Iterative Algorithm Research Articles

Auxiliary model maximum likelihood least squares-based iterative algorithm for multivariable autoregressive output-error autoregressive moving average systems

Identification of multivariable systems is of great significance to control systems. This paper focuses on the parameter identification problems for multivariable autoregressive output-error autoregressive moving average (M-AROEARMA) systems. On the basis of the decomposition strategy, the M-AROEARMA model is de- composed into multiple subsystem models. By means of the auxiliary model idea, the auxiliary model least squares-based iterative algorithm is derived. For the purpose of achieving highly accurate parameter identification performance under colored noises interference, an auxiliary model maximum likelihood least squares-based iterative algorithm is proposed by utilizing the maximum likelihood principle. The numerical simulation example demonstrates the effectiveness of the proposed algorithms.

An integrated optimization strategy for mission planning and control resource allocation for long-endurance unmanned aerial vehicle

PurposeWith burgeoning interest in the low-altitude economy, applications of long-endurance unmanned aerial vehicles (LE-UAVs) have increased in remote logistics distribution. Given LE-UAVs’ advantages of wide coverage, strong versatility and low cost, in addition to logistics distribution, they are widely used in military reconnaissance, communication relay, disaster monitoring and other activities. With limited autonomous intelligence, LE-UAVs require regular periodic and non-periodic control from ground control resources (GCRs) during flights and mission execution. However, the lack of GCRs significantly restricts the applications of LE-UAVs in parallel.Design/methodology/approachWe consider the constraints of GCRs, investigating an integrated optimization problem of multi-LE-UAV mission planning and GCR allocation (Multi-U&G IOP). The problem integrates GCR allocation into traditional multi-UAV cooperative mission planning. The coupling decision of mission planning and GCR allocation enlarges the decision space and adds complexities to the problem’s structure. Through characterizing the problem, this study establishes a mixed integer linear programming (MILP) model for the integrated optimization problem. To solve the problem, we develop a three-stage iterative optimization algorithm combining a hybrid genetic algorithm with local search-variable neighborhood decent, heuristic conflict elimination and post-optimization of GCR allocation.FindingsNumerical experimental results show that our developed algorithm can solve the problem efficiently and exceeds the solution performance of the solver CPLEX. For small-scale instances, our algorithm can obtain optimal solutions in less time than CPLEX. For large-scale instances, our algorithm produces better results in one hour than CPLEX does. Implementing our approach allows efficient coordination of multiple UAVs, enabling faster mission completion with a minimal number of GCRs.Originality/valueDrawing on the interplay between LE-UAVs and GCRs and considering the practical applications of LE-UAVs, we propose the Multi-U&G IOP problem. We formulate this problem as a MILP model aiming to minimize the maximum task completion time (makespan). Furthermore, we present a relaxation model for this problem. To efficiently address the MILP model, we develop a three-stage iterative optimization algorithm. Subsequently, we verify the efficacy of our algorithm through extensive experimentation across various scenarios.

Polyak’s Method Based on the Stochastic Lyapunov Function for Justifying the Consistency of Estimates Produced by a Stochastic Approximation Search Algorithm under an Unknown-But-Bounded Noise

In 1976–1977, Polyak published in the journal Avtomatica i Telemekhanika (Automation and Remote Control) two remarkable papers on how to study the properties of estimates of iterative pseudogradient algorithms. The first paper published in 1976 considered the general case based on the stochastic Lyapunov function, and the second one considered the linear case. The assumptions formulated in these papers and the estimates obtained in them can still be considered the state-of-the art. In the current paper, Polyak’s approach is applied to the study of the properties of estimates of a (randomized) stochastic approximation search algorithm for the case of unknown-but-bounded noise in observations. The obtained asymptotic estimates were already known earlier, and exact estimates for a finite number of observations are published for the first time.

