In the paper, we investigate the optimization problem(OP) by applying the optimal control method. The optimization problem is reformulated as an optimal control problem(OCP) where the controller(iteration updating) is...
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In the paper, we investigate the optimization problem(OP) by applying the optimal control method. The optimization problem is reformulated as an optimal control problem(OCP) where the controller(iteration updating) is designed to minimize the sum of costs in the future time instant, which thus theoretically generates the “optimal algorithm”(fastest and most stable). By adopting the maximum principle and linearization with Taylor expansion, new algorithms are proposed. It is shown that the proposed algorithms have a superlinear convergence rate and thus converge more rapidly than the gradient descent;meanwhile, they are superior to Newton's method because they are not divergent in general and can be applied in the case of a singular or indefinite Hessian matrix. More importantly, the OCP method contains the gradient descent and the Newton's method as special cases, which discovers the theoretical basis of gradient descent and Newton's method and reveals how far these algorithms are from the optimal algorithm. The merits of the proposed optimization algorithm are illustrated by numerical experiments.
The maximum principle has bridged mathematical optimization to optimal control,ushering in significant developments and refinements in optimal control theory,notably during the 1960s with the advent of linear quadrati...
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The maximum principle has bridged mathematical optimization to optimal control,ushering in significant developments and refinements in optimal control theory,notably during the 1960s with the advent of linear quadratic (LQ)control and linear quadratic estimation (LQE).This progression propelled optimal control theory into further advancements,encompassing stochastic control,robust/H-infinity control,model predictive control (MPC),networked control,and reinforcement learning *** control,established upon a rigorous mathematical foundation,extends static optimization theory to dynamic systems,exhibiting scientific essence,unity,and ***,since its inception,optimal control theory has served as an indispensable core role across all control-related domains,including communication-constrained control in networked systems,consensus control,cooperative control,and reinforcement learning control.
Reliability is a crucial metric in aerospace *** results of reliability assessments for components like aerospace electromagnetic relays directly impact the development and operational reliability of aerospace enginee...
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Reliability is a crucial metric in aerospace *** results of reliability assessments for components like aerospace electromagnetic relays directly impact the development and operational reliability of aerospace engineering *** methods for analyzing the reliability of aerospace electromagnetic relays have limitations,such as neglecting the combined effects of multiple uncertain factors,degradation of key component properties,and the influence of fluctuations in aerospace ***,these methods often assume a single-type uncertainty in the manufacturing process,leading to significant deviations between the analysis results and actual measurement *** address these issues,this study proposes an efficient timedependent reliability analysis method based on the HL-RF algorithm,considering a hybrid of probabilistic and interval uncertainty that accounts for degradation and environmental *** proposed method is applied to the reliability analysis of actual aerospace electromagnetic relay products and compared with traditional methods,demonstrating significant *** proposed method has been applied to the time-dependent reliability analysis of actual aerospace electromagnetic relay products under different environmental *** analysis results exhibit an error margin within 5.12% compared to actual measurement *** to analysis methods solely based on probabilistic uncertainty quantification or interval uncertainty quantification,this method reduces the analysis error by 52% and 67% *** compared to two other state-of-the-art methods that integrate probabilistic and interval uncertainty quantification,the error reduction is 23%.These demonstrate the superiority of the proposed method and validates its *** presented approach has the potential to be extended for reliability analysis in other aerospace electromechanical systems.
To improve the economic efficiency of urban integrated energy systems(UIESs)and mitigate day-ahead dispatch uncertainty,this paper presents an interconnected UIES and transmission system(TS)model based on distributed ...
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To improve the economic efficiency of urban integrated energy systems(UIESs)and mitigate day-ahead dispatch uncertainty,this paper presents an interconnected UIES and transmission system(TS)model based on distributed robust ***,interconnections are established between a TS and multiple UIESs,as well as among different UIESs,each incorporating multiple energy *** Bregman alternating direction method with multipliers(BADMM)is then applied to multi-block problems,ensuring the privacy of each energy system operator(ESO).Second,robust optimization based on wind probability distribution information is implemented for each ESO to address dispatch *** column and constraint generation(C&CG)algorithm is then employed to solve the robust ***,to tackle the convergence and practicability issues overlooked in the existing studies,an external C&CG with an internal BADMM and corresponding acceleration strategy is ***,numerical results demonstrate that the adoption of the proposed model and method for absorbing wind power and managing its uncertainty results in economic benefits.
Due to the effects of windless and sunless weather, new power systems dominated by renewable energy sources experience power supply shortages, which lead to severe electricity shortages. Because of the insufficient pr...
