Optimization Of Dynamic Systems Research Articles

Optimal potential shaping on SE(3) via neural ordinary differential equations on Lie groups

This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization problem on Lie groups. A gradient descent optimization algorithm is presented to tackle the optimization numerically. Our algorithm is scalable, and applicable to any finite-dimensional Lie group, including matrix Lie groups. By representing the system at the Lie algebra level, we reduce the computational cost of the gradient computation. In an extensive example, optimal potential energy shaping for control of a rigid body is treated. The optimal control problem is phrased as an optimization of a neural ODE on the Lie group SE(3), and the controller is iteratively optimized. The final controller is validated on a state-regulation task.

Dynamic optimization of die-less spinning process through autonomous modeling of time-varying forming law

Die-less spinning is a typical incremental forming technology with flexible processing parameters, including the roller path and loading parameters, whose forming law changes dynamically and easy-to-produce defects of excessive thinning and flange wrinkling. This brings a great challenge to the process design of die-less spinning. In this study, we proposed a novel dynamic optimization approach and system considering the time-varying forming law for the processing parameters in die-less spinning. The idea of proposed approach is that simulating the spinning process step by step through autonomous finite element modeling, real-time extracting and modeling the simulated spinning status at each forming step to capture the time-varying forming law, then gradually optimizing the processing parameters through efficient multi-objective optimization algorithm. By conducting the proposed dynamic optimization approach to the first spinning pass of die-less spinning, series of polynomial response surface models (PRSM) of wall thickness and flange wrinkling at various forming steps were developed to describe the time-varying forming law. On this basis, the roller path and matching loading parameters in each step were gradually optimized through a differential evolution algorithm with the multi-objective of minimizing wall thickness reduction, reducing flange wrinkling and maximizing forming efficiency. The optimized process produced better spun part than the traditional spinning process, presenting the wall thickness reduction ≤5 % and the flange wrinkling ≤2.5 mm. Furthermore, the time-varying influence of processing parameters on the wall thickness and flange wrinkling were elucidated based on the PRSM of spinning status at various forming steps.

Optimization of dynamic control systems using water cycle algorithm

In this paper, path optimization in dynamic control systems was performed using water cycle algorithm. The core principles and assumptions that guide the suggested technique are drawn from nature and are based on observations of the water cycle process and how rivers and streams naturally flow into the sea. The Water Cycle Algorithm has been recognized as a reliable method for dealing with large-scale optimization challenges, largely because of its proficient exploitation and exploration capabilities. This Algorithm does not require the continuity of functions when specifying the issue, unlike many gradient-based approaches. This is achieved through the use of a simple mathematical model that represents the water cycle process. This model is used to simulate the movement of water droplets in a cloud, where each water droplet represents a potential solution to the optimization problem. Although water cycle optimization has been utilized successfully to tackle optimization issues, this is the first time dynamic control optimization has been used. The control problem is switched out for an optimum programming problem in order to find optimal pathways utilizing the Shifted Chebyshev polynomial. The water cycle method was then used to resolve the new issue. The numerical results demonstrate the excellent precision with which this search method can discover solutions.

Intent-based AI system in packet-optical networks towards 6G [Invited

This paper presents an intelligent dynamic network optimization system for packet-optical transport networks as the industry moves towards 6G. Such a system leverages specific artificial intelligence techniques to dynamically manage the transport network, optimize resource allocation, and guarantee quality of services. A predictive and adaptive Markov decision process is defined by exploiting an ad hoc model of optical-packet nodes and network representation used for the environment description. Comparison of statistical and neural network-based approaches is done for traffic forecasting. QL, DQL, and PPO are compared to solve the reinforcement learning problem. Challenges and opportunities of applying this system in various scenarios are discussed, and assessment is done by simulations that showed advantages in the following aspects: minimization of bandwidth usage guaranteeing quality of services with respect to a conventional system, improvement of optical offload improvement to reduce power consumption and packet processing, and efficient load balancing.

