Online Optimal Control Research Articles

Deep Koopman-operator-based model predictive control for free-floating space robots with disturbance observer

This paper investigates the optimal tracking control problem of free-floating space robots in the presence of non-ideal factors, such as model uncertainties and external disturbances. To address this issue, we first leverage the deep Koopman operator, facilitated with a deep neural network, to establish an offline formulation of a global linearization model for a micro-nano free-floating space robot. Based on the estimated linearization model, we then employ the model predictive control method for online optimization control, achieving a significantly reduced computational burden. Additionally, a decay factor is integrated into the model predictive control optimization objective function to balance the precision of joint angles tracking with the suppression of base satellite attitude disturbance. To further address the modeling inaccuracies and external disturbances, we incorporate a disturbance observer based on a radial basis function neural network for online compensation within the model predictive control framework. This augmentation enhances tracking precision and robustness. Several groups of simulation results are carried out to demonstrate the effectiveness of the proposed method, showing its capability of energy consumption, disturbance rejection and enhanced robustness. These highlight the potential of the proposed method to improve the control performance of free-floating space robots, even in the absence of a precise dynamic model.

A novel optical orthogonality control approach based on noise propagation and its application in spin-exchange relaxation-free co-magnetometers

This paper presents a non-destructive optical orthogonality control method based on adaptive gradient descent for spin-exchange relaxation-free co-magnetometers (SERFCM). The spin-exchange optical pumping technique serves as the foundation of SERFCM measurement. Analyzing the impact of pump power fluctuation on the transverse polarizability of alkali metal atoms in the presence of non-orthogonal beams, considering stochastic noise propagation, is addressed. Subsequently, an optical orthogonal calibration scheme is proposed. Leveraging the proposed orthogonal calibration scheme, an adaptive gradient descent method based on the reference model is formulated, and simulation validates its effectiveness in addressing the rapid online optimization control of SERFCM optical quadrature. Experimental results indicate that the proposed optical orthogonal calibration scheme offers higher accuracy, with the proposed optical orthogonal control algorithm saving 34% of the time compared to the traditional algorithm. Finally, the stability of SERFCM is evaluated using Allan variance, demonstrating that the adjusted SERFCM enhances short-term stability by 84% at around 1s and long-term stability by 639% at around 300s.

Online optimal tracking control of unknown nonlinear singularly perturbed systems using single network adaptive critic with improved learning

This study is the first time devoted to seek an online optimal tracking solution for unknown nonlinear singularly perturbed systems based on single network adaptive critic (SNAC) design. Firstly, a novel identifier with more efficient parametric multi-time scales differential neural network (PMTSDNN) is developed to obtain the unknown system dynamics. Then, based on the identification results, the online optimal tracking controller consists of an adaptive steady control term and an optimal feedback control term is developed by using SNAC to solve the Hamilton–Jacobi–Bellman (HJB) equation online. New learning law considering filtered parameter identification error is developed for the PMTSDNN identifier and the SNAC, which can realize online synchronous learning and fast convergence. The Lyapunov approach is synthesized to ensure the convergence characteristics of the overall closed loop system consisting of the PMTSDNN identifier, the SNAC and the optimal tracking control policy. Three examples are provided to illustrate the effectiveness of the investigated method.

Tuning and testing an Online Feedback Optimization controller to provide curative distribution grid flexibility

Due to more volatile generation, flexibility will become more important in transmission grids. One potential source of this flexibility can be distribution grids. A flexibility request from the transmission grid to a distribution grid then needs to be split up onto the different Flexibility Providing Units (FPU)s in the distribution grid. One potential way to do this is Online Feedback Optimization (OFO). OFO is a new control method that steers power systems to the optimal solution of an optimization problem using minimal model information and computation power. This paper will show how to choose the optimization problem and how to tune the OFO controller. Afterward, we test the resulting controller on a real distribution grid laboratory and show its performance, its interaction with other controllers in the grid, and how it copes with disturbances. Overall, the paper makes a clear recommendation on how to phrase the optimization problem and tune the OFO controller. Furthermore, it experimentally verifies that an OFO controller is a powerful tool to disaggregate flexibility requests onto FPUs while satisfying operational constraints inside the flexibility providing distribution grid.

