Optimal Control Approach Research Articles

Intelligent Control Framework for Improving Energy System Stability Through Deep Learning-Based Modal Optimization Scheme

Ensuring the stability of power systems is essential to promote energy sustainability. The integrated operation of these systems is critical in sustaining modern societies and economies, responding to the increasing demand for electricity and curbing environmental consequences. This study focuses on the optimization of energy system stability through the coordination of power system stabilizers (PSSs) and power oscillation dampers (PODs) in a single-machine infinite bus energy grid configuration that has flexible AC alternating current transmission system (FACTS) devices. Intelligent control strategies using PSS and POD techniques are suggested to increase power system stability and generate supplementary control signals for both the generator excitation system and FACTS device switching control. An intelligent optimal modal control framework equipped with deep learning methods is introduced to control the generator excitation system and thyristor-controlled series capacitor (TCSC). By optimally choosing the weighting matrix Q and implementing close-loop pole shifting, an optimal modal control approach is formulated. To harness its adaptive potential in fine-tuning controller parameters, an auxiliary deep learning-based optimization algorithm with actor–critic architecture is implemented. This comprehensive technique provides a promising path to effectively reduce electromechanical oscillations, thereby enhancing voltage regulation and transient stability in power systems.

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.

Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

AbstractReal-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach. The Brown–McPhee model has been used to characterize the joint friction in the system. This model is suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. This novel methodology supports codesign of the multibody system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems, where the actuation and design are highly dependent on each other. Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

Women Empowerment Status in India: Mathematical Modelling and Optimal Control Approach

Women Empowerment Status in India: Mathematical Modelling and Optimal Control Approach

Shortest-path recovery from signature with an optimal control approach

AbstractIn this paper, we consider the signature-to-path reconstruction problem from the control-theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. In order to do that, we minimize a cost functional consisting of two competing terms, i.e., a weighted final-time cost combined with the $$L^2$$ L 2 -norm squared of the controls. Moreover, we can show that, by taking the limit to infinity of the parameter that tunes the final-time cost, the problem $$\Gamma $$ Γ -converges to the problem of finding a sub-Riemannian geodesic connecting two signatures. Finally, we provide an alternative reformulation of the latter problem, which is particularly suitable for the numerical implementation.

A nonlinear optimal control approach for dual-arm robotic manipulators

A nonlinear optimal control approach for dual-arm robotic manipulators

A Robust Super Twisting Controller Algorithm for Dual Star Induction Motor Based on Particle Swarm Optimization Algorithm

This research introduces an optimized control approach for a dual star induction motor (DSIM) using a combination of the Super Twisting Algorithm (STA) and Particle Swarm Optimization Algorithm (PSO) within the framework of indirect field-oriented control (IFOC) and two pulse width modulation (PWM) voltage sources. The primary aim of this study is to reduce torque fluctuations, minimize variations in stator current, and enhance the precision of speed control. The DSIM consists of two sets of three-phase windings with separate neutrals and a 30-degree electrical phase shift. The utilization of the STA control method addresses issues related to response time, steady-state error, and the impact of load disturbances, ultimately improving speed control. The Simulation conducted in MATLAB/SIMULINK are used to compare the performance of the proposed STA-PSO controller against a conventional Proportional-Integral (PI) controller. The outcomes demonstrate the substantial enhancements achieved by the STA-PSO controller in speed control, including reduced response time, improved steady-state error, and increased resilience against external disturbances. The proposed STA-PSO control strategy effectively mitigates torque and stator currents fluctuations in DSIM’s while offering superior speed control performance. These findings underscore the potential of the STA controller for enhancing control in various DSIM applications.

A Decoupled Feedback and Fast Norm Optimal Control approach for Normal and Superconducting RF Cavity disturbances compensation

Iterative learning controller (ILC)s of different types have been used in various engineering applications for system control in presence of repetitive disturbance, often encountered in batch control systems. A particle accelerator usually comprising of Radiofrequnecy (RF) cavities, when operated in pulsed mode processes particle beam similar to that in batch systems. However, an injected particle beam disturbs electric field inside RF cavity. In additions to beam loading disturbance encountered in all types of RF cavities, a superconducting cavity also encounters disturbance due to Lorentz force detuning. Under presence of such persisting disturbance/s, a Fast Norm Optimal ILC (FNOILC), helps achieve specified amplitude and phase stability of electric field, which results in beam of specified quality. A sophisticated control system helps achieve this objective. In this paper, FNOILC technique is explored for this purpose. Though, it has been reported for few accelerator facilities, in this work, a decoupling strategy is used in a feedback control loop, resulting into overall enhancement of control performance. Behavioral model of RF cavity is represented as dual input dual output system exhibiting two loops, found interacting due to nonzero cavity detuning. A decoupler is designed based on well known technique/s used in process control applications. Relative gain array element values are used to quantify interaction. In presence of beam loading disturbance, a FNOILC demonstrates an excellent control performance. A standard performance index has been used to assess control performance. It is found that use of decoupler in main feedback loop of RF cavity, enhances the resulting performance index. Besides, an ILC performance needs assessment with practical issues like model uncertainty, sensing delays, high detuning and observation noise. In this paper, most of conclusions are drawn based on large number of modeling and simulation studies carried out for lab prototype 650MHz cavity. Interesting studies like effects of low controller sampling frequency, feedback controller gain tuning, severe detuning, etc. are presented using a novel state plane representation. A zero phase filtering is simulated and proposed as an effective strategy when measurements have noise. This paper forms a case study which can be applied to any general system encountering repetitive disturbance. Additionally, paper also elaborates on FNOILC algorithm application for Lorentz force detuning compensation often encountered in superconducting cavity during pulse mode of operation.