Seasonal pumped hydropower storage role in responding to climate change impacts on the Brazilian electrical sector

Since Brazil's major energy resources are renewable and directly related to climate factors, it is among the countries most likely of being affected by climate change. Given Brazil's high hydropower storage capacity and the strong seasonal patterns of its renewable resources, introducing Seasonal Pumped Hydropower Storage (SPHS) can help mitigate these challenges. To this end, a methodology is proposed that links the dynamic system-optimization model – MESSAGEix - to regional climate model simulations, called the Brazilian Electricity System MESSAGEix Model (BESMM). This model, with its detailed hydropower representation, is capable of integrating data from three climate change scenarios with the country's energy system. Climate change introduces a new dimension to this approach, as there is evidence of increasing the seasonal imbalance of variable renewable resources in Brazil. BESMM results suggest that SPHS can play a fundamental role in achieving a 100 % renewable matrix by 2100 in RCP 2.6 scenario, as well as enhancing the renewable energy endowment in scenarios RCP 4.5 and RCP 8.5. A reduction of up to 68 % of CO2 emissions is predicted in scenarios incorporating SPHS, compared to scenarios without SPHS.

Modelling the unsteady lift of a pitching NACA 0018 aerofoil using state-space neural networks

The development of simple, low-order and accurate unsteady aerodynamic models represents a crucial challenge for the design optimisation and control of fluid dynamical systems. In this work, wind tunnel experiments of a pitching NACA 0018 aerofoil conducted at a Reynolds number $Re = 2.8 \times 10^5$ and at different free-stream turbulence intensities are used to identify data-driven nonlinear state-space models relating the time-varying angle of attack of the aerofoil to the lift coefficient. The proposed state-space neural network (SS-NN) modelling technique explores an innovative methodology, which brings the flexibility of artificial neural networks into a classical state-space representation and offers new insights into the construction of reduced-order unsteady aerodynamic models. The work demonstrates that this technique provides accurate predictions of the nonlinear unsteady aerodynamic loads of a pitching aerofoil for a wide variety of angle-of-attack ranges and frequencies of oscillation. Results are compared with a modified version of the Goman–Khrabrov dynamic stall model. It is shown that the SS-NN methodology outperforms the classical semi-empirical dynamic stall models in terms of accuracy, while retaining a fast evaluation time. Additionally, the proposed models are robust to noisy measurements and do not require any pre-processing of the data, thus involving only a limited user interaction. Overall, these features make the SS-NN technique an excellent candidate for the construction of accurate data-driven models from experimental fluid dynamics data, and pave the way for their adoption in applications entailing design optimisation and real-time control of systems involving lift.

100 years of extremum seeking: A survey

Extremum seeking (ES) is a powerful approach to the optimization and stabilization of unknown dynamic systems and is an active field of research in control theory. This paper surveys recent ES algorithm developments. ES has evolved from its origins as a simple but brilliant engineering invention in the 1922 paper of Leblanc to the breakthrough work of Krstić and Wang in 2000 in which the first general stability analysis was given, to the most recent and numerous analytical results which prove convergence for a wide range of general dynamic systems. This survey provides a thorough overview of the dynamic systems for which ES stabilization and optimization results have been provided, the various analytical methods for proving convergence, and an overview of many real world applications for which ES has been utilized in industry and at scientific laboratories.

Nonlinear-Control-Oriented Modeling of the Multi-Variable Underground Coal Gasification Process for UCG Project Thar: A Machine Learning Perspective

The Underground Coal Gasification (UCG) process is a complex and multi-physics phenomenon, thus making it difficult to develop a mathematical model that encapsulates all dynamical aspects. In this regard, data-driven modeling techniques offer a reliable alternative for prediction, control, and optimization of dynamical systems, but their application in UCG is still in the early stages. This work aims to bridge this gap by implementing three cutting-edge nonlinear identification structures: Non-linear Autoregressive with Exogenous Inputs (NARX), Hammerstein–Wiener (HW), and State-Space Neural Networks (SSNN) on the UCG process to obtain a multivariable control-oriented model. The contributions include synthesizing an excitation signal for data acquisition, outlining the non-linear system identification procedure, and comparing predictive capabilities using statistical tools. The simulation results demonstrate a rigorous comparison of various techniques for the heating value and flowrate of the syngas, which are the outputs of the UCG process. The results of the analysis show that NARX outperforms other structures in statistical metrics, with MAE, RMSE, and Best fit values of 1.51,1.9, and 0.9, respectively, for the heating value; and 0.25,0.31, and 0.94, respectively, for the flowrate. Consequently, the outputs of the NARX model are compared with the experimental data obtained from the UCG project Thar, which show a good match for both outputs.

