Real-time Optimization Approach Research Articles

Energy-efficient operation of portable air cleaners based on real-time prediction of non-uniform concentrations of indoor air pollutants in open offices

In an open office environment with high occupant density and random occupancy patterns, excessive energy consumption is often observed because mechanical ventilation (MV) is usually designed and operated assuming a full-occupancy-based ventilation rate (VR). Considering the duo challenges of post-pandemic and climate change, this study proposes a real-time monitoring and optimization approach for operating portable air cleaners (PACs) to assist and reduce the energy consumption of the MV while maintaining the minimal VR and improving indoor air quality (IAQ). The approach was as follows. First, by assuming four VRs and 36 different emission sources, numerical simulations were conducted and validated based on an actual open office on non-uniform concentrations of a surrogate for indoor air pollutants (IAPs) throughout the breathing zone. Second, the pre- and post-purified IAP distributions were obtained using a limited number of sensors and trained by two artificial neural networks. Third, the real-time optimization of PACs’ on/off operation and placements was accomplished by the particle swarm optimization algorithm to balance energy output and improve IAQ simultaneously. Results showed that by deploying four sensors, the predictions of post-purifying concentrations were in acceptable accuracy (i.e., CV-RMSE <2.0%) within 30–40s. Using at most three PACs resulted in a significant decline in local IAP concentration levels. Meanwhile, an average reduction of total energy consumption of MV and PACs was 34.6% compared to using MV to reach the same levels. Overall, this study supports the use of PACs to assist MV in achieving energy efficiency and good IAQ.

Pseudospectral convex optimization for on-ramp merging control of connected vehicles

It can be a daunting task for human drivers to merge into highways because of the intricate vehicle negotiations and potential risk within limited time and space. Connected vehicle (CV) technologies could be a solution to this problem and offer many benefits to the road safety, traffic mobility, and energy efficiency. However, real-time optimal control of CVs is still an open challenge, due to the nonlinear vehicle dynamics, non-convex fuel consumption model, and highly dynamic uncertain inter-vehicle interactions. To tackle these issues, a novel real-time optimal control approach that balances the computational efficiency and solution optimality is proposed for the purpose of onboard application. To this end, the pseudospectral collocation method is integrated with a sequential convex programming approach to develop two new optimization algorithms, which are implemented within a model predictive control (MPC) framework to allow for real-time generation of optimal merging speed profiles. One algorithm leverages the line search technique to improve convergence, and the other benefits from the trust region method for better computational efficiency. The optimality and convergence process of both proposed algorithms are investigated by comparing their solutions with a popular non-linear solver. Simulation results show that the proposed methods outperform the benchmark in terms of computational cost, fuel consumption, and traffic efficiency. In particular, the proposed fuel-economy merging rule can save 57.1% fuel consumption on average on four different traffic volumes. Meanwhile, the proposed optimal control algorithms can reduce 2.2% travel time on average comparing to the “first-in-first-out” merging rule.

Real-time optimization of urban channel gate control based on a segmentation hydraulic model

With the urban water resources becoming increasingly scarce, the optimal control engineering has emerged as a promising approach to improve the efficiency of water use in the environment. A hydraulic model is capable of accurately modeling and predicting the complex hydrodynamic processes occurring within a channel. However, its optimization and simulation time are often prolonged by the complexity of the channel system, resulting in poor real-time performance. This study presents a segmented hydraulic real-time optimization approach that combines rule-based simulation (RS) with real-time optimization (RTO). The aim of the proposed method is to reduce hydraulic model complexity and improve optimization time by dividing the full hydraulic model (FHM) into optimized segmented hydraulic model (SHMO) and non-optimized segmented hydraulic model (SHMN). The approach presents two main improvements: (1) a segmentation point recognition method based on RS is used to obtain SHMO from the FHM; and (2) a segmented optimization framework is employed to enable RTO based on SHMO. We demonstrate the effectiveness of the approach using a case study of China's Qing River. The results indicate that FHM can be successfully divided into SHMO and SHMN with similar simulation effect (R > 0.88 and RMSE < 0.1) by using the segmentation point recognition method, and the segmented hydraulic real-time optimization approach can reduce optimization time (average 68%) of hydraulics model. The case study indicated that the proposed method is a computationally efficient and feasible approach for real-time regulation of urban channel gate control based on hydraulic model.