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Due to the effects of windless and sunless weather, new power systems dominated by renewable energy sources experience power supply shortages, which lead to severe electricity shortages. Because of the insufficient proportion of controllable thermal power in these systems, this problem must be addressed from the load side. This study proposes an orderly power utilization(OPU) method with load as the primary dispatching object to address the problem of severe electricity shortages. The principles and architecture of the new urban power grid(NUPG) OPU are proposed to complete the load curtailment task and minimize the effects on social production and daily life. A flexible load baseline division method is proposed that considers the effects of factors such as gross domestic product, pollutant emission, and carbon emission to increase the flexibility and applicability of the proposed method. In addition, an NUPG OPU model based on the load baseline is proposed, in which the electric quantity balance aggregator(EQBA) serves as a regular participant in the OPU and eliminates the need for other user involvement within its capacity range. The electric quantity reserve aggregator(EQRA) functions as a supplementary participant in the OPU and primarily performs the remaining tasks of the EQBA. The electric power balance aggregator primarily offsets the power fluctuations of the OPU. Case studies demonstrate the effectiveness and superiority of the proposed model in ensuring the completion of the load curtailment task, enhancing the flexibility and fairness of OPUs, and improving the applicability of the proposed method.
Swarm Intelligence (SI) is a collective behavior that emerges from interaction between individuals in a group. Typical SI includes fish schooling, ant foraging, bird migration, and so on. A great deal of models have b...
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Swarm Intelligence (SI) is a collective behavior that emerges from interaction between individuals in a group. Typical SI includes fish schooling, ant foraging, bird migration, and so on. A great deal of models have been introduced to characterize the mechanism of SI. This article reviews several typical models and classifies them into four categories: self-driven particle models, with Boids model as the primary example;pheromone communication models, including the ant colony pheromone model which serves as the foundation for ant colony optimization;leadership decision models, utilizing the hierarchical dynamics model of pigeon flock as a prime instance;empirical research models, which employ the topological rule model of starling flock as a classic model. On this basis, each type of model is elaborated upon in terms of its typical model overview, applications, and model evaluation. More specifically, multi-agent swarm control, path optimization and obstacle avoidance, formation and consensus control, trajectory tracking in the dense crowd and social networks analysis are surveyed in the application of each category, respectively. Furthermore, the more precise and effective modeling techniques for leadership decision and empirical research models are described. Limitations and potential directions for further exploration in the study of SI are presented.
An adaptive control approach is presented in this paper for tracking desired trajectories in interactive manipulators. The controller design incorporates prescribed performance functions (PPFs) to improve dynamic perf...
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An adaptive control approach is presented in this paper for tracking desired trajectories in interactive manipulators. The controller design incorporates prescribed performance functions (PPFs) to improve dynamic performance. Notably, the performance of the output error is confined in an envelope characterized by exponential convergence, leading to convergence to zero. This feature ensures a prompt response from admittance control and establishes a reliable safety framework for interactions. Simulation results provide practical insights,demonstrating the viability of the control scheme proposed in this paper.
This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behavior...
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This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.
This paper studies finite-time stability and instability theorems in the probability sense for stochastic nonlinear timevarying systems. Firstly, a new sufficient condition is proposed to guarantee that the considered...
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This paper studies finite-time stability and instability theorems in the probability sense for stochastic nonlinear timevarying systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global ***, we propose new finite-time stability and instability criteria that relax the constraints on LV(the infinitesimal operator of Lyapunov function V) by the uniformly asymptotically stable function. On the one hand, these obtained results make up for the shortcomings of the existing results. On the other hand, the new finite-time stability theorems can be viewed as natural extensions of the existing results and also allow LV to be indefinite(negative or positive) rather than just only allow LV < ***, some simulation examples verify the validity of the theoretical results.
Under the condition of large inertia load,the stability of the servo system is more sensitive to the response speed and more likely to produce overshoot *** order to realize the requirements of high-precision and fast...
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Under the condition of large inertia load,the stability of the servo system is more sensitive to the response speed and more likely to produce overshoot *** order to realize the requirements of high-precision and fast-response control of permanent magnet synchronous motor(PMSM)under large inertia load,an improved feedforward control strategy based on position impulse compensation and PD iterative algorithm is proposed to improve the response speed of the PMSM servo system and reduce the overshoot *** paper analyzes the mathematical models of the speed servo system and position servo system of the PMSM,calculates position overshoot impulse of the PMSM servo system,and improves the traditional feedforward control strategy to reversely compensate when the position is about to ***,in order to further reduce the position overshoot,the PD iterative control algorithm is superimposed without increasing the complexity of the *** input signal is continuously corrected through multiple runs to achieve a smoother response *** effectiveness of the proposed feedforward control strategy is verified by simulation and experiment.
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