Optimal Control Techniques Research Articles

MODERNIZING CLASSICAL OPTIMAL CONTROL: HARNESSING DIRECT AND INDIRECT OPTIMIZATION

An introduction to optimal control, a fundamental concept in engineering and science disciplines, is a process of finding ways of controlling dynamic systems in such a way that they achieve certain goals while being subjected to given state limitations. The conventional approaches developed in the past have been integral to solving optimal control problems, including the maximum principle belonging to Pontryagin and the dynamic programming method. While relatively straightforward, these methods are not always amenable to higher-dimensional scenarios, interacting forces, or other non-trivial constraints. This paper presents a new methodology to extend classical optimal control, considering both direct and indirect optimization techniques. The direct methods, Euler and Runge-Kutta, Trapezoidal, and Hermite-Simpson, do not require the explicit derivation of the analytical control laws to execute control trajectories. Semi-analytical techniques, such as the shooting method, are based the control laws on proposed adjoint differential equations. This paper presents the basic outline of the classical optimal control problem and discusses the direct and indirect optimization methods. It is illustrated by referencing various examples, like the fixed-rate royalty payment approach. After outlining each framework, we identify the positive and negative aspects of the approach in questions of consistency and performance. Finally, the problems on the synergy of direct and indirect methods are considered further, and areas of further development of the presented methods and their integration with the more sophisticated tools, such as machine learning are identified. It can be concluded that the approach of using both direct and indirect optimization methods presents great potential in modernizing the classical optimal control, which challenges the conventional techniques and indicates potential for further development of the control system optimization.

Advanced optimal control approaches for immune boosting and clinical treatment to enhance dengue viremia models using ABC fractional-order analysis

IntroductionThis work focuses on the Dengue-viremia ABC (Atangana-Baleanu Caputo) fractional-order differential equations, accounting for both symptomatic and asymptomatic infected cases. Symptomatic cases are characterized by higher viremia levels, whereas asymptomatic cases exhibit lower viremia levels. The fractional-order model highlights memory effects and other advantages over traditional models, offering a more comprehensive representation of dengue dynamics.MethodsThe total population is divided into four compartments: susceptible, asymptomatic infected, symptomatic infected, and recovered. The model incorporates an immune-boosting factor for asymptomatic infected individuals and clinical treatment for symptomatic cases. Positivity and boundedness of the model are validated, and both local and global stability analyses are performed. The novel Adams-Bash numerical scheme is utilized for simulations to rigorously assess the impact of optimal control interventions.ResultsThe results demonstrate the effectiveness of the proposed control strategies. The reproduction numbers must be reduced based on specific optimal control conditions to effectively mitigate disease outbreaks. Numerical simulations confirm that the optimal control measures can significantly reduce the spread of the disease.DiscussionThis research advances the understanding of Dengue-viremia dynamics and provides valuable insights into the application of ABC fractional-order analysis. By incorporating immune-boosting and clinical treatment into the model, the study offers practical guidelines for implementing successful disease control strategies. The findings highlight the potential of using optimal control techniques in public health interventions to manage disease outbreaks more effectively.

A comparative analysis of intelligent energy modelling approaches for a grid-tied PVT system application

Renewable energy resources are a long-term answer to the current chronic energy dilemma. Solar photovoltaic (PV) systems are the most often used form of a practical solution for power supply and energy management in buildings. A PV-thermal (PVT) system is essential to lowering the demand for grid energy by capturing electrical and thermal energy from sunlight, optimising energy usage and encouraging sustainable energy practices. The most significant difficulty faced by developing countries, such as South Africa, is a lack of power supply to meet demand while limiting grid overload. An alternative source of energy is a critical component. This research compares two intelligent energy modelling methodologies: optimal control scheme-based open loop and model predictive control (MPC) in a PVT application. The primary goal of the modelling is to limit the electricity required from the grid while stressing the system’s energy efficiency and cost-effectiveness. The open loop approach uses mathematical optimisation techniques to establish the best control strategy for the PVT system. The ideal set-points for various system parameters are found by presenting the problem as an optimisation task to reduce grid power usage. The optimal control technique delivers a global optimisation solution based on the system dynamics and constraints. The MPC technique employs a predictive control technique of the PVT system to create optimal control actions in a receding horizon manner. The MPC algorithm anticipates future system behaviour and generates control actions that minimise grid power drawn by iteratively solving an optimisation problem at each time step. This robust online control scheme enables real-time modifications and responses to system disruptions that effectively and dynamically coordinate system behaviour.