A lie group PMP approach for optimal stabilization and tracking control of autonomous underwater vehicles

AbstractIn this research, we explore a finite horizon optimal stabilization and tracking control scheme for the dynamical model of a 6‐DOF Autonomous Underwater Vehicle (AUV). Dynamical equations of the AUV are represented in a Lie group () framework, encompassing both translational and rotational motions. Utilizing a left Lie group action on , we define error function for velocities via a right transport map to effectively address optimal trajectory tracking. The optimal control objective is formulated as a trade‐off problem, aiming to minimize both errors and control effort simultaneously. Left action on yields the left trivialized Hamiltonian function from which the concomitant state and costate dynamical equations are derived using Pontryagin's Minimum Principle (PMP). Consequently, the resulting two‐point boundary value problem is solved to obtain optimal trajectories. We demonstrate the optimality of the resulting solution obtained from the derived control law. For ensuring boundedness in the presence of small disturbances, this study incorporates the effects of internal parametric uncertainties associated with added mass and inertia components, along with the influence of external disturbances induced by ocean currents. Through simulation validations, we confirm the alignment of our results with the theoretical developments, demonstrating that the proposed control law effectively mitigates both parametric uncertainties and ocean current disturbances.

Modeling the Effects of Temperature in Enzymatic Biodiesel Synthesis of Jatropha Oil: An Optimal Control Approach.

Biodiesel, an alternative to diesel, is produced through the enzymatic transesterification of vegetable oil or animal fats. Enzymatic transesterification of oil is gaining more importance, as this method possesses no such disadvantages that are associated with the chemical process. Temperature is the most important factor in enzymatic transesterification for biodiesel synthesis. In this study, a mathematical model is developed to understand the effects of temperature on the enzymatic transesterification of Jatropha curcas oil. Reaction rates are expressed as a function of temperature using an appropriate function, and the effects of temperature on the overall enzymatic system are investigated using the mathematical model. A suitable temperature is determined using the mathematical model, keeping the other reaction conditions unchanged that gives maximum yield. Furthermore, an optimal control problem (OCP) is formulated to identify the temperature control strategy that maximizes the biodiesel yield while minimizing production costs. Simulated outcomes obtained from the mathematical model are analogized with the experimental results to make them acceptable. The optimal profile of temperature is determined from the developed OCP, which maximizes the biodiesel yield.

Artificial neural network-based control of powered knee exoskeletons for lifting tasks: design and experimental validation

Abstract This study introduces a hybrid model that utilizes a model-based optimization method to generate training data and an artificial neural network (ANN)-based learning method to offer real-time exoskeleton support in lifting activities. For the model-based optimization method, the torque of the knee exoskeleton and the optimal lifting motion are predicted utilizing a two-dimensional (2D) human–exoskeleton model. The control points for exoskeleton motor current profiles and human joint angle profiles from cubic B-spline interpolation represent the design variables. Minimizing the square of the normalized human joint torque is considered as the cost function. Subsequently, the lifting optimization problem is tackled using a sequential quadratic programming (SQP) algorithm in sparse nonlinear optimizer (SNOPT). For the learning-based approach, the learning-based control model is trained using the general regression neural network (GRNN). The anthropometric parameters of the human subjects and lifting boundary postures are used as input parameters, while the control points for exoskeleton torque are treated as output parameters. Once trained, the learning-based control model can provide exoskeleton assistive torque in real time for lifting tasks. Two test subjects’ joint angles and ground reaction forces (GRFs) comparisons are presented between the experimental and simulation results. Furthermore, the utilization of exoskeletons significantly reduces activations of the four knee extensor and flexor muscles compared to lifting without the exoskeletons for both subjects. Overall, the learning-based control method can generate assistive torque profiles in real time and faster than the model-based optimal control approach.

