Application Of Optimal Control Research Articles

Effective Application of IoT Power Electronics Technology and Power System Optimization Control

Effective Application of IoT Power Electronics Technology and Power System Optimization Control

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

A novel learning-based robust model predictive control strategy and case study for application in optimal control of FCEVs

With the gradual implementation of carbon-neutral policies, fuel cell electric vehicles (FCEVs) have gained widespread recognition as a promising solution. Due to multi-source electromechanical coupling, the powertrain of FCEVs constitutes a complex nonlinear system, necessitating an advanced energy management strategy for effective control to enhance economic performance. In this study, a novel learning-based robust model predictive control (LRMPC) is proposed for a 4WD FCEV, integrating a high-confidence velocity estimation model and an accurate state observation model to enhance energy-saving potential, robustness, and real-time application performance under various driving conditions. To enhance robustness and adaptability, deep forest with superior feature fusion abilities is employed to generate future velocity reference datasets based on FCEV operating scenarios. To improve state observation accuracy and control effectiveness, a novel built-in state observation model based on machine learning algorithms is established, leveraging knowledge of nonlinear systems within the FCEV powertrain. Subsequently, to enhance the real-time applicability of LRMPC, an explicit control scheme for multidimensional mapping based on explicit data tables is utilized for accurate state transformation, incorporating input features such as vehicle states and component states. Simulation evaluations and hardware-in-the-loop tests demonstrate the improved economic performance and real-time application ability of LRMPC, showcasing its promising performance.

Modeling environmental-born melioidosis dynamics with recurrence: An application of optimal control

Melioidosis is a significant health problem in tropical and subtropical regions, especially in Southeast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminating the disease from the community in these nations. This work aims to propose and analyze a human melioidosis model with recurrent phenomena and an optimal control model by incorporating time-dependent control functions. The basic reproduction number (R0) of the uncontrolled model is derived using the method of the next-generation matrix. Using the construction of a Lyapunov functional, we present the global asymptotic dynamics of the autonomous model in the presence of recurrent for both disease-free and endemic equilibria. The global asymptotic stability of the model’s equilibria shows the absence of a backward bifurcation for the model in both cases, whether in the absence or presence of relapse. The sensitivity analysis aims to identify the parameters that have the most significant impact on the model’s dynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changing effect of the most influential parameters on R0 are supported by numerical experiments, with the results being illustrated graphically. The model with time-dependent controls is analyzed using optimal control theory to assess the impact of various intervention strategies on the spread of the epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using two approaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.

Optimal control transport of neutral atoms in optical tweezers at finite temperature

The transport of neutral atoms in Rydberg quantum computers is a crucial step for the initial arrangement of the grid as well as the dynamic connectivity, recently successfully demonstrated. We study the application of optimal control and the quantum speed limit for the transport of neutral atoms in optical tweezers at finite temperatures and analyze how laser noise affects transport fidelity. Open-loop optimal control significantly enhances transport fidelity, achieving an improvement up to 89% for the lowest analyzed temperature of 1µK for a distance of 3µm. Furthermore, we simulate how the transport fidelity behaves in release-and-capture measurements, which are realizable in the experiment to estimate transport efficiency and implement closed-loop optimal control. Published by the American Physical Society 2024

Application of Optimal Control on Mathematical Model of Drug Distribution with Education and Criminal Law Aspect

Drugs are substances that, when used, can impact the body, particularly the central nervous system/brain. Prolonged drug use can lead to various disorders affecting physical, psychological, and social functioning. Generally, drug use cases occur among teenagers due to a lack of education and low literacy levels about the dangers of drug. In this study, control efforts by modeling the problem of drug use will be studied. In this study, modeling the problem of drug users with control efforts will be studied. There were additional controls for preventing drug abuse through school education, contact prevention through security and healthy living campaigns, and the procedures to report all drug abuse activities. The Pontryagin Minimum Principle is used to shows that the optimal controls influence the level of drug user distribution.