Real-time prediction of fuel consumption and emissions based on deep autoencoding support vector regression for cylinder pressure-based feedback control of marine diesel engines

Predictive models serving as virtual sensors for online optimization and feedback control of diesel engines is gaining increasing attention. However, existing prediction models fall short in simultaneously achieving high prediction accuracy and fast computational speed. In this paper, a novel machine learning algorithm called deep autoencoding support vector regression (DASVR) was proposed, which combines the powerful non-linear feature extraction capability of artificial neural network (ANN) with the good adaptability of support vector regression (SVR) to low-dimensional input spaces. ANN-based autoencoder is firstly employed to extract features from the original high-dimensional input space, forming a low-dimensional latent variable space. SVR is then employed to perform non-linear mapping between latent variables and target output variables. Experiments were conducted on a 16-cylinder marine diesel engine under different load, rail pressure, and injection timing conditions. Prediction models for fuel consumption, NOx, PM, HC, and PM emissions were established based on experimental data and DASVR algorithm. The maximum error of DASVR-based models for the five desired output variables is less than 3.8 % under different operating conditions. DAVSR-based predictive models outperform conventional ANN-based and SVR-based models in terms of both prediction accuracy and real-time capability, and can theoretically meet the real-time requirement below 3000 r/min.

Optimized energy management for plug-in hybrid vehicles with predicted driving cycles1

The traditional rule-based energy management strategy for plug-in hybrid vehicles has issues, such as difficulty in online correction and limited online optimization capabilities. In addition, the global optimization energy management strategy cannot be applied online or in real-time. Considering the above difficulties, this study proposes a real-time optimization energy management strategy based on the Markov chain for driving condition prediction and online optimization with the minimum principle. To verify the proposed control strategy, the plug-in hybrid vehicle dynamics model, driving condition prediction model, and online optimization control model were first established. The initial value of the battery state of charge was set to 0.4 under the UDDS (Urban Dynamometer Driving Schedule) standard cycle. The simulation results showed that the comprehensive fuel consumption cost was 1.66 yuan, which was 8.28% better than the energy economy of the traditional rule-based energy management strategy. At the same time, a complete vehicle test was also conducted based on a sample vehicle test platform. The experimental results indicated that the energy management strategy proposed herein exhibits better fuel economy compared to that exhibited by the traditional rule-based energy management strategy. Simulations and experiments have verified the effectiveness of the proposed control strategy in this study.

A data‐driven Bayesian approach for optimal dynamic product transitions

AbstractIn the processing industry, dynamic product transitions are essential for achieving high product quality, minimizing the use of raw materials and energy and reducing production costs. However, optimizing dynamic product transitions is a challenging task due to the complex dynamics of the process and the uncertainty in the measurements. In this article, a data‐driven Bayesian approach for optimal dynamic product transitions is proposed. The proposed approach is based on a dynamic optimization problem that is solved using a Bayesian optimization algorithm. One of the advantages of this approach for process optimization tasks is that it does not require a first‐principles dynamic mathematical model for drawing optimal solutions. The approach is applied to three case studies, and the results are comparable in performance quality with those obtained using a traditional gradient‐based optimization approach. The results show that the proposed approach is able to find optimal transition trajectories that meet the product composition requirements using smooth control actions. The approach is also able to cope with noisy measurements, which is an important feature in real‐world applications. The proposed approach has several advantages over traditional optimization approaches, including being data driven, able to cope with noisy measurements, computationally efficient, and it requires modest computational effort. Complex online optimal control problems can benefit from adopting a data‐driven Bayesian optimization scheme.

A Novel Machine Learning-Based Online Optimal Control Strategy for Fuel Cell in Electrified Transportation System

A Novel Machine Learning-Based Online Optimal Control Strategy for Fuel Cell in Electrified Transportation System

Periodic Event-Triggered MPC for Continuous-Time Nonlinear Systems With Bounded Disturbances

This paper is concerned with periodic event-triggering laws in robust model predictive control (MPC) for continuous-time constrained nonlinear systems. The online optimal control problem solved at triggering times is introduced. A periodic static event-triggering condition, in which a fixed sampling time interval plays an important role in avoiding Zeno behavior, is presented to alleviate continuous checking of event detections. Then a periodic dynamic event-triggering condition is investigated to further enlarge the minimal inter-execution time. Single-mode MPC with a prediction horizon larger than the control one is considered. Sufficient conditions of recursive feasibility for the online optimal control problem are derived. In order to relax the sufficient condition of stability, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ultimately Boundedness</i> properties are utilized in stability analysis. Finally, numerical simulation is provided to demonstrate the effectiveness of the proposed methods.