Higher-Order Iterative Learning Control Algorithms for Linear Systems

Iterative learning control (ILC) algorithms appeared in connection with the problems of increasing the accuracy of performing repetitive operations by robots. They use information from previous repetitions to adjust the control signal on the current repetition. Most often, information from the previous repetition only is used. ILC algorithms that use information from several previous iterations are called higher-order algorithms. Recently, interest in these algorithms has increased in the literature in connection with robotic additive manufacturing problems. However, in addition to the fact that these algorithms have been little studied, there are conflicting estimates regarding their properties. This paper proposes new higher-order ILC algorithms for linear discrete and differential systems. The idea of these algorithms is based on an analogy with multi-step methods in optimization theory, in particular, with the heavy ball method. An example is given that confirms the possibility to accelerate convergence of the learning error when using such algorithms.

The thrust balance model during the dragonfly hovering flight

In recent years, the micro air vehicle (MAV) oscillations caused by thrust imbalances have received more attention. This paper proposes a dual-wing thrust balance model (DTBM) that can solve the above problem by iterating the modified rotation angle formula. The core control parameter of the DTBM model is the au angle, which refers to the angle between the wing surface and the stroke plane at the mid-stroke position during the upstroke. For each degree change in the au angle, the range of variation in the dimensionless average thrust coefficient is between 0.0225-0.0268. A thrust coefficient of 0.0225 causes the dragonfly to move forward by 9.037 cm in one second, which is equivalent to 1.29 times its body length. By using DTBM, the average thrust coefficient can be reduced to below 0.001 in just a few iterations. No matter how complex the motion pattern is, the DTBM can achieve thrust balance within 0.278 s. Through our research, when selecting the deviation angle motion of real dragonflies, the dual-wing au angles exhibit a highly linear correlation with wing spacing, called linear motion. In contrast, the nonlinear variation of the au angle appears in the hindwing of the no-deviation motion and the forewing of the elliptical deviation motion. All of the nonlinear changes are referred to as nonlinear motion. Nonlinear variation of the au angle arises from larger disturbances of the lateral force during the upstroke. The stronger lateral force is closely related to the flapping trajectory. When the flapping trajectory causes the dual-wing to closely approach each other in the mid-stroke, a continuous positive pressure zone forms between the dual-wing. The collision of the leading-edge vortex and the shedding of the trailing-edge vortex is the special flow field structure in the nonlinear motion. Guided by the DTBM, future designs of MAVs will be able to better achieve thrust balance during hovering flight, requiring only the embedding of the iteration algorithm and prediction function of the DTBM in the internal chip.

An Iterative Exact Algorithm over a Time-Expanded Network for the Transportation of Biomedical Samples

In this article we propose an iterative algorithm to address the optimization problem of distributing a set of multiple highly perishable commodities in a healthcare network. In the biomedical sample transportation problem, numerous commodities with short lifespans presume multiple transportation requests at the same facility in a day and restrict the maximum time to reach their destination. These two characteristics create an interdependency between the routing and the pickup decisions in time that is highly complex. To address these timing issues, we model this problem as a service network design problem over a time-expanded network. Our solution method aggregates the network at two levels. First, the commodities are aggregated and artificially consolidated, reducing the symmetry arising when multiple transportation requests are solicited within a short period of time. Second, the space-time nodes in the network are constructed dynamically, thus reducing the size of the mathematical model to be solved at each iteration. Moreover, the method creates auxiliary networks to calculate good-quality primal bounds to the problem. Our algorithm proves to be efficient to solve a set of real-life instances from the Quebec laboratory network under the management of the Ministère de la Santé et des Services sociaux (Ministry of Health and Social Services) with a detailed network of up to 2,377 periods and 277 transportation requests. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants 2018-04609, 2020-06311]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0061 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0061 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Parameter Identification in Triple-Diode Photovoltaic Modules Using Hybrid Optimization Algorithms

Identifying the parameters of a triple-diode electrical circuit structure in PV modules is a critical issue, and it has been regarded as an important research area. Accordingly, in this study, a differential evolution algorithm (DEA) is hybridized with an electromagnetism-like algorithm (EMA) in the mutation stage to enhance the reliability and efficiency of the DEA. A new formula is presented to adapt the control parameters (mutation factor and crossover rate) of the DEA. Seven different experimental data sets are used to improve the performance of the proposed differential evolution with an integrated mutation per iteration algorithm (DEIMA). The results of the proposed PV modeling method are evaluated with other state-of-the-art approaches. According to different statistical criteria, the DEIMA demonstrates superiority in terms of root mean square error and main bias error by at least 5.4% and 10%, respectively, as compared to other methods. Furthermore, the DEIMA has an average execution time of 27.69 s, which is less than that of the other methods.