Optimal Battery Energy Storage Dispatch for the Day-Ahead Electricity Market

This work presents an innovative application of optimal control theory to the strategic scheduling of battery storage in the day-ahead electricity market, focusing on enhancing profitability while factoring in battery degradation. This study incorporates the effects of battery degradation on the dynamics in the optimisation framework. Considering this cost in economic analysis and operational strategies is essential to optimise long-term performance and economic viability. Neglecting degradation costs can lead to suboptimal operation and dispatch strategies. We employ a continuous-time representation of the dynamics, in contrast with many other studies that use a discrete-time approximation with rather coarse intervals. We adopt an equivalent circuit model coupled with empirical degradation parameters to simulate a battery cell’s behaviour and degradation mechanisms with good support from experimental data. Utilising direct collocation methods with mesh refinement allows for precise numerical solutions to the complex, nonlinear dynamics involved. Through a detailed case study of Belgium’s day-ahead electricity market, we determine the optimal charging and discharging schedules under varying objectives: maximising net revenues, maximising profits considering capacity degradation, and maximising profits considering both capacity degradation and internal resistance increase due to degradation. The results demonstrate the viability of our approach and underscore the significance of integrating degradation costs into the market strategy for battery operators, alongside its effects on the battery’s dynamic behaviour. Our methodology extends previous work by offering a more comprehensive model that empirically captures the intricacies of battery degradation, including a fine and adaptive time domain representation, focusing on the day-ahead market, and utilising accurate direct methods for optimal control. This paper concludes with insights into the potential of optimal control applications in energy markets and suggestions for future research avenues.

Accurate distances measures and machine learning of the texture-property relation for crystallographic textures represented by one-point statistics

The crystallographic texture of metallic materials is a key microstructural feature that is responsible for the anisotropic behavior, e.g. important in forming operations. In materials science, crystallographic texture is commonly described by the orientation distribution function, which is defined as the probability density function of the orientations of the monocrystal grains conforming a polycrystalline material. For representing the orientation distribution function, there are several approaches such as using generalized spherical harmonics, orientation histograms, and pole figure images. Measuring distances between crystallographic textures is essential for any task that requires assessing texture similarities, e.g. to guide forming processes. Therefore, we introduce novel distance measures based on (i) the Earth Movers Distance that takes into account local distance information encoded in histogram-based texture representations and (ii) a distance measure based on pole figure images. For this purpose, we evaluate and compare existing distance measures for selected use-cases. The present study gives insights into advantages and drawbacks of using certain texture representations and distance measures with emphasis on applications in materials design and optimal process control.

Multilayer adaptive critic design with digital twin for data-driven optimal tracking control and industrial applications

In this paper, an optimal trajectory tracking control problem for general nonlinear systems is investigated. An adaptive critic control method with the digital twin (DT) theory is developed. Divergent from the existing tracking control methods, the advantages of adaptive dynamic programming (ADP) and the theory of DT are combined in this paper, and the novel multilayer artificial system structure is constructed. The action-critic structure is employed by each artificial system to obtain an approximate optimal control policy. The model network (MN) is built by using the actual input and output data sets of the controlled system, which means the dependence on the dynamics of the system is overcame. Then, the weights of the trained action network (AN) and MN are passed to the real system to realize the optimal tracking control. The feasibility of the algorithm is proved by theoretical analysis. Finally, the algorithm is applied to a simple nonlinear torsional pendulum system and an industrial wastewater treatment system (WWTS), and the effectiveness of the algorithm is verified. The algorithm effectively realizes the tracking control of nonlinear systems.

Optimal control of large quantum systems: assessing memory and runtime performance of GRAPE

Gradient Ascent Pulse Engineering (GRAPE) is a popular technique in quantum optimal control, and can be combined with automatic differentiation (AD) to facilitate on-the-fly evaluation of cost-function gradients. We illustrate that the convenience of AD comes at a significant memory cost due to the cumulative storage of a large number of states and propagators. For quantum systems of increasing Hilbert space size, this imposes a significant bottleneck. We revisit the strategy of hard-coding gradients in a scheme that fully avoids propagator storage and significantly reduces memory requirements. Separately, we present improvements to numerical state propagation to enhance runtime performance. We benchmark runtime and memory usage and compare this approach to AD-based implementations, with a focus on pushing towards larger Hilbert space sizes. The results confirm that the AD-free approach facilitates the application of optimal control for large quantum systems which would otherwise be difficult to tackle.

