Application Of Optimal Control Theory Research Articles

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.

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.

A review of dynamic optimization in aquaculture production economics

AbstractDynamic optimization (DO) has been applied to aquaculture industry to determine optimal management strategies of aquaculture production systems. Optimal control of feeding, optimal stocking successions, and harvesting time among other factors has been studied. This work shows a review of the application of optimal control theory (OCT) and dynamic programming in economics and management of aquaculture. The Pontriagyn's maximum principle and the Bellman's optimality are the most commonly used mechanisms to solve control problems that optimize the producer's benefit or cost. Recently, model‐based predictive control has also been applied. Such tools have been used in aspects involving the design, planning, and monitoring of variables relevant to the optimal management of the culture system. It was found that in aquaculture there is low scientific productivity in the application of DO in bioeconomic models. In this review, an example of OCT applied to the control of feeding of farmed tilapia using a bioeconomic model is shown. DO represents a useful tool for optimal decision‐making and this review discusses the implications of the use of DO in aquaculture and recommendations for its use in the future.

Modeling the co-dynamics of vector-borne infections with the application of optimal control theory

Modeling the co-dynamics of vector-borne infections with the application of optimal control theory

Optimal Controllers for the Operation of Activated Sludge Treatment Systems

Objective: Application of Optimal Control Theory to the activated sludge process in order to regulate the removal of the carbonaceous part of the organic matter. Theoretical benchmark: Dynamic models of activated sludge processes are capable of enabling the development of innovative control systems. The Optimal Control Theory, aimed at optimizing the performance of dynamic systems, allows the establishment of control systems that enhance efficiency in adapting to changes in operating conditions, ensuring satisfactory process performance. Method: The proposed control systems were established from the application of Optimal Control Theory, considering the use of the dynamic model of the activated sludge process presented by International Association on Water Pollution Research and Control. Computer simulations were used to assess the performance of the control systems proposed. Results and conclusion: The proposed control systems were capable of curbing substantially the oscillations in the concentrations of biomass, of particulate matter produced by the degradation of biomass and those of the inert particulate substrate. The reductions in the oscillations of the slowly biodegradable part of the influent were relatively smaller. The controller was quite effective in leading the wastewater treatment system sooner to the new equilibrium conditions after the imposition of the disturbances in raw effluent. Implications of research: Development of control systems for activated sludge processes to regulate the removal of the carbonaceous fraction from organic matter. Originality/value: The establishment of optimal control systems for activated sludge processes can enable greater efficiency and operational capacity, especially in industrial facilities or densely populated urban settlements, where such wastewater treatment systems are most commonly used.

Synthesize the optimal control law for the antenna transmission system of the missile seeker

The appearance in the armed forces of some countries super-maneuverable aircraft has posed the problem of synthesizing the angle measuring equipment of the missile seeker with higher requirements for accuracy, fast acting, and stability when tracking the target. However, the operating principle of current angle measuring equipment does not allow simultaneous improvement of all the necessary criteria, even though such principles are based on the generation of the evaluation signals of angular coordinates and angular speed of line of sight in a loop circuit. Based on the application of optimal control theory, it is possible to synthesize the system’s many loop circuits, which simultaneously achieve the best criteria in terms of accuracy, impact speed, as well as tracking stability, and consumption energy for the control process.

Modeling and verification of helicopter roll-on takeoff based on optimal control theory

Purpose The paper aims to establish a comprehensive optimization analysis model for a helicopter roll on the ground and take off based on optimal control method. The trajectory and control of the entire process are studied, and the key factors affecting the helicopter takeoff distance are analyzed. Design/methodology/approach First, based on the equivalent stiffness and damping, the landing gear model is established, and a six-degree-of-freedom helicopter model is formed. Then, the simulation of the roll-on takeoff is transformed into a nonlinear optimal control problem (NOCP). Meanwhile, a hybrid single-multiple shooting method-based transcription process is used for discretizing the problem, leading to a finite nonlinear programming model, which is solved by sequential quadratic programming. Finally, the process was calculated and compared with flight test data, which verified the feasibility of the NOCP. The influence of takeoff weight, takeoff power and liftoff airspeed on the takeoff distance of the helicopter was analyzed. Findings The results show that the takeoff weight can be increased by 17% under the maximum takeoff power, which is roll-on takeoff at an altitude of 0 m. When the helicopter takes off with the maximum weight at an altitude of 5000 m, the liftoff airspeed should be over 49.2 km/h. Originality/value The novelty of this paper lies in the comprehensive consideration of helicopter taxiing and taking-off phases, and the application of optimal control theory to establish a comprehensive analysis model, which can quickly analyze the maximum takeoff weight, takeoff distance, optimal liftoff speed and so on. Meanwhile, the method is verified based on the flight data.