Malware containment with immediate response in IoT networks: An optimal control approach

The exponential growth of Internet of Things (IoT) devices has triggered a substantial increase in cyber-attacks targeting these systems. Recent statistics show a surge of over 100 percent in such attacks, underscoring the urgent need for robust cybersecurity measures. When a cyber-attack breaches an IoT network, it initiates the dissemination of malware across the network. However, to counteract this threat, an immediate installation of a new patch becomes imperative. The time frame for developing and deploying the patch can vary significantly, contingent upon the specifics of the cyber-attack. This paper aims to address the challenge of pre-emptively mitigating cyber-attacks prior to the installation of a new patch. The main novelties of our work include: (1) A well-designed node-level model known as Susceptible, Infected High, Infected Low, Recover First, and Recover Complete (SIHILRFRC). It categorizes the infected node states into infected high and infected low, according to the categorization of infection states for IoT devices, to accelerate containment strategies for malware propagation and improve mitigation of cyber-attacks targeting IoT networks by incorporating immediate response within a restricted environment. (2) Development of an optimal immediate response strategy (IRS) by modeling and analyzing the associated optimal control problem. This model aims to enhance the containment of malware propagation across IoT networks by swiftly responding to cyber threats. Finally, several numerical analyses were performed to fully illustrate the main findings. In addition, a dataset has been constructed for experimental purposes to simulate real-world scenarios within IoT networks, particularly in smart home environments.

Optimal Gliding Trajectories for Descent on Mars

In this paper, optimal gliding trajectories are analyzed, formulating an optimal control problem to be solved computationally via nonlinear programming. A multi-objective terminal cost function that minimizes the velocity, altitude, horizontal flight path angle, and the error of a desired terminal point is formulated. The results are validated via Monte Carlo simulations, analyzing the influence of the variations in the lift-to-drag ratios in the atmospheric entry. The results show feasible solutions for minimizing the distance to the desired final point, which have significant practical implications for the controlled gliding entry of a spaceplane on Mars. In this sense, the results also show that the longitudes of the landing points do not change too much for almost all trajectories, while the latitude of these points is in the interval of about 4 degrees for the majority of the trajectories. This suggests that it is possible to implement an optimal control approach with reasonable accuracy for the controlled gliding entry of a spaceplane on Mars, even in the presence of some uncertainties regarding the aerodynamic performance of the spacecraft, such as the lift-to-drag ratio.

Optimal control strategies for energy storage systems for HUB substation considering multiple distribution networks

With the global consensus to achieve carbon neutral goals, power systems are experiencing a rapid increase in renewable energy sources and energy storage systems (ESS). Especially, recent development of hub substations (HS/S) equipped with ESS, applicable for resolving site constraints if implemented as mobile transformers, is expanding the development of ESS-equipped facilities. However, these units require centralized control strategies considering variability within integrated networks. While studies on electric vehicle charging considering the variability of renewable energy or load are widely studied, ESS management scheme for individual substations requires further optimization, especially considering the state of distributed sources at lower levels and transmission system operators. Thus, in this study, an optimal control approach for ESS located at the connection point of transmission and distribution systems, including further consideration of the loss in distribution lines and the constraints of renewable energy sources is presented. This study attempts to derive proactive control strategies for ESS in HS/S to operate with various distribution networks. By establishing control priorities for each source through optimal operation strategy, a suitable capacity of ESS and its economic benefits for distribution network management can be examined. Validation of the current analysis results is performed by utilizing MATPOWER. By adapting the operational range of design scenarios, diverse distribution systems can be tested against multiple configurations of connected devices.

Existence of equilibrium in a dynamic supply chain game with vertical coordination, horizontal competition, and complementary goods

We consider supply chain competition and vertical coordination in a linear–quadratic differential game setting. In this setting, supply chains produce complementary goods and each of them includes a single manufacturer and a single retailer who coordinate their decisions through a revenue-sharing contract with a wholesale price and a fixed sales revenue share. We study a multiple leader-follower Stackelberg game where the manufacturers are the leaders and the retailers are the followers. Competition occurs at both levels of the supply chains. Retailers play Nash and compete in price; manufacturers also play Nash but they compete in choosing their production capacities by exploiting the equilibrium price decisions made by the retailers. We show that open-loop Nash equilibria exist when the manufacturers only receive a wholesale price (there are no longer exploiting the equilibrium price decision made by the retailers, however). When the manufacturers receive both a wholesale-price and a share of the retailers’ sales revenues, equilibria generally no longer exist. The non-existence of an equilibrium stems from the fact that the manufacturers’ instant profits are discontinuous functions of their production capacities. This discontinuity leads to a major technical difficulty in that one cannot apply standard optimal control approaches to study the equilibria of the dynamic game. Our results illustrate the possibility that competition between supply chains might not be sustainable when they sell complementary products and rely on a revenue-sharing agreement.