Stopping Sets of Algebraic Geometry Codes over Hyperelliptic Curves of Genus Two

Stopping sets are useful for analyzing the performance of a linear code under an iterative decoding algorithm over an erasure channel. In this paper, we consider stopping sets of one-point algebraic geometry codes defined by a hyperelliptic curve of genus g=2 defined by the plane model y2=f(x), where the degree of f(x) was 5. We completely classify the stopping sets of the one-point algebraic geometric codes C=CΩ(D,mP∞) defined by a hyperelliptic curve of genus 2 with m≤4. For m=3, we proved in detail that all sets S⊆{1,2,⋯,n} of a size greater than 3 are stopping sets and we give an example of sets of size 2,3 that are not.

Application of Machine Learning Techniques in Calibration and Data Reduction of Multi-Hole Probes

Abstract This work presents procedures to implement machine learning methods in the existing algorithms for multi-hole probe calibrations and data reduction. It is shown here, that utilizing artificial neural networks (ANNs) can reduce the amount of calibration data that needs to be acquired in order to obtain a specific calibration uncertainty, by more than 50% while simultaneously reducing data reduction times significantly. ANNs were used instead of the surface fitting methods, where first, the directional calibration coefficients related to the flow angles are calculated based on the pressure measurements, and then the flow angles are used as a set of the input parameters for the following ANNs to define Mach number and static and total pressure iteratively. In a second approach, novel calibration coefficients were used to directly relate the pressure measurements from five-hole probe to the quantities of interest thus, eliminating the need for iterative algorithms used in the conventional surface fitting methods. The advantageous features of this method are an average increase of less than 1% in the calibration uncertainty for flow angles and significant reduction of the data reduction times (few seconds). In addition, we confirmed the methodology to avoid over-fitting and under-fitting.

Design of even-order variable fractional delay FIR filters based on pivot element weighting iterative algorithm

Design of even-order variable fractional delay FIR filters based on pivot element weighting iterative algorithm

Forecasting economic growth by combining local linear and standard approaches

Today, developing economies are of major importance for global macroeconomic development. However, the empirical analysis and especially the forecasting of macroeconomic time series remain difficult due to a lack of sufficient data, data frequency, high volatility, and non-linear developments. These difficulties require more sophisticated approaches to obtain reliable forecasts. Therefore, we propose an improved forecasting method especially for growth data based on a data-driven local linear trend estimation with an extended iterative plug-in algorithm for determining the bandwidth endogenously. This approach allows a smooth trend estimation that takes care of temporary changes in trend processes. Further, the naïve random walk model is extended for forecasting by including a local linear, time-varying drift. We apply this method to GDP development for six developing and two advanced economies and compare different forecast combinations. The combinations that include the local linear approach and the random walk with a local linear trend improve forecasting accuracy and reduce variance.

Employing battery energy storage systems for flexible ramping products in a fully renewable energy power grid: A market mechanism and strategy analysis through multi-Agent Markov games

In high-proportion renewable energy power systems, flexible ramping products (FRPs) are critical for mitigating the volatility of renewable energy outputs and enhancing the adaptability of power systems. This paper aims to explore a fully renewable energy power system, with a battery energy storage system (BESS) as the sole provider of FRPs. An innovative market mechanism and new approaches to market equilibrium analysis are introduced. Initially, a common day-ahead (DA) market is established, covering both electricity and ancillary services with FRPs. The setup allows FRP providers to make bidding decisions and get rewarded based on actual ramping mileages. A bi-level multi-agent Markov game (MG) model is formulated. The upper level integrates the proposed strategies of wind power plants (WPP), photovoltaic power plants (PVP), and BESS, while the lower level encompasses the joint market clearing mechanism. An iterative solution algorithm, using reinforcement learning, is also introduced to address the model, effectively circumventing the privacy concerns associated with traditional mathematical programming methods. The proposed solution models and strategies are validated and demonstrated to be effective through two illustrative examples, highlighting their application and relevance in fully renewable energy power systems.

