Optimization Of Cost Function Research Articles

Finite-horizon approximate optimal attitude control based on adaptive dynamic programming for ultra-low-orbit satellite

This study investigates the finite-horizon approximate optimal attitude control problem for ultra-low-orbit satellites, addressing the complexities introduced by substantial disturbance, actuator faults, actuator saturation, and time constraint. Initially, a fixed-time concurrent learning fault and disturbance estimation approach is proposed that relieves persistent excitation constraints and isolates different influences individually. Subsequently, the cost function is designed with actuator fault estimation, ensuring that the control strategy consistently adheres to actuator saturation constraints and can compensate for current faults. Furthermore, based on the adaptive dynamic programming, an approximate optimal attitude control approach is proposed, which employs time-varying activation functions to approximate the optimal cost function. A fixed-time neural network weight adaptation strategy is designed to ensure the precision and reliability of the approximation. Finally, the numerical simulation confirms the validity and practical applicability of the proposed approach in satellite attitude control systems.

Gossip-based asynchronous algorithms for distributed composite optimization

The distributed composite optimization problem associated a multi-agent network is investigated in this paper. Different from conventional optimization issues, the cost function of composite optimization consists of a convex function and a regularization function (possibly nonsmooth). The gossip protocol is also introduced to enhance the robustness of the network, and a gossip-based distributed composite mirror descent algorithm is presented to deal with the previous problem, which adopts the asynchronous communication method. Moreover, the algorithm performance is analyzed and the theoretical results on the corresponding error bounds are obtained. Finally, the distributed logistic regression is provided as an example to validate the practicability of the proposed algorithm.

Event-triggered adaptive dynamic programming for cable-driven parallel rehabilitation system with uncertainties

An event triggered adaptive dynamic programming (ET-ADP) controller is proposed for the cable-driven parallel rehabilitation system (CDPRS). Firstly, an error dynamics of CDPRS considering composite uncertainty is established. Secondly, to reduce the computational burden, a single critic network ADP method is proposed to obtain the approximate optimal cost function, and an event-triggered mechanism is introduced to save the communication resources simultaneously. Thirdly, considering the unidirectional force characteristics of the cables, the null-space reallocation method is adopted to optimise the tension of the cables. Then, based on Lyapunov stability theory, the uniformly ultimately boundedness (UUB) of the closed-loop system is proved. Finally, effectiveness of the proposed optimal tracking control strategy is verified based on the Matlab/simulink platform.

Energy efficient mobile sink driven data collection in wireless sensor network with nonuniform data

In wireless sensor network, mobile sink is used to collect data from sensor nodes by periodically traversing the network to prevent hotspot problem. However, when sensor nodes generate data non-uniformly, the efficiency of data collection is constrained by rendezvous points and network topology. It becomes more challenging under network energy consumption constraint. Thus, this paper investigates non-uniform data generation in wireless sensor network and proposes an innovative approach: Optimal Clustering and Network Topology for Mobile Sink-Driven Data Collection, called OCNTMS. It focuses on determining optimal rendezvous points and their associated clusters. Through innovative methods such as weight-balanced clustering, cost function optimization, load-balanced link construction, and node forwarding selection, the OCNTMS can efficiently construct link sets within clusters and accurately plan the mobile sink’s traversal of rendezvous points. Simulation results show that the OCNTMS reduces energy consumption by 18% and increases network lifetime by 40% compared with existing approaches under the constraint of non-uniform data generation. This greatly improves the network energy efficiency and data transmission efficiency.

Automated search of an optimal configuration of FETI-based algorithms with the swarm and evolutionary algorithms

Finite Element Tearing and Interconnecting (FETI) methods are used in the engineering community to solve extremely large engineering simulations on clusters and supercomputers with thousands of computational nodes. This paper focuses on minimizing the execution time of these methods by searching for an optimal configuration with swarm and evolutionary algorithms (SEAs). It incorporates optimization of an expensive cost function (taking tens to hundreds of seconds) of discrete search space with up to hundreds of thousands of combinations constrained by its boundaries and incompatible individuals (invalid combination of FETI solver parameters). In addition, the optimization occurs in real time, i.e., during a simulation. Hence, the number of objective function evaluations must remain low (tens to lower hundreds). The paper compares the performance of 3 basic SEAs with a reduced population size (Differential Evolution, Particle Swarm Optimization, and Self-Organizing Migrating Algorithm), 4 micro SEAs (Micro Differential Evolution Ray, Improved Micro-Particle Swarm Optimization, Micro-Particle Swarm Optimization, and Micro-Genetic Algorithm), and a random search on 4 distinct time-dependent simulations of a heat transfer. The experiments show that basic SEAs with a small population (about 5 individuals) and a penalty system as protection against incompatible configurations represent the most effective solution. One can use them to find the optimal configuration of FETI-based methods in approximately 130 evaluations. It can improve the utilization of expensive hardware resources of modern computational clusters.