An efficient simulation procedure for the expected opportunity cost using metamodels

Many decision problems in modern industries involve the performance optimization of discrete-event dynamic systems. Because of the stochasticity of these systems, performance usually is evaluated through simulation. Finding the optimal designs of these systems can be modeled as a ranking and selection problem. This research considers the problem of selecting the best design from among numerous designs. We minimized the expected opportunity cost (EOC) of incorrect selection with a limited computing budget. The entire domain of designs could be divided into several adjacent partitions, and the performances of designs in each partition were estimated using a regression metamodel. We assumed the underlying function in each partition to be quadratic. Using large deviations theory, we then derived an asymptotically optimal budget allocation rule and developed a sequential allocation algorithm to implement the allocation rule. The EOC measure was compared with the probability of correct selection measure in a set of large-scale simulation optimization problems. Numerical experiments verified the effectiveness of our proposed simulation procedure.

A crowd-AI dynamic neural network hyperparameter optimization approach for image-driven social sensing applications

Image-driven social sensing (ISS) is emerging as a pervasive sensing paradigm that collects the status of the physical world by leveraging image data from human sensors. This paper studies a dynamic hyperparameter optimization problem in ISS applications and our objective is to dynamically determine the optimal hyperparameter configuration of an AI-based ISS solution that provides the accurate label for each image in the data stream of ISS applications. Our work is motivated by the observation that current ISS solutions leverage a static hyperparameter configuration that is often configured manually by AI experts, which fails to capture the potential large dynamics of ISS applications. To address this limitation, we develop DC-HPO, a dynamic crowd-assisted hyperparameter optimization system that utilizes crowdsourced human intelligence to dynamically steer the search of the optimal hyperparameter configuration for each image in the data stream of ISS applications. The experimental results on two ISS applications from real world (i.e., intelligent urban infrastructure monitoring and city environment cleanliness assessment) demonstrate that DC-HPO outperforms existing deep convolutional neural networks, crowd-AI models, and hyperparameter optimization methods in achieving the best ISS performance while keeping the lowest computational cost.

Characterisation of pressure‐concentration‐temperature profiles for metal hydride hydrogen storage alloys with model development

AbstractMetal hydride (MH) alloys have been applied to hydrogen storage and various energy conversion systems such as refrigeration, heat pump and heat transformer. However, to facilitate and efficiently investigate efficiently a particular application, an MH alloy must firstly be characterised with a purposely built test facility to measure profiles of pressure, MH hydrogen concentration and temperature (PCT). Obtaining detailed PCT profiles or curves could be an arduous and expensive task as each isothermal hydrogen absorption or desorption line requires hundreds of measurement points. It is thus desirable to develop an accurate correlative model for the PCT profiles with limited measurements of thermophysical property data for the purpose of characterisation of each MH alloy. This correlative model or characterisation process has been developed and is described in detail in this article. The correlative PCT MH alloy profiles can cover all applicable hydrogen storage phase regions of α, α + β and β as well as the phase transition dome curve and critical point such that a PCT phase diagram for a particular MH alloy can be depicted and characterised. As an application example, the correlative model is applied to predict an MH alloy's hydrogen storage capacity and hysteresis at a specific MH temperature. It has been discovered that each of these two parameters shows comparative trends in variation with reduced temperature. Correspondingly, for each parameter, a correlative function with reduced temperature has been produced. The MH alloy characterisation process is an essential step towards a detailed dynamic MH energy system modelling, simulation and optimisation as well as experimental investigation.

System reliability evaluation and dynamic optimization based on an improved reliability block diagram

Reliability block diagram (RBD) is an effective tool for modeling and evaluating system reliability. During operation, a system’s reliability may decrease significantly due to the failure of certain critical nodes and thus should be reconfigured. This paper presents a framework for system reliability evaluation and dynamic optimization based on RBD, designed from the perspective of system users. First, we improve the classic RBD model with a new encoding scheme and develop an accurate RBD computation algorithm that is easily recognized by computers and highly efficient. Second, we create an optimization algorithm based on Tabu Search to reconfigure the system after node failure, striking a balance between system reliability recovery and RBD variation amplitude. Finally, we provide some numerical examples and a computational experiment based on a practical instance from a navy fleet to demonstrate the correctness and effectiveness of our proposed methods.