Unit prediction horizon [formula omitted] based model predictive control for the fuel cell based plug-in hybrid electric vehicle with rule-based energy management system

Plug-in hybrid electric vehicles (PHEVs) provide a good alternative in achieving better performance and in the reduction of harmful gas emissions. The hybrid energy storage system (HESS) and the integrated charging unit constitute the PHEV under consideration. To meet the load demands, the proposed HESS is a coupled system comprising a fuel cell, high energy density battery, and high-power density super-capacitor. On-board charging involves the utilization of a DC–DC buck converter and an uncontrolled rectifier and two buck-boost converters are utilized to facilitate a smooth transfer of energy. A rule-based supervisory controller has been implemented for different load conditions which takes into account the state of charge of energy sources and also the total power inflow of the power sources. A model predictive control (MPC) technique is implemented to ensure that PHEVs function smoothly in terms of regulation of DC bus voltage and tracking of current. Unit prediction horizon i.e. only one step ahead looking into the future is considered for the MPC to make it computationally less expensive. MPC is designed in such a way that its performance is close to our favorite linear controller which in our case is the H∞ controller. The inverse optimal control technique is used for determining the weight matrices of the cost function. The proposed controller has been simulated using MATLAB. Also, the performance comparison is made between the designed MPC and the non-linear control approach i.e. integral sliding mode control and integral backstepping-based control to show that it achieves comparable or superior performance to the non-linear controller. The real-time performance of H∞ based MPC is verified using controller hardware in the loop experimental setup.

Smoking and alcoholism dual addiction dissemination model analysis with optimal control theory and cost-effectiveness.

A mathematical model of the dual addiction dissemination dynamics of alcoholism and smoking was created and examined in this work, along with cost-effectiveness and optimal control techniques. The primary goal of the research is to determine which cost-efficient management techniques are most helpful in lowering the problem of dual addiction dispersion in the community. The smoking addiction sub-model, the alcohol addiction sub-model, and the dual addiction model between alcohol and smoking were all calculated, and their stability was examined in this study. The effective reproduction numbers of the models are computed using the next-generation operator technique. When the model's effective reproduction number is smaller than one, the backward bifurcation phenomenon is seen. Six time-dependent control measures are taken into consideration when formulating and analyzing the optimum control issue. Utilizing and applying the parameter values and using MATLAB ode45 solver we performed numerical simulations for both the dual addiction model and its optimal control problem. Furthermore, using the incremental cost-effectiveness ratio (ICER), we carried out the cost-effectiveness analyses. The cost-effectiveness analysis shows that implementing all the protection (education) control measures simultaneously (i.e., implementing Strategy A) is the most cost-effective strategy. Finally, we recommend that the public health stakeholders must put great effort into the implementation of Strategy A to reduce the smoking and alcoholism dual addiction dissemination problem in the community.