Evaluating the choice of radial basis functions in multiobjective optimal control applications

Evolutionary Multi-Objective Direct Policy Search (EMODPS) is a prominent framework for designing control policies in multi-purpose environmental systems, combining direct policy search with multi-objective evolutionary algorithms (MOEAs) to identify Pareto approximate control policies. While EMODPS is effective, the choice of functions within its global approximator networks remains underexplored, despite their potential to significantly influence both solution quality and MOEA performance. This study conducts a rigorous assessment of a suite of Radial Basis Functions (RBFs) as candidates for these networks. We critically evaluate their ability to map system states to control actions, and assess their influence on Pareto efficient control policies. We apply this analysis to two contrasting case studies: the Conowingo Reservoir System, which balances competing water demands including hydropower, environmental flows, urban supply, power plant cooling, and recreation; and The Shallow Lake Problem, where a city navigates the trade-off between environmental and economic objectives when releasing anthropogenic phosphorus. Our findings reveal that the choice of RBF functions substantially impacts model outcomes. In complex scenarios like multi-objective reservoir control, this choice is critical, while in simpler contexts, such as the Shallow Lake Problem, the influence is less pronounced, though distinctive differences emerge in the characteristics of the prescribed control strategies.

Application of optimal control for wind integrated power system

<div align="center"><span>This paper presents the modeling and application of an optimal controller for frequency and tie-line power stability for a two-area interconnected hydro-thermal power plant having tandem compound non-reheat turbines integrated with wind power generation having doubly fed induction generator (DFIG) wind turbines in each area. The power system is interconnected using AC tie-lines. The designed optimal controller was implemented and the system dynamic responses for three power system model states were obtained considering a 1% load fluctuation in one of the areas. The optimal control strategy presented in this paper depends on formulating an error value and finding the feedback gains corresponding to each state of the system, which are easily attainable as outputs. The analysis was undertaken and verified by calculating the performance index value, the closed ring real and imaginary values, finding the feedback gains, and through graphical simulations of the three system models under investigation. The output of the optimal controller was enhanced when the DFIG-based wind turbines were installed in each area combined with a superconducting magnetic energy storage (SMES) unit and a thyristor control phase shifter (TCPS).</span></div>

Temperature transition optimization in cryogenic systems: Application to liquid nitrogen expenditure reduction in a thermal vacuum chamber case study

This paper presents outcomes regarding liquid nitrogen consumption reduction in a thermal vacuum chamber, with the motivation of lessening operational costs during space equipment testing. The article briefly outlines the optimal control application to thermal and cryogenic-related control systems based on a gas cycle, and assesses liquid nitrogen savings opportunities for a chamber including six shrouds with independent temperature requirements. In this case study, optimization of temperature transition profiles and a proposed modification in the control setup yielded potential savings from 14.1% to 20.4% in the examined experimental transitions.

Applications of the Linear Quadratic Regulator Optimal Control With Completely and Partially Observed Markovian Switching

Abstract We study optimal control problems where the dynamic system evolves according to a linear stochastic differential equation with (a) multiplicative and additive white noise, (b) a mixture of white noise, and (c) white noise and colored noise. The drift rate and the diffusion matrix of the linear dynamic system depend on a continuous-time Markov chain with finite state space that is (I) partially observed and (II) completely observed. Using the results of Wonham filter theory, we reduce the partially observed problems to one with complete observation. We solve the control optimal problems explicitly with the help of dynamic programing technique, and three applications are presented to illustrate our theoretical results.

