Optimal Control Program Research Articles

Dynamic Programming, Neuro-Dynamic Programming, Rollout Method and Model Predictive Control to Optimal Control of a Fermentation Process

This work presents the use of dynamic programming (DP), neuro-dynamic programming (NDP), rollout algorithm (RA) and model predictive control (MPC) for optimal control of batch cultivation of the yeast Kluyveromyces marxianus var. lactis MC5. DP is a widespread method for solving problems related to optimization and optimal process control. To reduce the “curse of dimensionality”, NDP has been implemented as an alternative. In NDP, a neural network is used to solve the dimensionality problem. A simpler NDP method, called RA, is used to approximate the optimal cost through the cost of a relatively good suboptimal policy, called the baseline policy. RA is a suboptimal method for deterministic and stochastic problems that can be solved by DP. In this paper we also present off-line MPC technique for tracking of constrained fermentation systems and it overcomes the problem by off-line optimizations prior to implementation. MPC is used to provide perturbation feedback and it is developed theoretical on base a controller as an illustration how we can avoid disturbances in the process optimisation. The developed control algorithm-combined NDP and MPC ensures maximum biomass production at the end of the process and feedback during disturbances and process stability and shows that robust stability can be ensured.

Sequential Convex Programming for Nonlinear Optimal Control in UAV Trajectory Planning

In this paper, an algorithm is proposed to solve the non-convex optimization problem using sequential convex programming. An approximation method was used to solve the collision avoidance constraint. An iterative approach was utilized to estimate the non-convex constraints, replacing them with their linear approximations. Through the simulation, we can see that this method allows for quadcopters to take off from a given initial position and fly to the desired final position within a specified flight time. It is guaranteed that the quadcopters will not collide with each other in different scenarios.

Event-Triggered Adaptive Dynamic Programming for Hierarchical Sliding-Mode Surface-Based Optimal Control of Switched Nonlinear Systems

Event-Triggered Adaptive Dynamic Programming for Hierarchical Sliding-Mode Surface-Based Optimal Control of Switched Nonlinear Systems

Dynamics of an [formula omitted] epidemic model with stochastic optimal control and awareness programs

An unaware susceptible-aware susceptible-vaccinated-infected-recovered (SuSaV IR) epidemic disease model has been developed and extensively examined to better understand the intricate dynamics of the disease transmission with saturated recovery function. A non-linear, monotonically increasing awareness function has been incorporated and its application is contingent upon the number of infected individuals. The spreading threshold R0 and its sensitivity indices are computed to determine both the prevalence and the potential decline of the spread of disease. Contour plots have been generated to explain how alterations in key parameters affect the evolution of infected individuals. In deterministic model, the condition R0<1 ensures the global stability of a disease-free state while R0>1 indicates the presence of a globally stable prevailing state. A numerical approach has been employed to pinpoint the stability switches for R0 which indicates transcritical bifurcation. Subsequently, a corresponding stochastic model is developed to investigate the impact of random external factors represented as white noise. In addition, the global existence and uniqueness of solutions, and the asymptotic behavior of solutions in the vicinity of steady-states are exhibited in the stochastic model. In the stochastic model, the extinction threshold Res is consistently below R0 due to noise intensity, leading to quicker disease extinction. In order to elucidate the influence of parameters and noise intensities on persistence threshold Rps and extinction threshold Res, a comprehensive sensitivity analysis and the variation of each noise intensity have been performed. This study shows that treatment can be used as an effective tool for controlling the spread of disease by lowering R0 and Rps. It has been empirically observed that high environmental fluctuations can serve as a suppressive factor for disease spread in stochastic model with R0,Rps>1 and the higher noise intensities lead to a faster disappearance of the disease. It is noticed that randomness in susceptible and infected individuals can exert a more significant influence on disease mitigation. The spread of infection exhibits a noteworthy dependence on environmental fluctuations. Additionally, to combat and mitigate the spread of disease, we have executed stochastic optimal control measures. Consequently, the control strategy has emerged as a potent tools for effectively managing the propagation of disease.