A comprehensive assessment of cost-optimal heat supply to new low-energy building areas in Sweden

Buildings in Sweden use a large share of energy produced nationally but produce a low share of direct carbon emissions due to high market share of heat pumps and district heating (DH), which uses biomass. Sweden has set stringent energy and climate goals for 2045 prescribing, among other things, reduced energy consumption in buildings. Consequently, new building areas are built based on low-energy building (LEB) standards. These buildings require space heating on cold days and hot water generally. There are four main heat supply options for these areas: (1) individual heat devices (2) decentralized DH, (3) connection to a nearby centralized DH, and (4) prosumers. In this study we developed and applied a dynamic energy system optimization model and designed a systematic analysis to assess cost-optimal heat supply to LEBs in the long-term, while addressing the climate targets. The results showed that low temperature decentralized DHs (LTDDH)s have the lowest cost and individual heat devices have the highest cost of heat supply to LEB areas. The cost-efficiency of LTDDH increases with if prosumers exist in more densely built LEB areas with higher annual heat demand. Additionally, stringent climate policy scenarios can further decrease the cost of LTDDH in LEB areas.

GoSafeOpt: Scalable safe exploration for global optimization of dynamical systems

Learning optimal control policies directly on physical systems is challenging. Even a single failure can lead to costly hardware damage. Most existing model-free learning methods that guarantee safety, i.e., no failures, during exploration are limited to local optima. This work proposes GoSafeOpt as the first provably safe and optimal algorithm that can safely discover globally optimal policies for systems with high-dimensional state space. We demonstrate the superiority of GoSafeOpt over competing model-free safe learning methods in simulation and hardware experiments on a robot arm.

Integrated topology and controller optimization using the Nyquist curve

The design of high-performance mechatronic systems is very challenging, as it requires delicate balancing of system dynamics, the controller, and their closed-loop interaction. Topology optimization provides an automated way to obtain systems with superior performance, although extension to simultaneous optimization of both topology and controller has been limited. To allow for topology optimization of mechatronic systems for closed-loop performance, stability, and disturbance rejection (i.e. modulus margin), we introduce local approximations of the Nyquist curve using circles. These circular approximations enable simple geometrical constraints on the shape of the Nyquist curve, which is used to characterize the closed-loop performance. Additionally, a computationally efficient robust formulation is proposed for topology optimization of dynamic systems. Based on approximation of eigenmodes for perturbed designs, their dynamics can be described with sufficient accuracy for optimization, while preventing the usual threefold increase of additional computational effort. The designs optimized using the integrated approach have significantly better performance (up to 350% in terms of bandwidth) than sequentially optimized systems, where eigenfrequencies are first maximized and then the controller is tuned. The proposed approach enables new directions of integrated (topology) optimization, with effective control over the Nyquist curve and efficient implementation of the robust formulation.

Physics-informed recurrent neural networks and hyper-parameter optimization for dynamic process systems

Many of the processes in chemical engineering applications are of dynamic nature. Mechanistic modeling of these processes is challenging due to the complexity and uncertainty. On the other hand, recurrent neural networks are useful to be utilized to model dynamic processes by using the available data. Although these networks can capture the complexities, they might contribute to overfitting and require high-quality and adequate data. In this study, two different physics-informed training approaches are investigated. The first approach is using a multi-objective loss function in the training including the discretized form of the differential equation. The second approach is using a hybrid recurrent neural network cell with embedded physics-informed and data-driven nodes performing Euler discretization. Physics-informed neural networks can improve test performance even though decrease in training performance might be observed. Finally, smaller and more robust architecture are obtained using hyper-parameter optimization when physics-informed training is performed.