Effective Pest Control Through Natural Predators: A Dynamical Plant–Pest–Predator Model

The impact of pests on crop yield is a significant worry for farmers, and finding an effective strategy to control insect population growth has become a pressing matter. This study explores the dynamic analysis of a model that incorporates natural predators to control crop pests. In the research, an analysis is conducted on the model’s positivity and boundedness, followed by an examination of the existence and stability of the equilibrium points. The study focused on analyzing bifurcations at a biologically feasible equilibrium point. The parameters considered for bifurcation are the predation rate by pests and the consumption rate of natural predators. In addition, an optimal control technique has been employed to enhance the growth of the plant population through the utilization of Pontryagin’s maximum principle. Moreover, the impact of the nine parameters on the model is examined through sensitivity analysis using the partial rank correlation coefficient method. Numerical simulations are conducted to validate the analytical findings, revealing the occurrence of bifurcation and the positive impact of control on plant population growth.

Optimal Control Techniques in Managing Red Palm Weevil Infestations: A Mathematical Approach

This article introduces a mathematical analysis of the red palm weevil (RPW) model that incorporates optimal control techniques. The investigation delves into the dynamics among date palm trees, the RPW, and tree micro-injection. The analysis assesses the impact of sex pheromone traps and tree trunk injections on the RPW population. Sufficient constraints are identified to provide both local stability and global stability analysis of equilibrium points. The paper uses Sotomayor’s theorem as a guide to compute local bifurcations near equilibrium points. The study concludes that adopting control strategies shows to a substantial decline in the RPW population, ultimately resulting in extinction. Numerical simulations are employed to visually illustrate and support the theoretical findings.

Reachable Set Computation with Terminal Velocity Constraints

This work establishes a general-purpose method for computing the exact boundary of the reachable set in a specified direction, with additional constraints imposed on the terminal velocities. Reachable sets with rest boundary conditions, that is, zero-velocity constraints imposed at initial and final times, are of interest for formation flying and spacecraft rendezvous and docking applications. The rest-to-rest reachability problem is extended to compute reachable neighboring circular orbits and a modified problem formulation is developed to exclusively compute the maximum and minimum reachable circular orbits. Reachable sets are computed by applying classical optimal control techniques to a maximum position optimization problem. A solution method for the optimization problem is outlined, which makes use of a Newton’s method solving schema. Additional constraints are added to the problem to compute maxima along specified directions, allowing for the characterization of the reachable set in as many directions as desired. Example reachable sets are computed to illustrate the use of this method on various systems, including an application to relative motion.

Optimal control model for the spread of Streptococcus suis in human population

Streptococcus suis infection is a zoonotic disease that can spread from pigs to humans. The infection can cause permanent deafness in people. Although it is considered as a neglected zoonotic pathogen, the prevalence of this infection has not measurably decreased in recent years. In this research, we proposed mathematical models of S. suis infection in both human and pig populations. Disinfectant sterilization in swine farms and educational campaigns were considered for cooperative control strategies. The aim of this study was to derive an optimal control strategy by using optimal control techniques associated with an existing epidemic model. Equilibrium points and the basic reproduction numbers were analyzed to determine the effect of control parameters in the constant case. For the optimal control problem, we showed numerically that the optimal control functions effectively reduced the number of infectious individuals within a finite time. However, the suggested control functions had more impact on the human group than the swine group. The sensitivity analysis implied that the control of swine population should be focused on the surveillance of weaning piglets.

Economic evaluation of a two-strain Hepatitis C vaccination model in Bangladesh using optimal control technique

Economic evaluation of a two-strain Hepatitis C vaccination model in Bangladesh using optimal control technique

AI based UPQC control technique for power quality optimization of railway transportation systems

Metro trains have non-linear load characteristics, which means that the power sent to them gets distorted. Problems are caused by changes in power, swells, harmonics, and other disturbances. In this research, an artificial intelligence-driven control method was used on a unified power quality conditioner (UPQC) to help reduce power quality problems and improve power quality. Three advanced control methods are built and compared using MATLAB Simulink. Some of these methods are the ANN Controller, the NARMA-L2 Controller, and the PI Controller, improved using the Adaptive Lizard Algorithm. The controls' usefulness is judged by how well they lower the total harmonic distortion (THD) in the source current. The results show that all three AI-based controls work much better than the system that was not paid for. The ANN Controller works the best, followed by the NARMA-L2 Controller, and the PI Controller improved with the Adaptive Lizard Algorithm. These AI-driven control methods can enhance power quality and ensure that metro rail systems run smoothly and efficiently, as shown by how well they work. Modern transportation networks need more advanced ways to handle power quality, and this research helps make those solutions come together.