Prediction model of the large commercial building cooling loads based on rough set and deep extreme learning machine

Efficient prediction of building air conditioning cooling loads contributes to optimizing and controlling heating, ventilation, and air conditioning (HVAC) systems. In this paper, the K-means++ algorithm is used to classify the air conditioning cooling loads to determine the number of discretization intervals and influencing factors of cooling loads. Then, the rough set (RS) theory is used to screen out the critical influencing factors of cooling loads to reduce the input dimensions of the prediction model. Finally, the particle swarm optimization (PSO) algorithm is used to optimize the weights and thresholds between input layers and hidden layers of the deep extreme learning machine (DELM) neural network. Based on the above methods, a K-means++-RS-PSO-DELM prediction model is established for building air conditioning cooling loads. In this paper, a total of 50 large commercial buildings are investigated to find the critical influencing factors of air conditioning cooling loads. Data from a large commercial building in Guilin is collected to train and test the proposed model. Meanwhile, the comparisons between the proposed model and the K-means++-RS-BP, the K-means++-RS-PSO-BP, the K-means++-RS-Elman, the K-means++-RS-PSO-Elman, the K-means++-RS-ELM, the K-means++-RS-PSO-ELM, and the K-means++-RS-DELM models are conducted to validate the applicability of the prediction model. Results show that the prediction deviation of the proposed model is 1.0016 and 0.9942 in short-term and medium-term predictions, which are smaller than that of other prediction models. The proposed model has a strong generalization ability to predict the air conditioning cooling load in large commercial buildings, which is beneficial for online optimal control of the HVAC system.

Combination optimization method of grid sections based on deep reinforcement learning with accelerated convergence speed

A modern power system integrates more and more new energy and uses a large number of power electronic equipment, which makes it face more challenges in online optimization and real-time control. Deep reinforcement learning (DRL) has the ability of processing big data and high-dimensional features, as well as the ability of independently learning and optimizing decision-making in complex environments. This paper explores a DRL-based online combination optimization method of grid sections for a large complex power system. In order to improve the convergence speed of the model, it proposes to discretize the output action of the unit and simplify the action space. It also designs a reinforcement learning loss function with strong constraints to further improve the convergence speed of the model and facilitate the algorithm to obtain a stable solution. Moreover, to avoid the local optimal solution problem caused by the discretization of the output action, this paper proposes to use the annealing optimization algorithm to make the granularity of the unit output finer. The proposed method in this paper has been verified on an IEEE 118-bus system. The experimental results show that it has fast convergence speed and better performance and can obtain stable solutions.

Rapid detection of micronutrient components in infant formula milk powder using near-infrared spectroscopy.

In order to achieve rapid detection of galactooligosaccharides (GOS), fructooligosaccharides (FOS), calcium (Ca), and vitamin C (Vc), four micronutrient components in infant formula milk powder, this study employed four methods, namely Standard Normal Variate (SNV), Multiplicative Scatter Correction (MSC), Normalization (Nor), and Savitzky-Golay Smoothing (SG), to preprocess the acquired original spectra of the milk powder. Then, the Competitive Adaptive Reweighted Sampling (CARS) algorithm and Random Frog (RF) algorithm were used to extract representative characteristic wavelengths. Furthermore, Partial Least Squares Regression (PLSR) and Support Vector Regression (SVR) models were established to predict the contents of GOS, FOS, Ca, and Vc in infant formula milk powder. The results indicated that after SNV preprocessing, the original spectra of GOS and FOS could effectively extract feature wavelengths using the CARS algorithm, leading to favorable predictive results through the CARS-SVR model. Similarly, after MSC preprocessing, the original spectra of Ca and Vc could efficiently extract feature wavelengths using the CARS algorithm, resulting in optimal predictive outcomes via the CARS-SVR model. This study provides insights for the realization of online nutritional component detection and optimization control in the production process of infant formula.