An efficient approach for dynamic-reliability-based topology optimization of braced frame structures with probability density evolution method

The present paper explores the feasibility of topology optimization of stochastic dynamical systems in the framework of the probability density evolution method (PDEM). A new method is proposed for solving dynamic-reliability-based topology optimization (DRBTO) problems by combining the PDEM, the ground structure approach and the solid isotropic material with penalization (SIMP) model. In the investigated optimization problems, the first-passage probability is considered as an objective or constraint function. To obtain a clear layout of the optimized structure, the topology of the structure is described by the ground structure approach together with the SIMP model. The PDEM is employed as an efficient approach to assess the first-passage probability. For improved numerical efficiency, an approximate formulation of the first-passage probability based on the important representative points (IRPs) is implemented. On the basis of the approximate formulation of the first-passage probability, a relationship between the sensitivity of the first-passage probability and the transient response is obtained. The adjoint sensitivity analysis of the transient response is introduced to avoid extra numerical efforts. Then, by incorporating the first-passage probability and its sensitivity into the method of moving asymptotes (MMA), the investigated DRBTO problems are solved in an effective manner. The DRBTO of a braced frame structure is presented to demonstrate the availability and effectiveness of the proposed method.

Chaos Game Optimization Algorithm for Parameters Identification of Different Models of Photovoltaic Solar Cell and Module

In order to achieve the optimum feasible efficiency, the electrical parameters of the photovoltaic solar cell and module should always be thoroughly researched. In reality, the quality of PV designs can have a significant impact on PV system dynamic modeling and optimization. PV models and calculated parameters, on the other hand, have a major effect on MPPT and production system efficiency. Because a solar cell is represented as the most significant component of a PV system, it should be precisely modeled. For determining the parameters of solar PV modules and cells, the Chaos Game Optimization (CGO) method has been presented for the Single Diode Model (SDM). A set of the measured I-V data has been considered for the studied PV design and applied to model the RTC France cell, and Photowatt-PWP201 module. The objective function in this paper is the Root Mean Square Error (RMSE) between the measured and identified datasets of the proposed algorithm. The optimal results that have been obtained by the CGO algorithm for five electrical parameters of PV cell and model have been compared with published results of various optimization algorithms mentioned in the literature on the same PV systems. The comparison proved that the CGO algorithm was superior.

A General Strategy for the Design and Evaluation of Heterobifunctional Tools: Applications to Protein Localization and Phase Separation.

To mimic the levels of spatiotemporal control that exist in nature, tools for chemically induced dimerization (CID) are employed to manipulate protein-protein interactions. Although linker composition is known to influence speed and efficiency of heterobifunctional compounds, modeling or in vitro experiments are often insufficient to predict optimal linker structure. This can be attributed to the complexity of ternary complex formation and the overlapping factors that impact the effective concentration of probe within the cell, such as efflux and passive permeability. Herein, we synthesize a library of modular chemical tools with varying linker structures and perform quantitative microscopy in live cells to visualize dimerization in real-time. We use our optimized probe to demonstrate our ability to recruit a protein of interest (POI) to the mitochondria, cell membrane, and nucleus. Finally, we induce and monitor local and global phase separation. We highlight the importance of quantitative approaches to linker optimization for dynamic systems and introduce new, synthetically accessible tools for the rapid control of protein localization.

Sampled-data extremum-seeking framework for constrained optimization of nonlinear dynamical systems

Most extremum-seeking control (ESC) approaches focus solely on the problem of finding the extremum of some unknown, steady-state input–output map, providing parameter settings that lead to optimal steady-state system performance. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on tunable system parameters, or constraints on measurable variables. In particular, constraints on measurable variables are typically unknown in terms of their relationship with the tunable system parameters. In addition, the constraints on system inputs as a result of the constraints on measurable variables may conflict with the otherwise optimal operational condition, and hence should be taken into account in the data-based optimization approach. In this work, we propose a sampled-data extremum-seeking framework for the constrained optimization of a class of nonlinear dynamical systems with measurable constrained variables. In this framework, barrier function methods are employed, exploiting both the objective function and constraint functions which are available through output measurement only. We show, under the assumption that the parametric initialization yield operating conditions that do not violate the constraints, that (1) the resulting closed-loop dynamics is stable, (2) constraint satisfaction of the inputs is guaranteed for all iterations of the optimization process, and (3) constrained optimization is achieved. We illustrate the working principle of the proposed framework by means of an industrial case study of the constrained optimization of extreme ultraviolet light generation in a laser-produced plasma source within a state-of-the-art lithography system.