA) is proposed. Firstly, based on a diversified initial population strategy, an improved circle chaotic mapping theory was proposed, and an initial population with more randomness and diversity was obtained by combining quantum computations with a quantum gate mutation mechanism. Secondly, using an enhanced search strategy, an adaptive T-distribution and a new position update formula were constructed to accelerate the convergence and enhance its variability. Finally, a dynamic evolution formula was designed for the precision elimination mechanism. Based on this, individuals with poor fitness are replaced by new individuals generated using this formula. In addition, a new boundary control strategy was proposed. The convergence of QMESSA was systematically proven, and the proposed algorithm was tested on 24 benchmark functions and CEC 2017 functions. The experiment results as well as the results of a Wilcoxon rank-sum test show that QMESSA achieves a better comprehensive performance than SSA and other advanced optimization algorithms. Finally, the superiority of QMESSA was verified for several classical practical application problems. The source code of QMESSA is available at https://ww2.mathworks.cn/matlabcentral/fileexchange/120013-project1-0.

Asynchronous Boundary Stabilization of Stochastic Markov Jump Reaction-Diffusion Systems

Dissipativity-based asynchronous boundary stabilization problem is addressed for stochastic Markov jump reaction-diffusion systems (SMJRDSs). In practical engineering, nonsynchronous behavior between system modes and controller modes is inevitable, and the incomplete matrix information makes the problem analysis difficult, so this work considers the asynchronous stabilization. Different from the distributed control, we apply a simple boundary control strategy, which greatly reduces the cost of the control design. Note that three issues need to be addressed: 1) how to model the asynchronous behavior? 2) how to design the asynchronous boundary controller? and 3) how to process the incomplete matrix information? We deal with these problems one by one. Based on a general hidden Markov model (HMM), an asynchronous boundary feedback controller is considered. Via the Wirtinger-type inequality, Schur complement technique, and transition matrix properties, sufficient conditions ensuring exponentially mean square stability and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(W, P, R)-\alpha $ </tex-math></inline-formula> dissipativity are established, which covers several special cases. Finally, a numerical example is presented to illustrate the proposed control strategies.

Observer-Based Event-Triggered Boundary Control of a Class of Reaction–Diffusion PDEs

This article presents an observer-based event-triggered boundary control strategy for a class of reaction–diffusion partial differential equations with Robin actuation. The observer only requires boundary measurements. The control approach consists of a backstepping output feedback boundary controller, derived using estimated states, and a dynamic triggering condition, which determines the time instants at which the control input needs to be updated. It is shown that under the proposed observer-based event-triggered boundary control approach, there is a minimal dwell time between two triggering instants independent of initial conditions. Furthermore, the well-posedness and the global exponential convergence of the closed-loop system to the equilibrium point are established. A simulation example is provided to validate the theoretical developments.

Distributed Parameter Modeling and Boundary Control of an Octopus Tentacle-Inspired Soft Robot

Inspired by soft organisms in nature, engineers have been exploring the mechanical design of soft robots manufactured by compliant materials. However, some limitations still exist in the modeling and control of soft robots. This article studies a cable-driven soft robot with shape and bending motion inspired by an octopus tentacle. By the extended Hamilton's principle, the dynamic equation of the soft robot is derived in a distributed parameter system (DPS), which is governed by a partial differential equation. The boundary control strategy for the soft robot is developed via Lyapunov-based design to achieve distributed bending angle tracking. The stability analysis of the closed-loop system is presented using LaSalle's invariance principle to show that the total energies in the system, and hence, the distributed states of the system, remain bounded and tend asymptotically to the desired values. Some simulation results are applied to demonstrate the applicability and effectiveness of the employed model and control. This study will promote the application of DPS theory in soft robots.