Optimal Control Of Systems Research Articles

Improved intelligent model predictive controller for the nuclear power reactor system

Abstract Over the last two decades, extensive research has been conducted to enhance the control performance of reactor power. Various methodologies have been suggested and implemented to achieve optimal power control in nuclear reactors. However, due to the diverse characteristics and inherent uncertainties in the models, devising optimal controllers for nuclear systems remains a complex task. To address this, numerous approaches have been adopted to ensure controllability and resilience, aiming for an optimal nuclear power reactor controller. The Model Predictive Control (MPC) algorithm has garnered significant attention as a viable approach to boost operational efficiency and overall system utility. In this research, Particle Swarm Optimization (PSO) method and MPC controller are combined together to form a novel algorithm termed PSO-MPC, aiming to amplify the system’s performance and overcomes the local minima problem that basically happens when using MPC controller. First, MPC controller is applied to the nuclear reactor model, then the suggested technique PSO-MPC also is applied to the system and a comparison of the outcomes using both techniques is done. The results demonstrate enhanced system response using the innovative technique.

Optimization of the integro-differential hyperbolic model

We consider a model of processes in viscoelastic media. The force arising inside the body may depend not only on the current values but also on the entire time history of the motion (for example, polymers, emulsions, and suspensions exhibit memory properties). Such processes often lead to the necessity of studying hyperbolic integro-differential equations with Volterra integral term. The main goal is to prove the existence and uniqueness of generalized solutions to the corresponding initial-boundary value problem, as well as to investigate the existence of optimal control for systems described by these models. The main results are obtained using the method of a priori inequalities in negative norms. In particular, we justify inequalities in negative norms for the integro-differential operator in certain functional spaces. The work begins with a short description of relevant results with similar formulations and referencing works with physical justification of the model. Afterwards, we describe the problem statement, constraints on equation parameters, and functional spaces used for the investigation. Below are the main results, in particular definitions of generalized solutions and properties on the well-posed of the initial-boundary value problem as well as the existence of optimal control. Control is carried out through the right-hand side of the equation using a certain special operator. It is possible to examine specific examples of such control operators (illustrating various control mechanisms) and the corresponding control spaces. By utilizing proven inequalities and relying on general results of S.I. Lyashko from the theory of a priori inequalities in negative norms, we establish sufficient conditions for the existence of optimal control. In particular, we impose the restrictions on the admissible set of controls and the quality criterion.

Data-enhanced convolutional network based on air conditioning system start/stop time prediction

Most enterprise workshop operators frequently adjust the start/stop time of air conditioning systems based on indoor and outdoor temperatures and humidity to accommodate changing demand and weather conditions. However, relying on personal subjective experience for these adjustments often leads to operational delays or energy waste due to the lack of precision in determining optimal timing. Predicting air conditioning system start and stop times is crucial for energy consumption and savings in HVAC systems. Traditional data-driven methods have been insufficient in this regard, as they mainly focus on feature mapping and overlook the dynamic coupling relationships of process variables, resulting in subpar predictions. In response to this challenge, the paper introduces a novel approach known as the Periodicity and Long-Term Convolutional Neural Network (PLCNN). This method converts one-dimensional regression prediction data into two-dimensional data containing time series features to capture the dynamic coupling characteristics of the air conditioning system while maintaining the independent variation relationships of features. Experimental results using real factory floor data have demonstrated the superior performance of the PLCNN method. Specifically, this method achieved a 14.96% lower error rate compared to the traditional method and an 8.18% improvement compared to the deep learning method. Moreover, the implementation of the PLCNN method in the optimal control of air conditioning systems led to a significant 19.43% reduction in total monthly energy consumption. In conclusion, the proposed method offers a promising alternative to traditional approaches to forecasting and provides a solution to the common challenges encountered in traditional prediction tasks.

Optimization of batch cooling crystallization systems considering crystal growth, nucleation and dissolution. Part I: Simulation

Optimal control of batch crystallization systems is still a focus and hot topic in the field of industrial crystallization, which seriously affects the consistency of batch product quality. In this paper, a new method with a new objective function and improved optimization algorithm was proposed for optimization of crystal size distribution (CSD) in case of fine crystals occurrence. The new objective function was developed with better margin metric and weighting technique to minimize fine crystal mass, meanwhile, a newly constructed sinusoidal weight function was introduced to improve the particle swarm optimization (PSO) algorithm. A precise control of CSD with suppressed numerical discrepancy caused by fine crystals removal was developed by combining seed recipe and temperature-swing. In addition, the effects of temperature curve segments on CSD during process optimization were systematically investigated to achieve optimal results. Two typical batch cooling crystallization systems were used to verify the effectiveness of the proposed method in controlling product CSD while minimizing fine crystal mass. Results demonstrated that the desired product CSD can be achieved with minor errors while the fine crystals could be shrunk to be negligible, i.e., the fine crystal mass and number can be reduced by over 90%. This work has an important guiding significance for the removal of fine crystals in industrial crystallization processes, especially when only operational optimization rather than equipment updating is considered.