Online energy management optimization of hybrid energy storage microgrid with reversible solid oxide cell: A model-based study

Microgrids (MGs) that contain a reversible solid oxide cell (rSOC) system and battery energy storage system (BESS) are gaining prominence in terminal load supply and renewable energy consumption. However, the economy and durability are highly dependent on the reliability of its energy management system (EMS). Herein, a model-based online optimal control strategy is proposed to obtain optimal schedule decisions for EMS. Firstly, the aging of BESS and the efficiency of the rSOC system are considered simultaneously, and are modeled in detail. Subsequently, the optimal energy management (OEM) is formulated as a multi-objective optimization problem based on the constructed model. On this basis, to improve the efficiency and accuracy of the optimization search, a novel multi-objective evolutionary algorithm is proposed and verified, which hybridizes the non-dominated sorting genetic algorithm-II and tabu search, and incorporates improved crossover and mutation operations. Afterwards, data from a commercial user in Ningxia, China was used for the case study. The results show that the proposed control strategy can effectively slow down the aging of BESS and improve the efficiency of the rSOC system compared to the rule-based control strategy. Furthermore, compare with the rule-based control and economic dispatching strategy, the MG obtained a higher self-sufficiency rate (93.28%) and a shorter payback period (14.57 years) under the proposed OEM strategy.

Neural‐based online finite‐time optimal tracking control for wheeled mobile robotic system with inequality constraints

AbstractIn this study, a finite‐time online optimal controller was designed for a nonlinear wheeled mobile robotic system (WMRS) with inequality constraints, based on reinforcement learning (RL) neural networks. In addition, an extended cost function, obtained by introducing a penalty function to the original long‐time cost function, was proposed to deal with the optimal control problem of the system with inequality constraints. A novel Hamilton‐Jacobi‐Bellman (HJB) equation containing the constraint conditions was defined to determine the optimal control input. Furthermore, two neural networks (NNs), a critic and an actor NN, were established to approximate the extended cost function and the optimal control input, respectively. The adaptation laws of the critic and actor NN were obtained with the gradient descent method. The semi‐global practical finite‐time stability (SGPFS) was proved using Lyapunov's stability theory. The tracking error converges to a small region near zero within the constraints in a finite period. Finally, the effectiveness of the proposed optimal controller was verified by a simulation based on a practical wheeled mobile robot model.

A reinforcement learning-based approach for online optimal control of self-adaptive real-time systems

A reinforcement learning-based approach for online optimal control of self-adaptive real-time systems

Graph neural network-based spatio-temporal indoor environment prediction and optimal control for central air-conditioning systems

Model-based optimal control has proven its effectiveness in optimizing the performance of central air-conditioning systems in terms of thermal comfort and energy efficiency. It was often assumed that temperature distribution in the entire air-conditioned space is uniform and can be represented by a single or averaged measurement in optimization. However, actual distribution in the air-conditioned space is usually uneven, which can affect thermal comfort and indoor air quality. The dynamics of air conditioning systems and their interactions with the built environment exist in both time and space domains. Conventional data-driven approaches typically concentrate on the temporal correlations only among building operation data, while neglecting the spatial correlations. This study proposed a spatio-temporal data-driven methodology for optimal control of central air conditioning systems, which aims to address the challenging issue of uneven spatial distributions of environmental parameters in air-conditioned space. The methodology consists of graph-based multi-source data integration, graph neural network-based indoor environment modeling and spatio-temporal model-based online optimal control. The proposed methodology is tested on real air handling unit-variable air volume (AHU-VAV) system in a high-rise office building through a cloud-based platform. Spatio-temporal data from building automation system (BAS), internet of things (IoT) devices and building information modeling (BIM) are integrated and organized as graph structure. Graph neural network models are developed for predicting the evolution of indoor air temperature distribution under different control settings. The developed graph neural network-recurrent neural network (GNN-RNN) model architectures show enhanced accuracy than conventional deep learning models (i.e., convolutional neural network-recurrent neural network (CNN-RNN), Dense-RNN). And the cloud-based online test demonstrates that the proposed model-based control strategy improves the percentage of time achieving Grade I thermal comfort from 36.5% (i.e., existing control strategy) to 81.3%.