Real-Time Cost Optimization Approach Based on Deep Reinforcement Learning in Software-Defined Security Middle Platform

In today’s business environment, reducing costs is crucial due to the variety of Internet of Things (IoT) devices and security infrastructure. However, applying security measures to complex business scenarios can lead to performance degradation, making it a challenging task. To overcome this problem, we propose a novel algorithm based on deep reinforcement learning (DRL) for optimizing cost in multi-party computation software-defined security middle platforms (MPC-SDSmp) in real-time. To accomplish this, we first integrate fragmented security requirements and infrastructure into the MPC-SDSmp cloud model with privacy protection capabilities to reduce deployment costs. By leveraging the power of DRL and cloud computing technology, we enhance the real-time matching and dynamic adaptation capabilities of the security middle platform (Smp). This enables us to generate a real-time scheduling strategy for Smp resources that meet low-cost goals to reduce operating costs. Our experimental results demonstrate that the proposed method not only reduces the costs by 13.6% but also ensures load balancing, improves the quality-of-service (QoS) satisfaction by 18.7%, and reduces the average response time by 34.2%. Moreover, our solution is highly robust and better suited for real-time environments compared to the existing methods.

One-Layer Real-Time Optimization Using Reinforcement Learning: A Review with Guidelines

This paper reviews real-time optimization from a reinforcement learning point of view. The typical control and optimization system hierarchy depend on the layers of real-time optimization, supervisory control, and regulatory control. The literature about each mentioned layer is reviewed, supporting the proposal of a benchmark study of reinforcement learning using a one-layer approach. The multi-agent deep deterministic policy gradient algorithm was applied for economic optimization and control of the isothermal Van de Vusse reactor. The cooperative control agents allowed obtaining sufficiently robust control policies for the case study against the hybrid real-time optimization approach.

Real-time optimization of train regulation and passenger flow control for urban rail transit network under frequent disturbances

Urban rail transit networks face frequent delays and oversaturation resulting from unexpected disturbances and high demands during rush hours, which inevitably leads to unstable train operations, poor service experiences, and potential accidents on crowded platforms. This paper explores the train regulation and passenger flow control strategies for large-scale urban rail transit networks. Specifically, we develop a mixed-integer nonlinear programming (MINLP) formulation to improve the punctuality and regularity in train operations, reduce the passenger waiting time, and alleviate the passenger flow burden of platforms, where the dynamic coupling interactions among network-wide passengers, trains and stations are systematically considered. To reduce the computational complexity and satisfy real-time requirements, we particularly devise a real-time optimization approach based on iterative nonlinear programming (INP) combined with Lagrangian relaxation (LR) under the rolling horizon (RH) framework, which effectively disposes of the intractable nonconvexity and constructs the desirable properties of decomposability and parallelism. The original problem is transformed into a sequence of line-level subproblems that can be solved quickly, so as to circumvent the computational burden. Moreover, to verify the effectiveness of our approach, we apply it to address numerical examples on a simplified network and the real-world Beijing Subway network. The realistic case studies illustrate that the proposed approach can reduce the train deviation from the original timetable, the passenger waiting time, and the passenger accumulation risk on the platform, by around 84.92%, 30.34% and 61.42% in comparison with the common rule-based strategy. Additionally, the computation time for the realistic large-scale experiment is acceptable for a real-time implementation.

Tracking necessary condition of optimality by a data-driven solution combining steady-state and transient data

One of the difficulties in practical implementations of the classic Real-Time Optimization (RTO) strategy is the integration between optimization and control layers, mainly due to the differences between the models used in each layer, which may result in unreachable setpoints coming from optimization to the control layer. In this context, Economic Model Predictive Control (EMPC) is a strategy where optimization and control problems are solved simultaneously. However, this strategy is based on the assumption that a nonlinear dynamic model is available, which may not be valid. Also, when considering a first-principles nonlinear model, the computational cost and convergence may be relevant issues. The present work presents an RTO framework based on an EMPC structure considering a Hammerstein model for the plant. This modeling approach can be applied even in the absence of first-principles models. The proposed EMPC considers the minimization of the economic objective function gradient calculated through a steady-state model based on a Gaussian Process. This strategy was applied to the Willians–Otto Reactor benchmark and presented superior results than the classic RTO and Hybrid RTO (H-RTO) approaches in closed-loop and a lower average iteration time than these other approaches.