Optimal dimensioning of renewable energy generation and storage systems

With high energy demand and large available area, agricultural farms offer significant potential for renewable energy investments, like photovoltaic systems and electrical energy storages. However, the profitability of such investments depends strongly on self-consumption, so accurate planning requires computation-intensive simulation and optimization considering local consumption. This study presents a novel methodology for the optimal dimensioning and configuration of photovoltaic systems and electrical energy storages using efficient techniques from continuous non-linear optimization. Combining physical and economic models with measured consumption data, an investment’s net present value over 20 years is maximized. Using gradient-based solver WORHP, the simulation, optimal control, and optimal dimensioning of the local energy system are calculated simultaneously, allowing for efficient computation over an entire year of hourly data to capture both daily and seasonal variations.The approach is demonstrated with simple use cases, including an exemplary day of a dairy farm’s consumption, for which optimal systems with and without storage achieve 77% and 43% of autarky, respectively. Saturation effects of optimal plant size can be observed when sizes are large enough for optimal self-consumption but not expanded further for grid export. With energy storage, this saturation is reached at higher values. Optimizing photovoltaic plants with different orientations to match the specific consumption patterns characteristic of the dairy farm achieves similar autarky as a single plant while reducing investment costs by more than 20%. While thorough validation and comparison against heuristic methods predominantly used in the field is part of ongoing research, the presented use cases demonstrate the flexibility and efficiency of the proposed method and highlight its promise as a planning tool in the agricultural domain and beyond.

Barrier-critic-disturbance approximate optimal control of nonzero-sum differential games for modular robot manipulators

In this paper, for addressing the safe control problem of modular robot manipulators (MRMs) system with uncertain disturbances, an approximate optimal control scheme of nonzero-sum (NZS) differential games is proposed based on the control barrier function (CBF). The dynamic model of the manipulator system integrates joint subsystems through the utilization of joint torque feedback (JTF) technique, incorporating interconnected dynamic coupling (IDC) effects. By integrating the cost functions relevant to each player with the CBF, the evolution of system states is ensured to remain within the safe region. Subsequently, the optimal tracking control problem for the MRM system is reformulated as an NZS game involving multiple joint subsystems. Based on the adaptive dynamic programming (ADP) algorithm, a cost function approximator for solving Hamilton–Jacobi (HJ) equation using only critic neural networks (NN) is established, which promotes the feasible derivation of the approximate optimal control strategy. The Lyapunov theory is utilized to demonstrate that the tracking error is uniformly ultimately bounded (UUB). Utilizing the CBF’s state constraint mechanism prevents the robot from deviating from the safe region, and the application of the NZS game approach ensures that the subsystems of the MRM reach a Nash equilibrium. The proposed control method effectively addresses the problem of safe and approximate optimal control of MRM system under uncertain disturbances. Finally, the effectiveness and superiority of the proposed method are verified through simulations and experiments.

Optimal control of discrete event systems under uncertain environment based on supervisory control theory and reinforcement learning

Discrete event systems (DESs) are powerful abstract representations for large human-made physical systems in a wide variety of industries. Safety control issues on DESs have been extensively studied based on the logical specifications of the systems in various literature. However, when facing the DESs under uncertain environment which brings into the implicit specifications, the classical supervisory control approach may not be capable of achieving the performance. So in this research, we propose a new approach for optimal control of DESs under uncertain environment based on supervisory control theory (SCT) and reinforcement learning (RL). Firstly, we use SCT to gather deliberative planning algorithms with the aim to safe control. Then we convert the supervised system to Markov Decision Process simulation environments that is suitable for optimal algorithm training. Furthermore, a SCT-based RL algorithm is designed to maximize performance of the system based on the probabilistic attributes of the state transitions. Finally, a case study on the autonomous navigation task of a delivery robot is provided to corroborate the proposed method by multiple simulation experiments. The result shows the proposed approach owning 8.27%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} performance improvement compared with the non-intelligent methods. This research will contribute to further studying the optimal control of human-made physical systems in a wide variety of industries.

Numerical optimal control for nonlinear dynamical systems involving mixed-valued inputs and joint probability path-constraints

Numerical optimal control for nonlinear dynamical systems involving mixed-valued inputs and joint probability path-constraints

Integrating reinforcement learning and supervisory control theory for optimal directed control of discrete-event systems

Directed control is crucial for implementing controllers on programmable logic controllers. A directed controller is one that actively selects at most one controllable event (control command) to execute at any instant. This study investigates the numerical optimization problem of directed control for discrete-event systems, such as traffic systems and robotic systems. By integrating supervisory control theory and reinforcement learning, an algorithmic procedure is designed to synthesize an optimal directed controller, which minimizes the total cost associated with event execution while ensuring the safety and liveness of the controlled system. Two improved Q-learning algorithms incorporating dynamic parameter adaptation strategies are developed to enhance the global search ability of basic Q-learning. To demonstrate applicability and effectiveness, we apply the proposed method to control a guideway system and a multi-train traffic system, respectively. The experimental results indicate the superiority of the proposed method over the comparison methods.