Dual-Mode Robust Fuzzy Model Predictive Control of Time-Varying Delayed Uncertain Nonlinear Systems With Perturbations

For time-varying delayed nonlinear systems with parameter uncertainties and persistent disturbances, an online and an offline robust fuzzy model predictive control (RFMPC) algorithms are proposed in this paper. Both methods guarantee the input-to-state stability (ISS) of the system. Furthermore, a novel alternative optimization (AOP) approach and a dual-mode OP/AOP strategy are proposed to prevent the performance deterioration of the online optimal control (OP) approach due to the challenges in addressing the bilinear matrix inequality (BMI) constraints. With the established AOP and dual-mode OP/AOP techniques, the optimization problem constrained by BMIs is transformed into convex, and a significantly more precise approximation of the ellipsoidal minimal robust positively invariant (EmRPI) set can be calculated. Besides, the system can eventually converge into a more compact ellipsoidal set. These two alternative optimization methods can be easily extended to various nonlinear systems. A numerical example and a continuous-time stirring tank (CSTR) example are provided to validate the effectiveness and advantages of the established methodologies.

A novel [formula omitted] control for T-S fuzzy systems with transform matching membership functions

This article studies H∞ optimization issue of Takagi-Sugeno (T-S) fuzzy systems with an improved transform matching membership functions (MFs) approach. Different from existing transform matching MFs control method, a polynomial disassembling strategy is first proposed for T-S fuzzy systems. Then, combining with parameterized linear matrix inequality (LMI) technique which can remove the inequality constraints between the MFs in systems and fuzzy controllers, sufficient conditions are presented to maintain asymptotic stability and desired H∞ performance for studied plants. Afterwards, a novel MFs online optimization algorithm is proposed for the first time to automatically adjust the values of scaling and bias parameters so as to realize better H∞ performance. In contrast to the traditional control using improved matching MFs, the practical behavior of disturbance attenuation index is reduced efficiently. Additionally, the proposed MFs online optimization algorithm is capable of sustaining the desired H∞ performance when the disturbance channels exist modeling errors, i.e., the practical disturbance attenuation index γ is still less than the preset value. For guaranteeing the convergence of cost function, sufficient condition is obtained based upon Lyapunov stability theory. Finally, two demonstrative simulations are presented to confirm the advantages and benefits of the novel MFs online optimization control strategy.

Joint Optimization of Data Transmission and Energy Harvesting in Relay Satellite Networks

Satellite network is considered a prominent architecture for future space-air-ground integrated networks, where the relay satellite network (RSN) plays an essential role in data transmission. However, the relay satellite network faces practical challenges. First, due to the dynamic network topology and limited resources such as storage capacity, antennas, and bandwidth, optimizing data transmission and resource allocation in a resource-constrained stochastic system is challenging. Second, satellites intermittently enter the eclipse zone, which leads to an unstable energy supply. Therefore, optimal energy management is required to balance energy supply and consumption. In this paper, we proposed an online optimal control algorithm, based on Lyapunov stability theory, to optimize data transmission and energy management jointly. Furthermore, the performance of our proposal is analyzed comprehensively, including the reasonable bounds for data and energy and the optimality of our proposed algorithm. Finally, extensive performance evaluation simulations are performed based on real-world satellite parameters. The simulation results indicate that the proposed method can achieve long-term network stability and energy sustainability. Moreover, the proposed algorithm shows an improvement of 9.6% and 20.3% in system utility compared to the non-optimized transmission method and non-optimized energy management algorithm, respectively.

Dynamic Performance Improvement of a Single-Phase VSI with Digital Implementation of an On-Line Optimal Trajectory Control Algorithm

A single-phase voltage source inverter (VSI) still suffers from a long settling time and significant voltage overshoot/undershoot under the abrupt step-change of load current. This article analyzes the comprehensive large-signal dynamic process and limitation of the linear controller during step change in load current. The combination of linear and nonlinear control is presented which is a realistic, simple, and low-cost technique for enhancing the dynamic response of the single-phase VSI. A nonlinear controller based on the simplified capacitor charge balance algorithm is employed to drive the inductor current and capacitor voltage to attain the target value by precisely following the projected optimal trajectory during the transient process in a brief period. A linear PI controller is utilized during the steady-state operations such as input voltage variations, temperature drifts, and component ageing. The complete mathematical derivation as well as a design method is presented to guide the practical hardware implementation for the given main circuit parameters and identified load step change. Even though accurate time instants can be obtained using off-line numerical calculations, reasonable simplifications are provided for real-time practical engineering applications in DSP. Finally, simulation and experimental verifications prove that the single-phase VSI achieves a substantial settling time decrease and reduced voltage oscillations.