Optimal control of a two-group malaria transmission model with vaccination.

Malaria is a vector-borne disease that poses major health challenges globally, with the highest burden in children less than 5 years old. Prevention and treatment have been the main interventions measures until the recent groundbreaking highly recommended malaria vaccine by WHO for children below five. A two-group malaria model structured by age with vaccination of individuals aged below 5 years old is formulated and theoretically analyzed. The disease-free equilibrium is globally asymptotically stable when the disease-induced death rate in both human groups is zero. Descarte's rule of signs is used to discuss the possible existence of multiple endemic equilibria. By construction, mathematical models inherit the loss of information that could make prediction of model outcomes imprecise. Thus, a global sensitivity analysis of the basic reproduction number and the vaccination class as response functions using Latin-Hypercube Sampling in combination with partial rank correlation coefficient are graphically depicted. As expected, the most sensitive parameters are related to children under 5 years old. Through the application of optimal control theory, the best combination of interventions measures to mitigate the spread of malaria is investigated. Simulations results show that concurrently applying the three intervention measures, namely: personal protection, treatment, and vaccination ofchildreen under-five is the best strategy for fighting against malaria epidemic in a community, relative to using either single or any dual combination of intervention(s) at a time.

Computability of magnetic Schrödinger and Hartree equations on unbounded domains

AbstractWe study the computability of global solutions to linear Schrödinger equations with magnetic fields and the Hartree equation on . We show that the solution can always be globally computed with error control on the entire space if there exist a priori decay estimates in generalized Sobolev norms on the initial state. Using weighted Sobolev norm estimates, we show that the solution can be computed with uniform computational runtime with respect to initial states and potentials. We finally study applications in optimal control theory and provide numerical examples.

Application of Optimal Control Theory to Inventory Problems That Are Increasing at PT. Canang Indah

This journal discusses optimal control of inventory problems that are increasing. The inventory in the company is needed, to meet every incoming demand. Inventory in minimum quantity can result in shortage of inventory. But inventory quantity maximum can result in losses, due to the minimum demand. The purpose of this research is to determine the level of optimal inventory in PT. Canang Indah. Using the optimal control theory model and analyzing the stability of the dynamic differential equation, to find the optimal inventory level. Obtained optimal inventory levels achieve stability at the time . For the planning length of 12 months includes: raw material inventory (logs sengon and rambung), production (finished materials in process) and finished particle board products that are in the warehouse. From this research optimal control theory can be applied in PT. Canang Indah to optimize inventory on the problem of increasing inventory.

Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented by u1(t), u2(t) and u3(t), respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge–Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.

Optimal control of deep petroleum borehole trajectory tracking

• A new problem of optimal tracking of a deep borehole trajectory is posed. • Target functions related to the hole smoothness, cost, and length are considered. • Optimal nonlinear control methods and gradient projection method are jointly used. • Examples of the optimal smoothing of deep projected trajectories are discussed. This paper is concerned with the application of optimal control theory to the problem of tracking deep oil and gas borehole trajectories. Based on the methods of differential geometry, the mathematical model of the trajectory curve with its curvature representing controlling variable is elaborated in the form of ordinary differential equations: The objective functional chosen as integral curvature, length or cost of the borehole are considered. The techniques for the optimization problem solving are developed with the use of the continuous version of the step-by-step anti-gradient projection on the hyper-planes of linearized constraints. At every step of the minimization procedure, the constraints spoilt by the linearization operations are restored through the use of the Newton method. Some examples are considered for a borehole with fixed and shifting boundary positions under conditions of minimizing its total curvature and length. It is shown that it is possible to improve the smoothness of the borehole trajectory using the outlined approach, and in so doing, reduce the friction and resistance forces impeding the drill string motion.

Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

Application of optimal control theory based on the evolution strategy (CMA-ES) to automatic berthing (part: 2)

Application of optimal control theory based on the evolution strategy (CMA-ES) to automatic berthing (part: 2)

Investigation of direct force control for aerocapture at Neptune

In this work, a direct force control numerical predictor-corrector guidance architecture is developed to enable Neptune aerocapture using blunt body aeroshells. A linear aerodynamics model is formulated for a Mars Science Laboratory-derived aeroshell. The application of optimal control theory shows that the ΔV-minimizing angle of attack and side-slip angle control laws are bang-bang. A closed-loop numerical predictor-corrector direct force control guidance algorithm is developed and numerically simulated using the Program to Optimize Simulated Trajectories II. A series of Monte Carlo simulations are conducted to assess the guidance robustness to uncertainties in vehicle aerodynamics, atmospheric density, and entry state. For the reference set of uncertainties, the direct force control vehicle achieves 99.7% successful science orbit insertion within a 330 m/s total ΔV budget for periapsis raise, apoapsis, inclination, and ascending node corrections. Improved atmospheric knowledge and delivery state accuracy are shown to improve the success to 100% and reduce the ΔV to 230 m/s. Direct force control is demonstrated to be an enabling technology for blunt body aerocapture at Neptune while providing comparable performance to existing slender body vehicles studied in literature.

An Optimal Control for a Two-Dimensional Spatiotemporal SEIR Epidemic Model

In this paper, we present an application of optimal control theory on a two-dimensional spatial-temporal SEIR (susceptible, exposed, infected, and restored) epidemic model, in the form of a partial differential equation. Our goal is to minimize the number of susceptible and infected individuals and to maximize recovered individuals by reducing the cost of vaccination. In addition, the existence of the optimal control and solution of the state system is proven. The characterization of the control is given in terms of state function and adjoint. Numerical results are provided to illustrate the effectiveness of our adopted approach.

Application of optimal control theory on optimal advertising expenditure in monopoly

Presented paper is being focused on Optimal control theory, Variation Calculus and its economic application. Aim of this research paper is to shortly describe Optimal control and Variation Calculus and to present how can we deal with these type of issues. The last part of this paper is presenting possible economic application of Optimal control, based on the maximization of profit in monopoly while introducing new product on the market. Our control variable is the advertising rate, which affects the profit of monopoly through advertising expenditures and as a state variable was the market share defined.

Application of Optimal Control Theory to Biomedical and Biochemical Processes

Optimal control theory is a highly developed subject. It has been applied in diverse fields of engineering, physics, economics, operation research, management sciences, policy planning etc. In particular, this subject has been successfully applied to bio-medical engineering problems like artificial heart, prosthesis. In this paper we present a brief summary of two recent papers on cancer immunotherapy and bio-reactors.

AGC of a multi sources power system with natural choice of power plants

This paper presents an application of optimal control theory in multi sources power system by considering natural choice of power plants participating in automatic generation control (AGC) scheme. However, for successful operation of large power system, the natural choices of generation suitable for AGC system are hydro and thermal power plants since gas and nuclear power plants are rarely participates in the AGC scheme. Therefore, this work presents design and implementation of proportional integral (PI) structured optimal AGC controller in the presence of hydro and thermal power plants by using state vector feedback control theory. Moreover, various case studies are identified to obtain: (i) Cost aspects of physical realization of optimal AGC controller, (ii) Closed loop system stability margin through patterns of eigenvalues and (iii) System dynamic performance. Further, results have shown that when optimal AGC scheme is implemented in power system, the dynamic performance of power system is outstanding over those obtained with genetic algorithms (GAs) tuned PI structured AGC controller. Besides, with optimal AGC controller, cheaper cost of control structure, increased in system closed loop stability margin and outstanding dynamic performance of power system have been found when lessening in hydro generation is replaced by generation from thermal power plants for various case studies under investigation.

Application of optimal control theory based on the evolution strategy (CMA-ES) to automatic berthing

To realize autonomous ships in the near future, possibility of automatic berthing has been investigated. Automatic berthing is not an easy task because of some complexities that are included in the problem, such as the nonlinearity of the low-speed maneuvering model, danger of collision with berth, etc. In this research, as a first step, the authors solved the off-line automatic berthing problem. Here, the optimal control problem was modeled as minimum-time problem, and the collision risk with the berth was taken into account. The authors attempted to apply the covariance matrix adaption evolution strategy (CMA-ES), which is considered state-of-the-art in evolutionary computation approaches for optimization of real-valued variables. In the problem dealt with here, a propeller and a rudder were used only as control inputs; so, the degree of difficulty was significantly high. Nevertheless, optimal control method based on the CMA-ES successfully gave us the offline results for typical situations considered. It is noteworthy that preparation of a feasible initial control input was not required in the calculation process, which made the proposed procedure robust. The calculation method proposed here is offline, but the results could be applied as an initial guess in an online (real-time) control problem.