VAN-DAMME: GPU-accelerated and symmetry-assisted quantum optimal control of multi-qubit systems

We present an open-source software package, VAN-DAMME (Versatile Approaches to Numerically Design, Accelerate, and Manipulate Magnetic Excitations), for massively-parallelized quantum optimal control (QOC) calculations of multi-qubit systems. To enable large QOC calculations, the VAN-DAMME software package utilizes symmetry-based techniques with custom GPU-enhanced algorithms. This combined approach allows for the simultaneous computation of hundreds of matrix exponential propagators that efficiently leverage the intra-GPU parallelism found in high-performance GPUs. In addition, to maximize the computational efficiency of the VAN-DAMME code, we carried out several extensive tests on data layout, computational complexity, memory requirements, and performance. These extensive analyses allowed us to develop computationally efficient approaches for evaluating complex-valued matrix exponential propagators based on Padé approximants. To assess the computational performance of our GPU-accelerated VAN-DAMME code, we carried out QOC calculations of systems containing 10 - 15 qubits, which showed that our GPU implementation is 18.4× faster than the corresponding CPU implementation. Our GPU-accelerated enhancements allow efficient calculations of multi-qubit systems, which can be used for the efficient implementation of QOC applications across multiple domains. Program summaryProgram Title: VAN-DAMMECPC Library link to program files::https://doi.org/10.17632/zcgw2n5bjf.1Licensing provisions: GNU General Public License 3Programming language: C++ and CUDANature of problem: The VAN-DAMME software package utilizes GPU-accelerated routines and new algorithmic improvements to compute optimized time-dependent magnetic fields that can drive a system from a known initial qubit configuration to a specified target state with a large (≈1) transition probability.Solution method: Quantum control, GPU acceleration, analytic gradients, matrix exponential, and gradient ascent optimization.

Analysis of a Dry Friction Force Law for the Covariant Optimal Control of Mechanical Systems with Revolute Joints

This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control.

ADP-based adaptive control of ship course tracking system with prescribed performance

In this paper, an adaptive dynamic programing (ADP)-based adaptive control problem is studied for the ship course tracking system with prescribed performance. Firstly, the complex sea conditions will bring difficulty to ship course tracking when unmanned ship sailing on sea. In order to overcome this difficulty, a prescribed performance feedforward term is designed in the controller to improve the course tracking ability of ship. Secondly, by defining a cost function, an ADP technology is exploited to achieve an optimal control of ship course tracking system. Finally, the stability of the closed loop system is turned out by Lyapunov stability theory and all signals are uniformly ultimately bounded (UUB). Simulation results validate the effectiveness of the proposed method.

Real-time optimal hierarchy control of HVAC system with maximized ancillary service support in smart buildings: An experimental approach

This article proposes a real-time optimum control algorithm for Heating, Ventilation, and Air Conditioning (HVAC) units of a commercial building aimed to maximize the ancillary power available for frequency regulation services. First, the prediction of energy consumption of air conditioning zones using long short-term memory (LSTM) is achieved, which helps forecast the aggregated regulation capacity bid of the building in the energy markets. Furthermore, to minimize energy costs and thermal discomfort of building dwellers, an optimization algorithm is designed considering the day-ahead electricity tariffs. Moreover, using installed sensors in a lab-scaled hardware prototype, the proposed algorithm is also shown to be capable of interacting with a Building Energy Management System (BEMS) and investigating the electrical and thermal properties of the HVAC unit. The BEMS controller uses an ethernet protocol to interface with the sensors installed at various operational points throughout the HVAC system. The optimal operation of the HVAC system has been executed with the real-time thermal feedback system, which counterbalances the uncertain thermal load or renewable power availability in the building confronted in real-time operation. The simulation results show the performance of the Artificial Neural Network (ANN) based compressor model in deep learning integrated with the other components of the HVAC unit and thermal model of the air-conditioning zone. Finally, the experimental results display the real-time implementation of multiple thermal and electrical conditions within the proposed control scheme of the HVAC unit. This shows the potential of ancillary services capacity through commercial buildings can be maximized with flexible loads and thereby help in power grid support.