Theoretical Analysis on Active Polarization Control of Fiber Laser Based on Root Mean Square Propagation Algorithm

High-power linearly polarized fiber lasers are widely used in coherent beam combination, nonlinear frequency conversion, and gravitational wave detection. With the increase in output power, it is challenging for fiber lasers to maintain a high polarization extinction ratio (PER). Combined with intelligent techniques, active polarization control is a prospective method to obtain the laser output with high PER and high stability. We demonstrate a comprehensive model of an active polarization control system. The root mean square propagation (RMS-Prop) algorithm is used to control the non-polarization-maintaining (non-PM) fiber laser to generate linearly polarized laser. The parameters of the RMS-Prop algorithm are theoretically analyzed, including cost function, perturbation amplitude, and global learning rate. The simulation results show that PER is the optimal cost function. When the perturbation amplitude is 0.06 and the global learning rate is 0.6, the system can achieve the optimal control speed and accuracy. By comparison with the stochastic parallel gradient descent (SPGD) algorithm, the RMS-Prop algorithm has an advantage in obtaining higher PER.

Learning‐based tracking control of AUV: Mixed policy improvement and game‐based disturbance rejection

AbstractA mixed adaptive dynamic programming (ADP) scheme based on zero‐sum game theory is developed to address optimal control problems of autonomous underwater vehicle (AUV) systems subject to disturbances and safe constraints. By combining prior dynamic knowledge and actual sampled data, the proposed approach effectively mitigates the defect caused by the inaccurate dynamic model and significantly improves the training speed of the ADP algorithm. Initially, the dataset is enriched with sufficient reference data collected based on a nominal model without considering modelling bias. Also, the control object interacts with the real environment and continuously gathers adequate sampled data in the dataset. To comprehensively leverage the advantages of model‐based and model‐free methods during training, an adaptive tuning factor is introduced based on the dataset that possesses model‐referenced information and conforms to the distribution of the real‐world environment, which balances the influence of model‐based control law and data‐driven policy gradient on the direction of policy improvement. As a result, the proposed approach accelerates the learning speed compared to data‐driven methods, concurrently also enhancing the tracking performance in comparison to model‐based control methods. Moreover, the optimal control problem under disturbances is formulated as a zero‐sum game, and the actor‐critic‐disturbance framework is introduced to approximate the optimal control input, cost function, and disturbance policy, respectively. Furthermore, the convergence property of the proposed algorithm based on the value iteration method is analysed. Finally, an example of AUV path following based on the improved line‐of‐sight guidance is presented to demonstrate the effectiveness of the proposed method.

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The reconstruction of MR images has always been a challenging inverse problem in medical imaging. Acceleration of MR scanning is of great importance for clinical research and cutting-edge applications. One of the primary efforts to achieve this is using compressed sensing (CS) theory. The CS aims to reconstruct MR images using a small number of sampled data in k-space. The CS-MRI techniques face challenges, including the potential loss of fine structure and increased computational complexity. We introduce a novel framework based on a regularized sparse recovery problem and a sharpening step to improve the CS-MRI approaches regarding fine structure loss under high acceleration factors. This problem is solved via the Half Quadratic Splitting (HQS) approach. The inverse problem for reconstructing MR images is converted into two distinct sub-problems, each of which can be solved separately. One key feature of the proposed approach is the replacement of one sub-problem with a denoiser. This regularization assists the optimization of the Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} (SL0) norm in escaping local minimums and enhances its precision. The proposed method consists of smoothing, feature modification, and Smoothed \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{\\ell}_{0}$$\\end{document} cost function optimization. The proposed approach improves the SL0 algorithm for MRI reconstruction without complicating it. The convergence of the proposed approach is illustrated analytically. The experimental results show an acceptable performance of the proposed method compared to the network-based approaches.