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.

Optimal IOFL-based economic model predictive control technique for boiler-turbine system

The optimal control design of the boiler-turbine system is vital to ensure feasibility and high responsiveness over desired load variations. Using the traditional linear control techniques realization of this task is difficult, as the boiler-turbine mechanism has strong nonlinearities. Besides, environmental and economic concerns have replaced existing tracking control ones as the primary concerns of advanced power plants. Thus, this study proposes an optimal economic model predictive controller (EMPC) scheme for this unit on the basis of the input/output feedback linearization (IOFL) method. By employing the IOFL method, this unit is decoupled into a new linearized model that is utilized for developing the suggested optimal IOFL EMPC technique. The proposed control scheme is formulated in an economic quadratic programming form that considers the input-rate and input limits of the unit for optimal economic performance. In addition, an adaptive iterative algorithm is utilized for constraints mapping with guaranteeing a feasible solution in a finite number of steps without violation of original constraints over the entire predictive horizon. The outcomes of the simulation show that the suggested optimal IOFL EMPC scheme offers an improved dynamic and economic output performance over fuzzy hierarchical MPC, fuzzy EMPC, and nonlinear EMPC techniques during various load variations.

Optimized backstepping‐based finite‐time containment control for nonlinear multi‐agent systems with prescribed performance

AbstractIn this article, a finite‐time optimal containment control method is proposed for nonlinear multi‐agent systems with prescribed performance. First, a neural network‐based reinforcement learning algorithm is developed under the optimized backstepping framework. The algorithm employs an identifier‐critic‐actor architecture, where the identifiers, critics and actors are used to estimate the unknown dynamics, evaluate the system performance, and optimize the system, respectively. Subsequently, in order to guarantee the transient performance of the tracking error, the original system is converted into an equivalent unconstrained system. Then, the tracking errors are allowed to converge to a prescribed set of residuals in finite time by combining prescribed performance control and finite‐time optimal control techniques. Furthermore, by using the Lyapunov stability theorem, it is verified that all signals are semi‐globally practical finite‐time stable, and all followers can converge to a convex region formed by multiple leaders. Finally, the effectiveness of the proposed scheme is demonstrated by a practical example.

Modeling, analyzing and simulating the Measles transmission dynamics through efficient computational optimal control technique

Modeling, analyzing and simulating the Measles transmission dynamics through efficient computational optimal control technique

Assessing the impact of immunotherapy on oncolytic virotherapy in the treatment of cancer

AbstractCombined oncolytic virotherapy and immunotherapy are novel treatment protocols that represent a promising and advantageous strategy for various cancers, surpassing conventional anti-cancer treatments. This is due to the reduced toxicity associated with traditional cancer therapies. We present a mathematical model that describes the interactions between tumor cells, the immune response, and the combined application of virotherapy and interleukin-2 (IL-2). A stability analysis of the model for both the tumor and tumor-free states is discussed. To gain insight into the impact of model parameters on tumor cell growth and inhibition, we perform a sensitivity analysis using Latin hypercube sampling to compute partial rank correlation coefficient values and their associated p-values. Furthermore, we perform optimal control techniques using the Pontryagin maximum principle to minimize tumor burden and determine the most effective protocol for the administered treatment. We numerically demonstrate the ability of combined virotherapy and IL-2 to eliminate tumors.