Optimal Design of Raising Retirement Age

Population aging threatens the future fiscal balance of the public pension system across many countries, and policymakers have often undertaken parametric pension reform as a solution. However, any reform will inevitably introduce intergenerational conflicts and thus needs a gradual transition to allow individuals to slowly adapt to their new retirement plans. In this article, we study the optimal schedule for lifting the full retirement age using the optimal control approach. Given the aggregate actuarial loss of the pension system, our target is to smoothly distribute the deficit across different generations, subject to a fairness constraint that prohibits any cohorts from taking advantage of others. We further illustrate our results using China as an empirical example and investigate the impacts of different actuarial assumptions, benefit accrual formulae, and population structures.

An improved data-driven predictive optimal control approach for designing hybrid electric vehicle energy management strategies

This paper proposes an improved “prediction + optimal control” method for energy management in hybrid electric vehicles equipped with planetary gears. A differentiable predictor and a differentiable optimal controller are developed using supervised learning and reinforcement learning approaches, respectively. Three training steps are performed for the initial predictor, the optimal controller, and the final predictor. This method improves the traditional energy management predictive optimal control approach by incorporating an additional step of retraining the differentiable predictor. This adjustment ensures that the predictor does not blindly improve its performance based on evaluation criterion irrelevant to energy management, which was commonly used in previous studies. Instead, it focuses on enhancing the overall performance of energy management under the “prediction + optimal control” framework. The approach introduced in this paper is compared with the globally optimal dynamic programming results and traditional predictive optimal control methods on the Next Generation Simulation (NGSIM) data. Our method outperforms traditional approaches in energy management on both the training dataset and the test dataset. This further illustrates that the conventional practice of presumptuously optimizing predictors in “prediction + optimal control” methods can be improved using the proposed method.

Observer‐based adaptive neural networks optimal control for spacecraft proximity maneuver with state constraints

AbstractThis article proposes an adaptive neural network (NN) optimal control approach for autonomous relative motion control of non‐cooperative spacecraft in proximity. The proposed method aims to minimize fuel consumption under various challenges including model uncertainty, state constraints, external disturbances, and input saturation. To account for uncertain parameters of non‐cooperative target and external disturbances, we start by designing a NN disturbance observer. Subsequently, a novel optimal control index function is presented. An adaptive NN based on the actor‐critic (A‐C) framework and backstepping theory is then utilized to approximate the solution of Hamilton–Jacobi–Bellman (HJB) equation and obtain an optimal control law. The Lyapunov framework is leveraged to establish the stability of the closed‐loop control system. Finally, numerical simulations are conducted to assess the feasibility and effectiveness of the proposed control scheme in comparison with an existing approach.

Optimal control technique applied to the minimization of uncertainty measurements in surveying instruments

The objective of this study was to develop an optimal control approach by numerical calculus to predict how to reduce the overall uncertainty of survey instruments unable to directly measure inaccessible points. To reach our goal, two approaches were used to attain the objective. The first was inspired by mathematical models related to three methods appropriately selected and contained in Zhuo’s work proposed in 2012. These were Remote Elevation Measurement (REM), Remote Elevation Dual Measurement (REDM), and Front-to-Back Measurement (FBM) methods whose uncertainties on the measurements of points were deduced using error propagation equations. Optimal control technique helps us to show that for the REM, the height h of the prism contributed more than 70% compared to the global uncertainty for ranges [Formula: see text] from the prism. For the REDM, when the distance between two consecutive stations increases, the weight of the contribution of the two zenith angles [Formula: see text] and [Formula: see text] tends to 50% each for [Formula: see text] close to [Formula: see text], which is to be avoided. For the FBM, the weight of the contribution during the front measurement process before is negligible. The second approach used the Swedish regulation of SIS-TS 21143:2009 which classified total stations according to types of uncertainty to compare the results given by the total station of class T3 unable to directly measure inaccessible points with the more sophisticated class T1 station with direct measurements. Thus, for small spans at the rear measurements [Formula: see text], the height [Formula: see text] of the front prism has the greatest relative contribution more than 90% for zenithal differences [Formula: see text]. This results of our analysis were convincing and provided designers with the data to minimize the overall uncertainties essential in the conception of total stations.

Hamiltonian quantum generative adversarial networks

We propose Hamiltonian quantum generative adversarial networks (HQuGANs) to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the success of classical generative adversarial networks in learning high-dimensional distributions. The quantum optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardware, but also offers a more natural characterization of overparameterization compared to the circuit model. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using simple two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth controls. We analyze the computational cost of implementing HQuGANs on quantum computers and show how the framework can be extended to learn quantum dynamics. Furthermore, we introduce a cost function that circumvents the problem of mode collapse that prevents convergence of HQuGANs and demonstrate how to accelerate the convergence of them when generating a pure state. Published by the American Physical Society 2024