Parallel transmit hybrid pulse design for controlled on-resonance magnetization transfer in R1 mapping at 7T.

This work proposes a "hybrid" RF pulse design method for parallel transmit (pTx) systems to simultaneously control flip angle and root-mean-squared ( ). These pulses are generally only designed for flip angle, however, this can lead to uncontrolled , which then leads to variable magnetization transfer (MT) effects. We demonstrate the hybrid design approach for quantitative imaging where both flip angle and are important. A dual cost function optimization is performed containing the normalized mean squared errors of the flip angle and distributions weighted by a parameter . Simulations were conducted to study the behavior of both properties when simultaneously optimizing them. In vivo experiments on a 7T MRI system with an 8-channel pTx head coil were carried out to study the effect of the hybrid design approach on variable flip angle (= 1/T1) mapping. Simulations showed that both flip angle and can be homogenized simultaneously without detriment to either when compared to an individual optimization. By homogenizing flip angle and , maps were more uniform (coefficient of variation 6.6% vs. 13.0%) compared to those acquired with pulses that only homogenized flip angle. The proposed hybrid design homogenizes on-resonance MT effects while homogenizing the flip angle distribution, with only a small detriment in the latter compared to a pulse that just homogenizes flip angle. This improved mapping by controlling incidental MT effects, yielding more uniform maps.

Optimization control strategy for diesel urea-selective catalytic reduction (SCR) urea injection based on the interior point method (IP) + higher order SCR model

In order to ensure that the NOx and NH3 emissions of diesel engines comply with the Euro VII emission standards, this paper optimizes the urea injection using a SCR model combined with the interior point method. First, the equations of the higher-order SCR model were simplified by the variable substitution method and the line method and solved by the backward difference formula to improve computational accuracy. The Levenberg-Marquardt algorithm was used to calibrate the chemical reaction rate parameters to optimize model performance. Second, an optimization cost function was designed to optimize the upstream NH3 concentration in combination with the interior point method and the higher-order SCR model to meet the requirements of Euro VII emission standards. Third, the model effect was verified by performing WHTC hot-start testing on an engine complying with the National VI emission standard. The results show that the average error between the measured NOx concentration and the calculated is 1.49 ppm, which verifies the high accuracy of the model. Finally, the effects of the interior point method, NSGA-II, and MOPSO algorithms in optimizing the upstream NH3 concentration were compared. The results showed that the interior point method outperformed the other algorithms in terms of optimization time and effect, with an optimization time of 149 s, a NOx conversion rate of 97.36 %, and an average downstream NH3 concentration of 4.65 ppm. This achieved a high NOx conversion rate and low NH3 slip in accordance with the requirements of the Euro VII regulation.

Interference cancellation system of a microwave resonator filter for 4G and 5G applications

This paper aimed at designing a microwave resonator filter for use in 4G and 5G applications. A band resonator filter was designed and implemented using microstrip technology. Poor performance of a microstrip microwave resonator filter is due to spurious harmonics and unwanted frequencies which are always present and cause interferences of signals hindering effective communication. The coupling matrix was first obtained using polynomial functions of transmission and reflection coefficients. A cost function for optimization was developed and particle swarm optimization techniques were used to optimize the coupling matrix. The transversal matrix was developed and converted to the folded matrix for practical filter implementation. A bandpass filter was designed and simulated using high- frequency structure simulator software. Unwanted frequencies are eliminated by employing a novel square open loop resonator structure. The filter was designed to specification and the results show that unwanted frequencies were eliminated corresponding to the frequency of the outer resonator and therefore performs better than comparable filter.

A hybrid RVO-MPPI approach for efficient collision avoidance for multiple autonomous underwater vehicles