Evaluation of Two Vaccines against Foot-and-Mouth Disease Used in Transcaucasian Countries by Small-Scale Immunogenicity Studies Conducted in Georgia, Azerbaijan and Armenia.

In countries endemic for foot-and-mouth disease (FMD), routine or emergency vaccinations are strategic tools to control the infection. According to the WOAH/FAO guidelines, a prior estimation of vaccine effectiveness is recommendable to optimize control programs. This study reports the results of a small-scale immunogenicity study performed in Transcaucasian Countries. Polyvalent vaccines, including FMDV serotypes O, A (two topotypes) and Asia1 from two different manufacturers, were evaluated in Georgia, Azerbaijan and Armenia. Naïve large and small ruminants were vaccinated once and a subgroup received a second booster dose. The titers of neutralizing antibodies in sera collected sequentially up to 180 DPV were determined through the Virus Neutralization Test versus homologous strains. This study led to the estimate that both the vaccines evaluated will not induce a protective and long-lasting population immunity, even after a second vaccination, stressing that consecutive administrations of both vaccines every three months are mandatory if one aspires to achieve protective herd immunity.

Constrained-Cost Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

For discrete-time nonlinear systems, this research is concerned with optimal control problems (OCPs) with constrained cost, and a novel value iteration with constrained cost (VICC) method is developed to solve the optimal control law with the constrained cost functions. The VICC method is initialized through a value function constructed by a feasible control law. It is proven that the iterative value function is nonincreasing and converges to the solution of the Bellman equation with constrained cost. The feasibility of the iterative control law is proven. The method to find the initial feasible control law is given. Implementation using neural networks (NNs) is introduced, and the convergence is proven by considering the approximation error. Finally, the property of the present VICC method is shown by two simulation examples.

Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems With Trajectory-Based Initial Control Policy

Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems With Trajectory-Based Initial Control Policy

Analysis of the spatio-temporal dynamics of Buxus hyrcana Pojark defoliation using spaceborne satellite data

Abstract This study aims to assess the spatio-temporal defoliation dynamics of box tree, one of the few evergreen species of the Hyrcanian Forests. For this, we integrated multi-temporal leaf-off optical Sentinel-2 and radar Sentinel-1 data from 2017 to 2021 with elevation data. A state-of-the-art sample migration approach was used to generate annual reference samples of two categories (defoliated and healthy box tree) for a set of target years 2017–2020. This approach is based on field samples of the reference year 2021 and two similarity measures, the Euclidean distance and the spectral angle distance. The analysis of spectral and radar profiles showed that the migrated samples were well representative of both defoliated and healthy box trees categories. The migrated samples were then used for spatially mapping the two classes using support vector machine classification. The results of support vector machine classification indicated a large extent of box tree mortality. The most significant changes from healthy box trees to defoliated ones, or vice versa, occurred during the years 2017 and 2018. In the consecutive years of 2019, 2020, and 2021, no significant changes in the distribution of healthy or defoliated box trees were observed. The statistical assessment also revealed that mortality of evergreen understory tree species can be mapped with practically sufficient overall accuracies reaching from 84% (in 2017) to 91%–92% (in 2020 and 2021) using spaceborne remote sensing data. This information using freely accessible satellite data can benefit forest managers responsible for monitoring landscapes affected by the box moth and facilitates the identification of optimal control programs.

Online Adaptive Dynamic Programming for Optimal Self-Learning Control of VTOL Aircraft Systems With Disturbances