Optimal Model-Free Mean-Square Consensus for Multi-Agents with Markov Switching Topology

Due to the real applications, optimal consensus reinforcement learning with switching topology is still challenging due to the complexity of topological changes. This paper investigates the optimal consensus control problem for discrete multi-agent systems under Markov switching topologies. The goal is to design an appropriate algorithm to find the optimal control policies that minimize the performance index while achieving consensus among the agents. The concept of mean-square consensus is introduced, and the relationship between consensus error and tracking error to achieve mean-square consensus is studied. A performance function for each agent under switching topologies is established and a policy iteration algorithm using system data is proposed based on the Bellman optimality principle. The theoretical analysis shows that the consensus error realizes mean-square consensus and the performance function is optimized. The efficacy of the suggested approach is confirmed by numerical simulation using an actor–critic neural network. As a result, the value function is the optimum and the mean-square consensus can be reached using this technique.

Adaptive variable gain linear active disturbance rejection control parameter optimization in magnetic levitation

The magnetic levitation ball system is characterized by strong nonlinearity, multiple disturbances, and intrinsic instability, which has long been a thorny problem in the field of control engineering. The magnetic levitation system can be continuously and stably levitated, even in a complex environment. In this thesis, the model of the magnetic levitation ball system is firstly constructed according to the kinetic theory and simplified according to the actual situation. After that, a linear active disturbance rejection control (LADRC) controller for the magnetic levitation ball system is designed. Considering that there are many parameters in the LADRC controller and it is difficult to obtain the optimal control effect by manual tuning, an adaptive variable gain LADRC algorithm is proposed to optimize the control strategy of LADRC parameters. An adaptive iterative algorithm is used to adaptively adjust the bandwidth of the linear extended state observer (LESO) in LADRC, and the convergence of the algorithm is demonstrated by using the Lyapunov function. To solve the problem that the proportional and differential gains of the LADRC controller can only be adjusted unidirectionally and simultaneously, this paper proposes an error variable gain algorithm. The aim is to realize the non-unidirectional and more detailed adjustment of the controller parameters, and it is rigorously analyzed and demonstrated through simulation and experiment. The results show that the proposed algorithm is better than proportional–integral–derivative (PID), sliding mode control (SMC), and LADRC in terms of dynamic performance, steady-state performance, and anti-interference.

Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence

In this paper, we propose a method for optimizing the parameter values in iterative reconstruction algorithms that include adjustable parameters in order to optimize the reconstruction performance. Specifically, we focus on the power divergence-based expectation-maximization algorithm, which includes two power indices as adjustable parameters. Through numerical and physical experiments, we demonstrate that optimizing the evaluation function based on the extended power-divergence and weighted extended power-divergence measures yields high-quality image reconstruction. Notably, the optimal parameter values derived from the proposed method produce reconstruction results comparable to those obtained using the true image, even when using distance functions based on differences between forward projection data and measured projection data, as verified by numerical experiments. These results suggest that the proposed method effectively improves reconstruction quality without the need for machine-learning techniques in parameter selection. Our findings also indicate that this approach is useful for enhancing the performance of iterative reconstruction algorithms, especially in medical imaging, where high-accuracy reconstruction under noisy conditions is required.