Collision-avoidance path planning for Autonomous Underwater Vehicles (AUVs) in complex underwater environments presents a significant challenge, particularly considering the maneuverability limitations of fin-rudder-controlled AUVs. This study proposes a novel navigation approach that combines the strengths of Reciprocal Velocity Obstacle (RVO) principles and Model Predictive Path Integral (MPPI) control to enhance autonomous obstacle avoidance for multiple AUVs. The key innovation lies in leveraging RVO-based obstacle avoidance velocities to enhance both action sampling and cost function optimization in MPPI framework. Specifically, a neural network trained through supervised learning is utilized to convert the RVO-provided avoidance velocities into desired actions for MPPI. Additionally, these velocities are incorporated into the MPPI cost function, thereby enhancing the optimization process and facilitating convergence towards optimal, collision-free navigation solutions. Simulation experiments validated the method's capability to provide effective obstacle avoidance behavior across various complex scenarios. Results indicate that this approach successfully integrates MPPI's predictive capabilities with RVO's velocity avoidance logic, enabling AUVs to navigate efficiently through complex underwater environments while ensuring mission safety and effectiveness. This approach offers a promising new solution for autonomous navigation of AUVs, with potential applications in ocean exploration, underwater search and rescue, and other maritime operations. Future research will explore the performance of this approach in real-world underwater environments and consider the impact of additional dynamic factors.

Ideal Arrival and Service Control Model Policy Based on Fuzzy Queuing System of Uncertainty Measure

In this work, we investigate how to optimize costs for a single-server queuing system operating in a fuzzy, unpredictable environment. Constructing the overall optimal cost and cost function of the queuing system under uncertainty in the fuzzy paradigm is the aim of the inquiry. The fuzzy analysis is carried out to offer a more practical answer to the issues at hand, as opposed to the model's usual crisp responses. The model's crisp and fuzzy systems have different theoretical advances that have been determined, and the estimated costs are easily verifiable and comparable. Lastly, sensitivity analysis has also been carried out utilising numerical analysis to evaluate the theoretical conclusions of the model that is being studied.

ε-Nash Equilibrium of Pursuer–Evader–Defender Missile Navigation Dynamic Games

This research is dedicated to developing a min–max robust control strategy for a dynamic game involving pursuers, evaders, and defenders in a multiple-missile scenario. The approach employs neural dynamic programming, utilizing multiple continuous differential neural networks (DNNs). The competitive controller devised addresses the robust optimization of a joint cost function that relies on the trajectories of the pursuer–evader–defender system, accommodating an uncertain mathematical model while adhering to control restrictions. The dynamic programming min–max formulation facilitates robust control by accounting for bounded modeling uncertainties and external disturbances for each game component. The value function of the Hamilton–Jacobi–Bellman (HJB) equation is approximated by a DNN, enabling the estimation of the closed-loop formulation for the joint dynamic game with state restrictions. The controller’s design is grounded in estimating the state trajectory under the worst possible uncertainties and perturbations, providing a robustness factor through the robust neural controller. The learning law class for the time-varying weights in the DNN is generated by studying the HJB partial differential equation for the missile motion for each player in the dynamic game. The controller incorporates the solution of the obtained learning laws and a time-varying Riccati equation, offering an online solution to the control implementation. A recurrent algorithm, based on the Kiefer–Wolfowitz method, adjusts the initial conditions for the weights to satisfy the final condition of the given cost function for the dynamic game. A numerical example is presented to validate the proposed robust control methodology, confirming the optimization solution based on the DNN approximation for Bellman’s value function.

Effective machine lifespan management using determined state–action cost estimation for multi-dimensional cost function optimization

ABSTRACT This study introduces a comprehensive framework designed to enhance production efficiency by integrating maintenance strategies, energy costs, and production specifications. This integration is achieved through a novel empirical method for estimating state–action costs, suitable for both machines with measurable and non-measurable states-of-health. We address the challenge of under-determination in state–action cost optimization by employing a k-means clustering approach, ensuring robustness and applicability. Utilizing an adapted SARSA algorithm, our framework optimally controls shop-floor machinery to minimize the global cost function. The efficacy of the state–action cost estimation method is validated using NASA’s C-MAPSS dataset. Additionally, the optimization strategy is further corroborated through its successful implementation in an autonomous mining cart model on the shop floor. Our results highlight the framework’s ability to optimize machine lifetime and production processes effectively, providing tailored solutions that adapt to varying operational conditions without depending on predefined machine degradation models and costs.

Optimization of Life Cycle Cost and Environmental Impact Functions of NiZn Batteries by Using Multi-Objective Particle Swarm Optimization (MOPSO)

Optimization of Life Cycle Cost and Environmental Impact Functions of NiZn Batteries by Using Multi-Objective Particle Swarm Optimization (MOPSO)

Optimal control of linear cost networks

We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the Bellman equation giving the optimal cost function and resulting sparse state feedback for these systems can be stated explicitly, with the solution given by a linear program. Our framework admits a range of network routing problems with underlying linear dynamics. These dynamics can be used to model traditional graph-theoretical problems like shortest path as a special case, but can also capture more complex behaviors. We provide an asynchronous and distributed value iteration algorithm for obtaining the optimal cost function and control law.