Dissimilarity-driven ensemble model-based real-time optimization for control of building HVAC systems

Model-based real-time optimization (MRTO) is proven as an effective tool that can capture the complex dynamics of heating, ventilation, and air conditioning (HVAC) systems and improve its energy performance. Despite the energy benefits offered by MRTO, these approaches are rarely implemented in actual buildings. This is due to the reason that these approaches are very difficult to implement because they require the synthesis of a reliable and accurate performance model of the system. The reliability of decision-making with MRTO is directly related to the accuracy of these performance models. In addition, the model has to be computationally efficient for practical implementation. The development of such a model requires the most effort and is a major challenge in the implementation of MRTO. Several HVAC performance models are already available in the literature, and these can be classified as semiphysical models and data-driven models. The semiphysical models are generalized models with simplification assumptions that can provide consistent performance, however, with reduced accuracy. Contrastingly, the data-driven models can offer better accuracy; however, they lack robustness in terms of operational ranges. These factors affect the energy performance of MRTO, and an improper parametrized model could result in performance that is even worse than the conventional fixed setpoint or rule-based approaches. A dissimilarity-driven ensemble model-based real-time optimization (DEMRTO) approach is presented in this study that incorporates a dissimilarity-driven ensemble model in the framework of real-time optimization. The dissimilarity-driven ensemble model combines semiphysical models and data-driven models in a systematic manner to use one's strengths to address others' weaknesses, rather than developing a new form of a model. The performance of the proposed integrated approach was examined using case studies over three weather seasons in Hong Kong. The results showed as compared to the fixed setpoint approach the DEMRTO approach can provide significant energy savings up to 11.085% setpoint, and around 2.785% reduction in energy use as compared with the conventional MRTO approach. It was demonstrated that the proposed approach can capture diversity in load conditions and provide consistency in model prediction to improve reliability in decision-making with real-time optimization.

Multi-Objective Real-Time Tuning of SVC Used in Electrified Traction Systems.

Electric train system is a very large load for the power network. This load consumes a large amount of reactive power. In addition, it causes a massive unbalance to the network, which results in many problems such as voltage drops, high transmission losses, reduction in the transformer output ability, negative sequence current, mal-operation of protective relays, etc. In this paper, a novel real-time optimization approach is presented to adjust the static VAR compensator (SVC) for the traction system to realize two objectives; current unbalance reduction and reactive power compensation. A multi-objective optimization technique entitled non-dominated sorting genetic algorithm (NSGA-II) is used to fulfill the regarded objectives simultaneously. A comprehensive simulator has been designed for electric train network modeling that is able to adjust the parameters of SVC in an optimum manner at any time and under any circumstances. The results illustrate that the provided method can efficiently reduce the unbalancing in current as well as supply the demanded reactive power with acceptable precision.

Analytical RTO for a critical distillation process based on offline rigorous simulation

The economic performance of distillation processes has been always addressed by techniques supporting and completing Model Predictive Control (MPC), which are known as Real Time Optimization (RTO). RTO, via simulation model, has been deeply studied and applied to distillation processes, nevertheless, the cost associated with the development of such online simulation models is often an obstacle for industries to change their operations. Hence, this work presents an unconventional RTO approach, named “analytical RTO”, which calculates the setpoint of manipulated variables according to operating strategy exploiting an analytical generalized formulation. The proposed RTO is built for a specific unit, that is a Propane-Propylene super-fractionator producing polymer grade Propylene (99.5%), and it is based on an offline simulation model developed in UniSim Design. Sensitivities analysis of the revenue with the manipulated variables is obtained with the simulation model and used to derive a simple, yet quite effective analytical RTO formulation, taking into account the fluidynamic limit of the unit studied. Comparing such an approach with the simulations, the results show a satisfactory match of the analytical estimations with the optimal points calculated by the rigorous model.

Feedback attitude control of spacecraft using two single gimbal control moment gyros

In this paper, feedback attitude control of an underactuated spacecraft with two single gimbal control moment gyros (SGCMGs) is considered. For a two-SGCMG system in an arbitrary configuration, a feedback control method based on a real-time optimization approach is proposed. Here, the gimbal angle trajectories as the solution to the minimum-time control are parameterized by the time polynomials, and their coefficients are modified at each sampling period. Numerical simulations are performed to demonstrate the validity of the proposed method as well as a certain robustness against unmodeled dynamics. Furthermore, the experimental verification is also conducted to demonstrate the actual effectiveness.