Tailored presolve techniques in branch‐and‐bound method for fast mixed‐integer optimal control applications

AbstractMixed‐integer model predictive control (MI‐MPC) can be a powerful tool for controlling hybrid systems. In case of a linear‐quadratic objective in combination with linear or piecewise‐linear system dynamics and inequality constraints, MI‐MPC needs to solve a mixed‐integer quadratic program (MIQP) at each sampling time step. This paper presents a collection of exact block‐sparse presolve techniques to efficiently remove decision variables, and to remove or tighten inequality constraints, tailored to mixed‐integer optimal control problems. In addition, we describe a novel approach based on a heuristic presolve algorithm to compute a feasible but possibly suboptimal MIQP solution. We present benchmarking results for a C code implementation of the proposed BB‐ASIPM solver, including a branch‐and‐bound (B&B) method with the proposed tailored presolve techniques and an active‐set based interior point method (ASIPM), compared against multiple state‐of‐the‐art MIQP solvers on a case study of motion planning with obstacle avoidance constraints. Finally, we demonstrate the feasibility and computational performance of the BB‐ASIPM solver in embedded system on a dSPACE Scalexio real‐time rapid prototyping unit for a second case study of stabilization for an underactuated cart‐pole with soft contacts.

Geometric Numerical Methods for Lie Systems and Their Application in Optimal Control

A Lie system is a nonautonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, the so-called (nonlinear) superposition rule of a finite number of particular solutions and some parameters to be related to initial conditions. This superposition rule can be obtained using the geometric features of the Lie system, its symmetries, and the symmetric properties of certain morphisms involved. Even if a superposition rule for a Lie system is known, the explicit analytic expression of its solutions frequently is not. This is why this article focuses on a novel geometric attempt to integrate Lie systems analytically and numerically. We focus on two families of methods based on Magnus expansions and on Runge–Kutta–Munthe–Kaas methods, which are here adapted, in a geometric manner, to Lie systems. To illustrate the accuracy of our techniques we analyze Lie systems related to Lie groups of the form SL(n,R), which play a very relevant role in mechanics. In particular, we depict an optimal control problem for a vehicle with quadratic cost function. Particular numerical solutions of the studied examples are given.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application.

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R0<1 and the exogenous reinfection rate greater than a threshold (η>η∗). The analytical results show that reducing R0<1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

Semismoothness for Solution Operators of Obstacle-Type Variational Inequalities with Applications in Optimal Control

We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. convexity properties) are Newton differentiable when considered as maps between suitable Lebesgue spaces and equipped with the strong-weak Bouligand differential as a generalized set-valued derivative. It is shown that this Newton differentiability allows to solve optimal control problems with -cost terms and one-sided pointwise control constraints by means of a semismooth Newton method. The superlinear convergence of the resulting algorithm is proved in the infinite-dimensional setting, and its mesh independence is demonstrated in numerical experiments. We expect that the findings of this paper are also helpful for the design of numerical solution procedures for quasi-variational inequalities and the optimal control of obstacle-type variational problems.

Model-Free H∞ Output Feedback Control of Road Sensing in Vehicle Active Suspension Based on Reinforcement Learning

Abstract An active suspension system ensures the controllability of a vehicle in the vertical direction, which greatly enhances the control redundancy and safety of an intelligent driven vehicle. However, many calibrated model parameters are not conducive to the application of optimal control. To reduce the control cost of active suspension, a model-free H∞ output feedback control method is studied in this research. First, the optimal governing equation of the active suspension is transformed into a zero-sum game problem of two players, and an off-policy reinforcement learning algorithm is established to solve the game algebraic Riccati equation. This method could overcome the disadvantage of constant interactions between Q-learning and the environment. Secondly, with the consideration that some state variables are difficult to measure, a data-driven H∞ output feedback controller is designed using road sensing information and historical measurement data, and the Bellman equation of the system is solved using the least squares method to obtain the optimal control solution of the active suspension. The simulation and rapid prototype experimental results show that the proposed method could produce the optimal control strategy of the system without model parameters, overcome the strong dependence and sensitivity of traditional design methods to model parameters and improve the robust control effect of the active suspension.

Issue Information

Optimal Control Applications and MethodsVolume 44, Issue 3 p. 1053-1054 ISSUE INFORMATIONFree Access Issue Information First published: 04 May 2023 https://doi.org/10.1002/oca.2911AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Volume44, Issue3Special Issue: Data‐based Learning Control for Optimization of Nonlinear SystemsMay/June 2023Pages 1053-1054 RelatedInformation