In this paper, a novel online adaptive dynamic programming control algorithm is developed to solve optimal control problems for Vertical Take Off and Landing (VTOL) aircraft systems. Considering the input disturbances of the VTOL systems and adding perturbation interference term to the value function, a robust policy iteration-based ADP method will be introduced to obtain the optimal controller with an approximate optimal control approach. The convergence property is developed to ensure the value function converges to a finite neighborhood of the optimal one. The uniform ultimate boundedness (UUB) of the iterative errors will be strictly proved by Lyapunov stability theory. Finally, we will give mathematical simulation results with the developed method. Compared with sliding mode control (SMC) and linear quadratic regulator (LQR) methods, the simulation results illustrate better overall performance of the novel method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —As an effective tool to solve the optimal control problem of complex nonlinear systems, adaptive dynamic programming (ADP) can effectively overcome the computational problems caused by “curse of dimensionality”. VTOL aircraft system is a typical strongly coupled, underactuate, non-minimum phase system, and the sudden random disturbances will make the control task more challenging. Aiming at the particularity of VTOL system, a new online policy iteration-based ADP algorithm is developed to obtain optimal control with an approximate optimal control strategy in this paper. Decoupling and disturbances can be effectively avoided. convergence will be analyzed to make sure the value function converge to a finite neighborhood of the optimal value function. The UUB property of the system will be proved by the Lyapunov approach.

Characterization Of Clinical, Heamogram, Leukogram Changes and Stress Indicator in LSD Infected Cows and OSD Infected Buffaloes in Egypt

The limited understanding of the infectious diseases induced stress impedes efforts to establish optimal treatment and control programs to maximize the animal health and production. This study was therefore conducted to characterize the clinical and hematological changes duringLumpy skin disease (LSD) and Oedematous skin disease (OSD) in cows and Egyptian buffaloes respectively. The study was conducted using convenience samples of 90 cows and 35 Egyptian buffaloes during outbreaks in Qalyubia governorate, Egypt. Clinical, bacteriological, and molecular diagnosis of the diseases were performed. Automatic-cell-counter was used for hemogram and leukogram. Serum cortisol concentration was measured using ELISA kits. The statistical significance was set at P &lt; 0.05. The LSD infected cows showed marked decreases in RBCs count, Hb, HCT, WBCs, and lymphocytes, and significant increases in granulocytes, MCV, and MCH compared to the healthy animals. In OSD infected buffaloes, RBCs count, Hb, HCT, WBCs, lymphocytes, granulocytes, MCV, MCH, and MCHC were significantly decreased.Serum cortisol concentration was significantly increased in LSD infected cows and OSD infectedbuffaloes compared to healthy animals. We concluded that LSD and OSD causes injurious shifts in the hemogram, leukogram, and cortisol concentration that indicated deleterious impact on the animal health, production, and well-being.

Optimization of Solar-Sail Control When a Vehicle Moves along Cyclic Heliocentric Trajectories

This paper considers the problem of constructing time-optimal trajectories for a spacecraft (SC) with a solar sail. The trajectories under consideration consist of repeated cycles of spacecraft movement to the target heliocentric orbit and back to the initial one. A model of a perfectly reflecting sail is used, which allows using the programs for optimal control of the sail angle, obtained on the basis of the Pontryagin maximum principle. The heliocentric motion is modeled in a flat polar coordinate system, and the spacecraft itself makes cyclic flights between two terrestrial planets along a closed trajectory. A boundary-value problem is formulated, in the solution of which the approach of the spacecraft to the target planet with the equalization of velocities is ensured (the encounter problem). Simulations of four cycles of Earth–Mercury–Earth and Earth–Mars–Earth motion with a characteristic acceleration of the solar sail of 0.25 mm/s2 have been carried out, for which the duration of one cycle is on average 2000 and 2341 days, respectively. Optimal sail-orientation control programs are obtained for a wide range of launch dates, and methods of searching for and choosing the initial values of conjugate variables are shown. The obtained results demonstrate the ability of a spacecraft with a solar sail to implement controlled motion along closed trajectories with a minimum duration of individual Earth–destination planet–Earth flights.

Fourier–Hermite Dynamic Programming for Optimal Control

In this paper, we propose a novel computational method for solving non-linear optimal control problems. The method is based on the use of Fourier–Hermite series for approximating the action-value function arising in dynamic programming instead of the conventional Taylor-series expansion used in differential dynamic programming (DDP). The coefficients of the Fourier–Hermite series can be numerically computed by using sigma-point methods, which leads to a novel class of sigma-point based dynamic programming methods. We also prove the quadratic convergence of the method and experimentally test its performance against other methods.

Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control

Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.

Computer modeling and software research of car and engine parts

Problem. The development of automotive technology for various purposes and the improvement of existing car models, requires a fast and flexible design process. Spatial models of details and nodes are the starting points for design, and the necessary design documentation is performed on their basis. When manufacturing parts on CNC machines, it is necessary to quickly obtain a control program that will increase the accuracy of the product by ensuring the optimal trajectory of the mutual movement of the part and the tool. Therefore, the creation of a comprehensive methodology for the design of car parts, their basic inspection and obtaining design documentation is an important technical task. Goal. The main goal of the work is to determine the rational sequence and basic principles of computer-aided design, research and manufacturing of car and engine parts, and the development of mathematical spatial models of surfaces in order to optimize control programs for CNC machines. Methodology. The approaches adopted in the work for solving the set goal are based on general design principles. The methods of conducting static and dynamic calculations, as well as spatial mathematical modeling of the processes of manufacturing parts were also used. Results. A comprehensive methodology for designing parts of engines and cars has been developed. The main principles of creating spatial models have been determined in order to achieve their flexibility and simple editing. Methods of automating the development of drawings and design documentation are described. The software options for the primary verification of static strength and frequency analysis are considered. A calculation program has been developed for constructing transient and amplitude-phase-frequency characteristics. The mathematical spatial modeling of typical surfaces of the camshaft is provided with the aim of further research and optimization of the development of a control program for processing on a CNC machine tool. Originality. The defined basic principles of designing parts of engines and cars provide an opportunity to create a flexible spatial model and more fully automate the process of drawing up technical documentation. The developed mathematical spatial models of the supporting and working surfaces of the camshaft make it possible to write a control program with the determination of the optimal trajectory of the mutual movement of the part and the tool. Practical value. The obtained results can be recommended when designing car parts and assemblies.

Event-triggered adaptive dynamic programming for optimal tracking control of unmanned surface vessel with input constraints

In this paper, an event-triggered control mechanism scheme based on dynamic surface control and adaptive dynamic programming (DSC-ETCADP) is proposed for optimal trajectory tracking of the unmanned surface vessel (USV) with input constraints. First, the control structure is designed using dynamic surface control (DSC) as feedforward control and adaptive dynamic programming as feedback control, which not only ensures the tracking of reference trajectory but also improves the control accuracy. Second, due to the data-driven nature of adaptive dynamic programming (ADP) and the ability to adjust parameters online, it can be solved by USV with unknown disturbance. Third, the event-triggered mechanism can save computation and reduce the number of executions of the controller, in addition to avoiding Zeno behavior. Finally, according to the Lyapunov stability theory, all signals in the closed-loop system are globally uniformly and ultimately bounded (UUB). The DSC-ETCADP scheme is compared with DSC method. Simulation results demonstrate the effectiveness of the proposed method.

Inventory Management in Supply Chains Based on a Linear Discrete System with a Quadratic Quality Criterion

Purpose of research. To analyze theoretical studies of models and methods used in the theory of inventory management and directions of their practical implementation. To present the problem of optimal inventory management as a discrete control problem. Tasks of this type are formulated in cases where there is a need to form strategies of management of material and production inventories in supply chains, taking into account their organization at a certain time interval. To propose a method for solving the corresponding management problem.Methods. As a basic model, we consider the process of inventory management in the warehouse, in which a certain balance between the products released from the warehouse into production, released for sale, as well as its residues, which form the inventory of the next period must be fulfilled. The process of inventory management in supply chains during the planning period is based on the procedure of finding the appropriate control action for a linear discrete controlled system with a quadratic quality index. Implementation of control uses the principle of feedback. The computer algebra system Wolfram Mathematica is chosen as a tool for implementing the control.Results. Within the framework of studying the methods of finding the optimal control, two solution methods were singled out - the method of finding the optimal program control and the method of determining the optimal control according to the feedback principle. In the process of verification of the obtained solution, several model examples with different initial conditions were considered.Conclusion. The results of testing the proposed discrete model showed that the feedback method makes it possible to quite efficiently solve the inventory management problem with different initial conditions, which is described by a system of difference equations.