Data-based approach for wing shape design optimization

Aircraft design is a trade-off among different objectives and constraints, so multiple design rounds are usually required. Aerodynamic shape optimization based on high-fidelity computational fluid dynamics is consequently expensive, especially for wing design in the transonic regime. To address the interactive demand in aircraft design, we present a data-based approach to real-time high-fidelity wing shape optimization. Accurate and fast data-based models are constructed to perform aerodynamic analyses in lieu of costly computational fluid dynamic simulations. For the versatility of the data-based models, 135,108 training data that cover wing samples of different aerodynamic shapes, flight speeds, and flight altitudes are used. The verification on 47,967 wings shows that mean relative errors of CL, CD, and CM compared to computational fluid dynamic simulations are all within 0.4%. The models are further verified in multiple single-point, multi-point, and multi-objective wing design optimization problems. The optimized wings have similar shapes to those obtained by computational-fluid-dynamics-based optimization, and the differences in CD are merely one∼two counts. These results demonstrate the effectiveness of the data-based approach to fast and high-fidelity wing design. This work showcases a real-time high-fidelity optimization approach to high-dimensional nonlinear engineering problems using data-based models.

Deep neural networks-based real-time optimal navigation for an automatic guided vehicle with static and dynamic obstacles

In this paper, a hybrid-intelligent real-time optimal control approach based on deep neural networks (DNNs) is proposed to improve the autonomy and intelligence of automatic guided vehicles (AGVs) navigation control. We first formulate the motion planning problem of an AGV with static and dynamic obstacles as a nonlinear optimal control problem (OCP). Subsequently, a direct method incorporating a smooth transformation technique is utilized to obtain the high-fidelity optimal solutions off-line. The optimal state-action samples are then extracted from the optimal trajectories generated by the OCP from perturbed initial states and stored as a large optimal trajectory data set. Thereafter, the DNNs architecture is designed and trained off-line through the collected data set to learn the optimal state-action relationship. As a result, the well-trained DNNs are used to produce the corresponding to optimal feedback actions on-board. The main advantage of our approach is that the time-consuming computation process is only carried out off-line and thus the traditional repeated off-line planning for the AGV due to changes such as the perturbed initial conditions in the system can be effectively avoided. Numerical experimental results are carried out to demonstrate our designed DNNs-based optimal control approach can generate the optimal control instructions on-board to steer the AGV to the desired location with high robustness to initial conditions as well as satisfying different obstacle constraints.

A Real-Time-Capable Closed-Form Multi-Objective Redundancy Resolution Scheme for Seven-DoF Serial Manipulators

Using a closed-form inverse kinematics solution for motion planning has many advantages compared to traditional numerical approaches, most notably much faster computation times and better suitability for real-time applications. Steady progress has been made to develop an analytic inverse kinematics solution for seven degrees of freedom (DoF) manipulators without joint offsets. Redundancy resolutions have been proposed to push the individual joint angles away from their limits. However, no further objectives are considered in these closed-form solutions. We propose a multi-objective real-time optimization approach that is able to minimize joint velocities and accelerations, while still avoiding joint limits. A closed-form solution to the optimization is derived, which only requires a single intuitive tuning parameter. We provide a free and open-source software implementation of the full kinematics algorithm that covers the complete solution space. The null-space motion resulting from our method is evaluated, achieving faster motion times and smoother arm motions along Cartesian paths in comparison to the state-of-the-art approach. Finally, experimental results with a KUKA iiwa robot are reported.

Real-Time Optimal Approach and Capture of ENVISAT Based on Neural Networks

A neural network-based controller is developed to enable a chaser spacecraft to approach and capture a disabled Environmental Satellite (ENVISAT). This task is conventionally tackled by framing it as an optimal control problem. However, the optimization of such a problem is computationally expensive and not suitable for onboard implementation. In this work, a learning-based approach is used to rapidly generate the control outputs of the controller based on a series of training samples. These training samples are generated by solving multiple optimal control problems with successive iterations. Then, Radial Basis Function (RBF) neural networks are designed to mimic this optimal control strategy from the generated data. Compared with a traditional controller, the neural network controller is able to generate real-time high-quality control policies by simply passing the input through the feedforward neural network.

Real-time optimal control for irregular asteroid landings using deep neural networks

To improve the autonomy and intelligence of asteroid landing control, a real-time optimal control approach is proposed using deep neural networks (DNN) to achieve precise and robust soft landings on asteroids with irregular gravitational fields. First, to reduce the time consumption of gravity calculation, DNNs are used to approximate the irregular gravitational fields of asteroids based on the samples calculated by a polyhedral method. Second, an approximate indirect method is presented to solve the time-optimal landing problems with high computational efficiency by taking advantage of the trained DNN-based gravity model and a homotopic technique. Then, five DNNs are developed to learn the functional relationship between the state and optimal actions obtained by the approximate indirect method, The resulting DNN-based landing controller can generate the optimal control instructions according to the flight state and achieve the real-time optimal control for asteroid landings. Finally, simulation results of the time-optimal landings for Eros are given to substantiate the effectiveness of these techniques and illustrate the real-time performance, control optimality, and robustness of the developed DNN-based optimal landing controller.