A geometric solution to microphone array position calibration and its confidence interval analysis

Wireless acoustic sensor networks (WASNs) comprised of spatially distributed acoustic nodes have been increasingly popular in many areas such as speech enhancement, blind source separation, and audio surveillance, where node position information is generally required to implement relevant processing algorithms. In this article, we focus on the node position calibration only using direction-of-arrival (DOA) information with each node consisting of a microphone array. State-of-the-art techniques translate the position calibration into optimization of DOA-based cost functions, and have shown notable success. However, a compromise between position calibration accuracy and computational load still exists. Furthermore, none of the existing studies can offer a quantitative evaluation of calibration performance before the optimization procedure is finished. To address these problems, a geometric solution to array node position calibration is proposed using DOA measurements. For a given array node, DOAs of three sources are first utilized to construct cylinder, plane, and cone equations. Next, the two-dimensional projection of intersections among these equations is calculated using Sylvesterresultantmatrix. Finally, a closed-form solution of node position in three-dimensional space is established. Moreover, explicit mathematical derivation of the confidence interval analysis on the calibration results under given node angle estimation error condition is presented, indicating that the proposed method can provide predictable performance with corresponding probabilities. The Cramér-Rao bound (CRB) is further investigated. Simulation results reveal that as compared with existing methods our approach achieves comparable calibration accuracy with much less computational burden. Real-world experiments also verify its effectiveness.

Complex-Valued FastICA Estimator with a Weighted Unitary Constraint: A Robust and Equivariant Estimator

Independent component analysis (ICA), as a statistical and computational approach, has been successfully applied to digital signal processing. Performance analysis for the ICA approach is perceived as a challenging task to work on. This contribution concerns the complex-valued FastICA algorithm in the range of ICA over the complex number domain. The focus is on the robust and equivariant behavior analysis of the complex-valued FastICA estimator. Although the complex-valued FastICA algorithm as well as its derivatives have been widely used methods for approaching the complex blind signal separation problem, rigorous mathematical treatments of the robust measurement and equivariance for the complex-valued FastICA estimator are still missing. This paper strictly analyzes the robustness against outliers and separation performance depending on the global system. We begin with defining the influence function (IF) of complex-valued FastICA functional and followed by deriving its closed-form expression. Then, we prove that the complex-valued FastICA algorithm based on the optimizing cost function is linear-equivariant, depending only on the source signals.

Enhancing Cryptographic Primitives through Dynamic Cost Function Optimization in Heuristic Search

The efficiency of heuristic search algorithms is a critical factor in the realm of cryptographic primitive construction, particularly in the generation of highly nonlinear bijective permutations, known as substitution boxes (S-boxes). The vast search space of 256! (256 factorial) permutations for 8-bit sequences poses a significant challenge in isolating S-boxes with optimal nonlinearity, a crucial property for enhancing the resilience of symmetric ciphers against cryptanalytic attacks. Existing approaches to this problem suffer from high computational costs and limited success rates, necessitating the development of more efficient and effective methods. This study introduces a novel approach that addresses these limitations by dynamically adjusting the cost function parameters within the hill-climbing heuristic search algorithm. By incorporating principles from dynamic programming, our methodology leverages feedback from previous iterations to adaptively refine the search trajectory, leading to a significant reduction in the number of iterations required to converge on optimal solutions. Through extensive comparative analyses with state-of-the-art techniques, we demonstrate that our approach achieves a remarkable 100% success rate in locating 8-bit bijective S-boxes with maximal nonlinearity, while requiring only 50,000 iterations on average—a substantial improvement over existing methods. The proposed dynamic parameter adaptation mechanism not only enhances the computational efficiency of the search process, but also showcases the potential for interdisciplinary collaboration between the fields of heuristic optimization and cryptography. The practical implications of our findings are significant, as the ability to efficiently generate highly nonlinear S-boxes directly contributes to the development of more secure and robust symmetric encryption systems. Furthermore, the dynamic parameter adaptation concept introduced in this study opens up new avenues for future research in the broader context of heuristic optimization and its applications across various domains.