This paper investigates the optimal control problem of orbital rendezvous for spacecraft in near-circular orbits with a low-thrust propulsion system. Two optimality criteria are considered: time-optimal and motor-time-optimal control. A linearized ma...
Battery systems are one of the most important components for the development of flexible energy storage for future applications. These comprise energy storage in both the mobility sector and stationary applications. To ensure the safe operation of mu...
This purely theoretical study considers two new geometric state-space properties of the classical linear time-optimal control problem with one input and real non-positive eigenvalues of the system, with constraints only on the control input and witho...
This paper proves a new lemma that characterizes controllability for linear Volterra control systems and shows that the usual controllability assumption for the variational linearized system near an optimal pair is superfluous. Building on this, it e...
In this work, we consider robotic systems for which the mass tensor is identified to be the metric in a Riemannian manifold. Cost functional invariance is achieved by constructing it with the identified metric. Optimal control evolution is revealed i...
In this paper, we consider an optimal control problem in the equilibrium thermodynamics of gases. The thermodynamic state of the gas is given by a Legendrian submanifold in a contact thermodynamic space. Using Pontryagin’s maximum principle, we...
We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interv...
In this paper, an efficient implementation of the Tau method is presented for finding the open-loop Nash equilibrium of noncooperative nonzero-sum two-player differential game problems with a finite-time horizon. Regarding this approach, the two-poin...
In this paper, optimal control theory is applied to a system of ordinary differential equations representing a hantavirus infection in rodent and alien populations. The effect of the optimal control in eliminating the rodent population that caused th...
In this work, we modified a dynamical system that addresses COVID-19 infection under a fractal-fractional-order derivative. The model investigates the psychological effects of the disease on humans. We establish global and local stability results for...
In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strain with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two...
This paper presents a neural network-based path planning method for fixed-wing UAVs under terminal roll-angle constraints. The nonlinear optimal path planning problem is first formulated as an optimal control problem. The necessary conditions derived...
This paper presents a novel approach to the controllability of nonlinear dynamic systems using recurrent neural networks (RNNs). We develop a comprehensive theoretical framework that integrates controllability analysis, stability verification via Lya...
Computer virus attacks result in significant losses each year, drawing considerable attention from enterprises, governments, academic institutions, and various other sectors. Researchers have proposed various approaches to fight against computer viru...
Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model co...
In pursuit–evasion scenarios, the pursuer typically possesses a lethal zone. If the evader effectively utilizes perceptual information, they can narrowly escape the lethal zone while minimizing energy consumption, thereby avoiding excessive and...
This work concerns the optimal control of a passive particle in viscous flows. This is relevant since, while there are many studies on optimal control in inviscid flows, there is little to no work in this context for viscous flows, and viscosity cann...
The fashion apparel industry is facing an increasingly growing demand, compounded by the short sales lifecycle and strong seasonality of clothing, posing significant challenges to inventory management in the retail sector. Despite some retailers like...
We propose a life-expectancy pay-off function (LEP) for determining optimal cancer treatment within a control theory framework. The LEP averages life expectancy over all future outcomes, outcomes that are determined by key events during therapy such...
Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train sp...
Many mathematical models have explored the dynamics of cholera but none have been used to predict the optimal strategies of the three control interventions (the use of hygiene promotion and social mobilization; the use of treatment by drug/oral re-hy...
This paper addresses the problem of optimizing obesity, which has been a challenging issue in the last decade based on recent data revealed in 2024 by the World Health Organization (WHO). The current work introduces a new mathematical model of the dy...
We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to poin...
Efficient train driving plays a vital role in reducing the overall energy consumption in the railway sector. An energy minimising control strategy can be computed using the framework given by optimal control theory; in particular, the Pontryagin maxi...
A SEIR control model describing the Ebola epidemic in a population of a constant size is considered over a given time interval. It contains two intervention control functions reflecting efforts to protect susceptible individuals from infected and exp...