A Variant of the Growing Neural Gas Algorithm for the Design of an Electric Vehicle Charger Network

The Growing Neural Gas (GNG) algorithm constitutes an incremental neural network model based on the idea of a Self-Organizing Map (SOM), that is, unsupervised learning algorithms that reduce the dimensionality of datasets by locating similar samples close to each other. The design of an electric vehicle charging network is an essential aspect in the transition towards more sustainable and environmentally friendly mobility. The need to design and implement an efficient network that meets the needs of all users motivates us to propose the use of a model based on GNG-type neural networks for the design of the network in a specific geographical area. In this paper, a variant of this iterative neural network algorithm is used with the objective that, from an initial dataset of points in the plane, it calculates a new simplified dataset with the main characteristic that the final set of points maintains the geometric shape and topology of the original set. To demonstrate the capabilities of the algorithm, it is exemplified in a real case, in which the design of an electric vehicle charging network is proposed. This network is built by applying the algorithm, taking as the original set of points the ones formed by the nodes of the gas station network in the geographical area studied. Several tests of running the algorithm for different sizes of the final dataset are performed, showing the differences between the original network and the computationally generated one.

Constrained solutions of generalized coupled discrete-time periodic matrix equations with application in state observer design for linear periodic systems

PurposeIt is desired to provide a diversified iterative scheme for solving the constrained solutions of the generalized coupled discrete-time periodic (GCDTP) matrix equations from the perspective of optimization.Design/methodology/approachThe paper considers generalized reflexive solutions of the GCDTP matrix equations by applying the Jacobi gradient-based iterative (JGI) algorithm, which is an extended variant of the gradient-based iterative (GI) algorithm.FindingsThrough numerical simulation, it is verified that the efficiency and accuracy of the JGI algorithm are better than some existing algorithms, such as the GI algorithm in Hajarian, the RGI algorithm in Sheng and the AGI algorithm in Xie and Ma.Originality/valueIt is the first instance in which the GCDTP matrix equations are solved applying the JGI algorithm.

The classical iterative HHL-based hemodynamic simulation quantum linear equation algorithm for abdominal aortic aneurysm

The classical iterative HHL-based hemodynamic simulation quantum linear equation algorithm for abdominal aortic aneurysm

Is Pessimism Provably Efficient for Offline Reinforcement Learning?

We study offline reinforcement learning (RL), which aims to learn an optimal policy based on a data set collected a priori. Because of the lack of further interactions with the environment, offline RL suffers from the insufficient coverage of the data set, which eludes most existing theoretical analysis. In this paper, we propose a pessimistic variant of the value iteration algorithm (PEVI), which incorporates an uncertainty quantifier as the penalty function. Such a penalty function simply flips the sign of the bonus function for promoting exploration in online RL, which makes it easily implementable and compatible with general function approximators. Without assuming the sufficient coverage of the data set (e.g., finite concentratability coefficients or uniformly lower-bounded densities of visitation measures), we establish a data-dependent upper bound on the suboptimality of PEVI for general Markov decision processes (MDPs). When specialized to linear MDPs, it matches the information-theoretic lower bound up to multiplicative factors of the dimension and horizon. In other words, pessimism is not only provably efficient but also, minimax optimal. In particular, given the data set, the learned policy serves as the “best effort” among all policies as no other policies can do better. Our theoretical analysis identifies the critical role of pessimism in eliminating a notion of spurious correlation, which arises from the “irrelevant” trajectories that are less covered by the data set and not informative for the optimal policy. Funding: Z. Yang acknowledges the Simons Institute (Theory of Reinforcement Learning). Z. Wang acknowledges the National Science Foundation [Awards 2048075, 2008827, 2015568, and 1934931], the Simons Institute (Theory of Reinforcement Learning), Amazon, J. P. Morgan, and Two bSigma.

A Geometric Numerical Integration with Simple Cell Mapping for Global Analysis of Nonlinear Dynamical Systems

In order to improve the efficiency in computing the global properties of nonlinear systems, some effective methods have been proposed for the global analysis of these systems. However, there are only few investigations focusing on the numerical algorithms of the system response trajectories. This paper presents a higher-efficiency geometric numerical integration method with simple cell mapping for solving the basins of attraction of nonlinear systems. This numerical algorithm is based on the rule of Lie derivative, using it to calculate the trajectories of the nonlinear systems. Then, the global structure is studied by the numerical algorithm associated with a simple cell mapping method. Compared with the traditional Runge–Kutta methods of orders 4 and 5, it is demonstrated that the proposed Lie derivative iterative algorithm has significant advantages in efficiency.