Machine learning model‐based optimal tracking control of nonlinear affine systems with safety constraints

AbstractThis work focuses on the development of a machine learning (ML) model‐based framework for safe optimal tracking control of a class of nonlinear control‐affine systems to ensure simultaneous closed‐loop stability and safety. Specifically, a novel multilayer feedforward neural network (FNN) with a control‐affine architecture is designed to model nonlinear dynamic systems. Subsequently, a model‐based reinforcement learning (RL) framework is presented, utilizing a novel cost function with Control Lyapunov‐Barrier Function (CLBF) properties, to learn both the control policy and the optimal value function for an infinite‐horizon optimal tracking control problem for nonlinear systems with safety constraints. The efficacy of the proposed methodology is demonstrated through simulations of a one‐link robot manipulator and a chemical process example.

Knowledge-Data Driven Optimal Control for Nonlinear Systems and Its Application to Wastewater Treatment Process.

Optimal control is developed to guarantee nonlinear systems run in an optimum operating state. However, since the operation demands of systems are dynamically changeable, it is difficult for optimal control to obtain reliable optimal solutions to achieve satisfying operation performance. To overcome this problem, a knowledge-data driven optimal control (KDDOC) for nonlinear systems is designed in this article. First, an adaptive initialization strategy, using the knowledge from historical operation information of nonlinear systems, is employed to dynamically preset parameters of KDDOC. Then, the initial performance of KDDOC can be enhanced for nonlinear systems. Second, a knowledge guide-based global best selection mechanism is used to assist KDDOC in searching for the optimal solutions under different operation demands. Then, dynamic optimal solutions of KDDOC can be obtained to adapt to flexible changes in nonlinear systems. Third, a knowledge direct-based exploitation mechanism is presented to accelerate the solving process of KDDOC. Then, the demand response speed of KDDOC can be improved to ensure nonlinear systems with optimal operation performance in different states. Finally, the performance of KDDOC is validated on a simulation and a practical process. Several experimental results illustrate the effectiveness of the proposed optimal control for nonlinear systems.

Dynamic event-triggered optimal control for stochastic interconnected nonlinear systems with matched disturbances via adaptive dynamic programming

This paper presents a dynamic event-triggered adaptive dynamic programming (DETADP) algorithm to study the optimal control issue of stochastic interconnected nonlinear systems with matched disturbances. By constructing an improved cost function related to the actuator faults for each auxiliary subsystem, the original control issue is converted into finding an array of decentralized optimal control policies. In order to eliminate the effect of matching perturbations, an integral sliding mode control strategy is developed using the DETADP algorithm to ensure optimal performance for general nonlinear dynamics. When the system trajectories converge to a sliding-mode surface, equivalent sliding mode dynamics are transformed into reformulated auxiliary systems with a modified cost function. Then, a DETADP algorithm is introduced under an identifier-critic network framework, where the identifier aims to determine the stochastic dynamic, the critic aims to acquire the solutions of Hamilton–Jacobi–Bellman(HJB) equations. Furthermore, a novel dynamic event-triggering condition is designed to determine the occurrence of an event by introducing a dynamic variable. By using the Lyapunov stability theory, all signals in the closed-loop system are proved to be uniformly ultimately bounded. Finally, practical simulation examples are conducted to validate the effectiveness of the designed method.

Optimal Consensus Control for Continuous-Time Linear Multiagent Systems: A Dynamic Event-Triggered Approach.

This article investigates the optimal consensus problem for general linear multiagent systems (MASs) via a dynamic event-triggered approach. First, a modified interaction-related cost function is proposed. Second, a dynamic event-triggered approach is developed by constructing a new distributed dynamic triggering function and a new distributed event-triggered consensus protocol. Consequently, the modified interaction-related cost function can be minimized by applying the distributed control laws, which overcomes the difficulty in the optimal consensus problem that seeking the interaction-related cost function needs all agents' information. Then, some sufficient conditions are obtained to guarantee optimality. It is shown that the developed optimal consensus gain matrices are only related to the designed triggering parameters and the desirable modified interaction-related cost function, relaxing the constraint that the controller design requires the knowledge of system dynamics, initial states, and network scale. Meanwhile, the tradeoff between optimal consensus performance and event-triggered behavior is also considered. Finally, a simulation example is provided to verify the validity of the designed distributed event-triggered optimal controller.

Optimal control of automatic voltage regulator system using hybrid PSO-GWO algorithm-based PID controller

Optimal control of automatic voltage regulator system using hybrid PSO-GWO algorithm-based PID controller

Constrained Reinforcement Learning-Based Closed-Loop Reference Model for Optimal Tracking Control of Unknown Continuous-Time Systems

Constrained Reinforcement Learning-Based Closed-Loop Reference Model for Optimal Tracking Control of Unknown Continuous-Time Systems

Optimal Bipartite Tracking Control for Heterogeneous Systems Under DoS Attacks

Optimal Bipartite Tracking Control for Heterogeneous Systems Under DoS Attacks