We study a minimum-time (time-optimal) control problem for a nonlinear pendulum-type oscillator, in which the control input is the system’s natural frequency constrained to a prescribed interval. The objective is to transfer the oscillator from...
The paper proposes a generic methodology to incorporate constraints (pollutant emission, battery health, drivability) into on-line energy management strategies (EMSs) for hybrid electric vehicles (HEVs) and plug-in hybrid electric vehicles (PHEVs). T...
We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we con...
CAR T-cell immunotherapy is a new development in the treatment of leukemia, promising a new era in oncology. Although so far, this procedure only helps 50–90% of patients and, like other cancer treatments, has serious side effects. In this work...
China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and af...
This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian syste...
The following paper deals with a new property of linear time-optimal control problems with real eigenvalues of the system. This property unveils the possibility of synthesizing the time-optimal control without describing the switching hyper-surfaces....
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Diarrhea is responsible for killing around 525,000 children every year, even though it is preventable and treatable. This research focuses on both houseflies’ roles and humans’ roles in carrying pathogens causing diarrhea as multiple dise...
This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal...
This paper introduces a novel fractional-order model using the Caputo derivative operator to investigate the virus dynamics of adaptive immune responses. Two infection routes, namely cell-to-cell and virus-to-cell transmissions, are incorporated into...
We primarily focus on the formulation, theoretical, and numerical analyses of a non-autonomous model for tuberculosis (TB) prevention and control programs in a population where individuals suffering from the double trouble of tuberculosis and diabete...
Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope...
The aim of this paper is to propose mathematical models to predict and optimize the cost of wastewater treatment using bacteria and oxygen under fluctuating resource and cultivation conditions. We have thus developed deterministic mathematical models...
This study examines the scientific production focused on the Maximum Principle between 1962 and 2021. Results indicate a consistent increase in the absolute number of publications over time. In relative terms, there is a resurgence of interest in thi...
In this work, we investigated a simple mathematical model describing the consumption of virus-infected phytoplankton by zooplankton in a chemostat. The system was studied by calculating the basic reproduction number, the equilibrium points, and their...
Many significant real world challenges arise as optimization problems on different classes of control systems. In particular, ordinary differential equations with symmetries. The purpose of this review article is twofold. First, we give the informati...
This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is a curvilinear functional defined by a given differential one-form, while the optim...
The paper deals with an infinite-horizon optimal control problem with general asymptotic endpoint constraints. The fulfillment of constraints of this type can be viewed as the minimal necessary condition for the sustainability of solutions. A new ver...
The paper analyses dynamical growth models predicting the cyclic development of investigated economic factors. The provided research deals with an optimal control problem based on the economic growth model with the production function of Cobb–D...
We provide a rigorous mathematical formulation of Deep Learning (DL) methodologies through an in-depth analysis of the learning procedures characterizing Neural Network (NN) models within the theoretical frameworks of Stochastic Optimal Control (SOC)...
A electroelastic engine with a longitudinal piezoeffect is widely used in nanotechnology for nanomanipulators, laser systems, nanopumps, and scanning microscopy. For these nanomechatronics systems, the transition between individual positions of the s...
This work presents the results of a research study focused on the development and evaluation of an algorithmic optimal control framework for energy-efficient operation of screw compressors in smart power systems. The proposed approach is based on the...
Establishing a scientific ecological compensation mechanism for air pollution is crucial for air protection. This study models the ecological compensation mechanism of the Stackelberg differential game between the local regulator and an enterprise wi...
Within a given time interval we consider a nonlinear system of differential equations describing psoriasis treatment. Its phase variables define the concentrations of T-lymphocytes, keratinocytes and dendritic cells. Two scalar bounded controls are i...
We introduce a new optimal control problem where the controlled dynamical system depends on multi-order (incommensurate) fractional differential equations. The cost functional to be maximized is of Bolza type and depends on incommensurate Caputo frac...
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