Recovery of Aircraft Motion Parameters Using the Optimal Control Algorithms

A method for solving the signal recovery problem based on a direct search for the optimal program control is considered. It is based on the parameterization of the desired signals and finding a solution by numerical optimization in a finite-dimensional space using any genetic or population algorithm. In order to check the efficiency of the method, the problem of finding the angular velocities and orientation angles of the aircraft from the data available onboard in the absence of direct measurements is given. Different variants of signal parameterization are compared based on Hermitian cubic splines.

REFINEMENT OF OPTIMAL CONTROL PROBLEM FOR PRACTICAL IMPLEMENTATION OF ITS SOLUTION

The solution of the optimal control problem in the classical formulation is control in the form of a function of time. The implementation of such a solution leads to an open control system and therefore cannot be applied directly in practice. It is believed that solving the classical optimal control problem leads to an optimal control program and program trajectory in state space. To implement the movement of the control object along the program trajectory, it is necessary to build an additional movement stabilization system. The problem of synthesizing a system for stabilizing movement along a program trajectory and the requirements that this system should meet do not arise from the classical setting of the optimal control problem. An updated statement of the optimal control problem is given, which includes an additional requirement for an optimal trajectory, and the solution of which can be directly applied in practice in a real control object.

CUDA-інтеграція контурів керування авіаційного газотурбінного двигуна

The problem of accelerating the process of designing aircraft gas turbine engines and their control systems, the system "AIRCRAFT-AVIATION ENGINE-FUEL", and forming the technical type of an aircraft engine, adapting to new operating conditions within the framework of experimental design bureaus (EDB) and the industry is using automated systems with low computing performance and incomplete description. Information technologies for developing engines allow duplication and mismatch of data, loss of information and time during transmission and processing for making parametric and structural decisions. To better adaptation of the characteristics of an aviation engine (AE) to the tasks solved by an aircraft in flight, it is necessary to integrate control systems. Integrated control systems are especially effective for managing today's multi-mode aircraft. On the basis of their control, optimal control programs for the power plant (PP) are formed using the criteria for evaluating the effectiveness of the aircraft. This article proposes a paradigm for building integrated control loops for an aircraft gas turbine engine, which can be formed by automating control processes, an automatic control system, and combined control programs. The objective of this research is the processes of constructing adaptive control loops for aircraft gas turbine engines. The subject of this study is the adaptive control of aircraft gas turbine engines using embedded control loops and CUDA architecture. The goal is to improve the dynamic characteristics of an aircraft gas turbine engine through adaptive control using control loops, considering various aircraft flight modes and engine operating modes. Objectives: to determine the main controllable elements of an aircraft engine, adjustable parameters and factors for constructing control loops according to the principle of adaptation; describe the mechanism of joint management of gas turbine engines; to study the processes of building an integration circuit "aircraft - power plant" and develop the concept of an integrated ACS; define the CUDA paradigm for parallel computing of control loops. Conclusions. The scientific novelty lies in the formation of a paradigm for developing adaptive control models for gas turbine engines, considering different aircraft flight modes and engine operation modes.

Dimension reduction based adaptive dynamic programming for optimal control of discrete-time nonlinear control-affine systems

Dynamic programming based methods have been widely used in solving discrete-time nonlinear constrained optimal control problems. However, applying these methods in real-time is challenging because a large amount of memory is needed and the associated computational cost is high. Here, a search space dimension reduction strategy is proposed for a class of nonlinear discrete-time systems that are control-affine and invertible. Specifically, a bio-inspired motion rule is combined with inverse dynamics to reduce the value iteration search space to one dimension. The corresponding suboptimal control algorithm is developed and its optimality is analysed. An adaptation rule is developed to estimate uncertainties and improve the base policy. The closed-loop system is proven to be asymptotically stable. The advantages of the algorithm including much smaller computational cost and significantly reduced memory usage are demonstrated with two simulation examples.