Sparse randomized policies for Markov decision processes based on Tsallis divergence regularization

This work investigates a somewhat different point of view on Markov decision processes by reinterpreting them as a randomized shortest paths problem on a bipartite graph, therefore establishing bridges with entropy-regularized reinforcement learning. The graph structure contains the set of states as “left” nodes and the set of actions as “right” nodes. In that context, the action-to-state transition probabilities are provided by the environment whereas the state-to-action probabilities correspond to the (stochastic) policy to be found. The randomized shortest paths formalism (minimizing expected cost to the goal state subject to (Shannon or Tsallis) relative entropy regularization) is then readily applied to this bipartite structure, providing a possibly sparse stochastic policy interpolating between a least-cost and a purely random policy. The algorithm computing the policy is closely related to the dual linear programming formulation of the Markov decision processes to which the relative entropy regularization term, multiplied by a scaling factor balancing exploitation and exploration (the temperature), is added. It is derived from well-known techniques of discrete optimal control, relying on costates (Lagrange parameters) backward computation. In summary, the proposed algorithm allows the design of optimal stochastic – but still sparse – policies, ranging from a purely rational to a random behavior, depending on the temperature parameter.

Evaluating the impact of double dose vaccination on SARS-CoV-2 spread through optimal control analysis

This paper presents a new nonlinear epidemic model for the spread of SARS-CoV-2 that incorporates the effect of double dose vaccination. The model is analyzed using qualitative, stability, and sensitivity analysis techniques to investigate the impact of vaccination on the spread of the virus. We derive the basic reproduction number and perform stability analysis of the disease-free and endemic equilibrium points. The model is also subjected to sensitivity analysis to identify the most influential model parameters affecting the disease dynamics. The values of the parameters are estimated with the help of the least square curve fitting tools. Finally, the model is simulated numerically to assess the effectiveness of various control strategies, including vaccination and quarantine, in reducing the spread of the virus. Optimal control techniques are employed to determine the optimal allocation of resources for implementing control measures. Our results suggest that increasing the vaccination coverage, adherence to quarantine measures, and resource allocation are effective strategies for controlling the epidemic. The study provides valuable insights into the dynamics of the pandemic and offers guidance for policymakers in formulating effective control measures.

High-efficiency realization of the super-robust Rydberg Deutsch gate

Quantum logic gates are the essential components of quantum computation and have broad practical applications, especially for the multiple-qubit logic gates. Compared with appliying a series of single- and two-qubit gates, constrcuting quantum computation with multiple-qubit logic gates can be more efficient and high-fidelity. As a three-qubit logic gate, Deutsch gate enables the realization of any feasible quantum computations. Based on neutral atoms, we present a scheme of super-robust Deutsch gate via optimal control technique. Utilizing the Rydberg blockade effect of neutral atoms, we design an implementable D(β) based on the three-step program. One of the notable advantages of this function is that β can be achieved arbitrarily between 0 and π with the operation of target atom. In addition, we give an analytical solution agreed very well with numerical simulations for the residual blocking effect between next-neighbor atoms that affects the performance quality of Deutsch gate. The fidelity of our proposed scheme is demonstrated by numerical simulation of the master equation based on the full Hamiltonian, and the robustness of our scheme with control errors is also illustrated. Our proposal offers an alternative promising scheme for fault-tolerant quantum computation. Published by the American Physical Society 2024

Adaptive PMSM Control of Ship Electric Propulsion with Energy-Saving Features

Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors (PMSMs) an attractive solution due to their characteristics. This paper discusses the control problem of a PMSM based on the input–output feedback linearization method combined with the optimal and adaptive control techniques. The method presented here integrates the parameter tuning process with the optimal design of the baseline controller. Since the load disturbances are treated as an additional unknown parameter, there is no need to introduce an integral action to deal with the resulting steady-state error. An important feature of the designed controller is the so-called energetic optimization of the system; i.e., in addition to the aforementioned adaptive and optimal controller, it has a feature of ensuring zero reactive power consumed by the system. The performed simulations of the machine speed stabilization process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental (load) disturbances. Besides achieving high-quality control, an essential feature of this approach is the elimination of the tuning problem.