Mixed-Integer Nonlinear Programming (MINLP) for production optimisation of naturally flowing and artificial lift wells with routing constraints

Real-time decision making by production engineers in a petroleum field can be very challenging, especially when multiple wells with diverse operating conditions and production behaviours are present. Hence, semi-analytic or heuristic procedures are unlikely to yield an optimal operating strategy. This study implements a Real-Time Production Optimisation (RTPO) approach to maximising production from naturally flowing, gas-lifted and Electrical Submersible Pump (ESP)-assisted wells while satisfying multiple operational constraints. This is achieved via the application of reduced order models which are developed by querying a black box production network simulator multiple times using different inputs. Also exploited in this work is the inherent decomposable property of the production network into smaller components (wells, valves pipelines and separators), such that mass balance equations comprise the algebraic constraints of the optimisation framework which is solved as a MINLP. The adopted formulation also offers the advantage of flexibility for problem adjustment under different practical operating conditions which are presented as case studies. The changes incorporated into the production system include: increased liquid handling capacity of downstream separators, decreased well productivity/increased water cut and well intervention problems. The ability of the adopted framework to provide accurate and speedy computations of the optimal production scenario makes it reliable for real-time decision support.

Real-Time Optimal Control for Spacecraft Orbit Transfer via Multiscale Deep Neural Networks

This study is motivated by the requirement of on-board trajectory optimization with guaranteed convergence and real-time performance for optimal spacecraft orbit transfers. To this end, a real-time optimal control approach is proposed using deep learning technologies to obtain minimum-time trajectories of solar sail spacecraft for orbit transfer missions. First, the minimum-time two-dimensional orbit transfer problem is solved by an indirect method, and the costate normalization technique is introduced to increase the probability of finding the optimal solutions. Second, by making novel use of deep learning technologies, three deep neural networks are designed and trained offline by the obtained optimal solutions to generate the guidance commands in real time during flight. Consequently, the long-standing difficulty of on-board trajectory generation is resolved. Then, an interactive network training strategy is presented to increase the success rate of finding optima by supplying good initial guesses for the indirect method. Moreover, a multiscale network cooperation strategy is designed to deal with the recognition deficiency of deep neural networks (DNNs) with small input values, which helps achieve highly precise control of terminal orbit insertion. Numerical simulations are given to substantiate the efficiency of these techniques, and illustrate the effectiveness and robustness of the proposed DNN-based trajectory control for future on-board applications.

Adaptive modeling for reliability in optimal control of complex HVAC systems

The model-based real-time optimization (MRTO) of heating, ventilation, and air-conditioning (HVAC) systems is an efficient tool for improving energy efficiency and for effective operation. Model-based real-time optimization of HVAC systems needs to regularly optimize the set points for local-loop operation, taking into account the interactions between HVAC components with the help of system-performance models. MRTO relies on the accuracy of the performance model to provide reliability in decision making. In practice, due to high diversity in ambient conditions and load demands, system-model mismatches are difficult to avoid. This paper presents an adaptive, model-based, real-time optimization (AMRTO) approach for large-scale, complex HVAC systems, to counter any model mismatches by updating the performance model in real time with real-time measurements. Furthermore, to make this approach practically applicable and to keep the online training process computationally manageable, an empirical-physical model of HVAC system components was set up that is suitable for online training, and hybrid genetic algorithms (HGAs) method was used for faster, yet reliable, online training of the performance model. A case study was used to evaluate the performance of the proposed approach. The results demonstrated that the proposed AMRTO was able to provide energy saving approximately 8% and reduce the online computational burden by 99%.

An Integrated Frequent RTO and Adaptive Nonlinear MPC Scheme Based on Simultaneous Bayesian State and Parameter Estimation

Changes in process parameters and measured/unmeasured disturbances shift the optimal point at which the economic benefits are maximized. Combinations of real time optimization (RTO) techniques, which periodically determine the economically optimum operating point using steady state optimization, and model predictive control (MPC) have been widely employed in the process industry for operating process plants optimally in the face of drifting disturbances and/or parameters. Due to the long wait time between two successive RTO invocations and model inconsistency between the RTO and MPC layers, the conventional RTO schemes can end up operating the plant suboptimally if the process parameters/unmeasured disturbances change significantly during the wait time. Recently proposed frequent RTO approaches attempt to address this difficulty by increasing the frequency of RTO invocation. An online update of the steady state model employed by the RTO layer using dynamic operating data is a major concern in implementati...