Search Results (231)

Decarbonizing heavy-duty road freight transportation requires efficient energy management in zero-emission powertrains. This study investigates energy management strategies (EMSs) for a heavy-duty Fuel Cell Plug-in Hybrid Electric Vehicle (FC-PHEV). Rather than the typical charge-sustaining operation, these strategies are designed for charge-depleting operation, in which each route begins with a charged battery and ends at a lower state of charge (SOC), leveraging the vehicle’s plug-in capability. The EMSs are evaluated primarily in terms of energy consumption, while battery C-rate and fuel cell ramp rate are used as simple stress indicators for comparative analysis. A backward-facing vehicle model is developed to test several EMSs, including both optimization- and rule-based strategies. The Equivalent Consumption Minimization Strategy (ECMS) emerged as a promising option, motivating further testing with a forward-facing model and additional drive cycles. The simulation results show that ECMS consumed only 1.1% more energy than the global optimal solution found by Pontryagin’s Minimum Principle (PMP) and 7.5% less energy than a simple rule-based strategy, on average across five drive cycles. These results show that ECMS can be effective for a heavy-duty FC-PHEV operating in charge-depleting mode, extending its demonstrated applicability beyond charge-sustaining and light-duty vehicles. Full article

The time-optimal rendezvous problem is crucial for efficiently executing on-orbit servicing (OOS) missions in the future. To fulfill the detection requirement during rendezvous process, it is an essential issue that the maneuvering spacecraft flies over the designated waypoint. This paper presents an innovative methodology for planning the time-optimal spacecraft rendezvous trajectory, involving the constraints related to a flyover waypoint and being forced by a constant thrust. The method is specifically designed to handle the optimal problems with the shortest and unspecified flyover time and terminal rendezvous time. First, this article outlines the scenarios for a time-optimal rendezvous that incorporates the constraints of a flyover waypoint. Second, a time-normalized relative dynamic model for maneuvering spacecraft is derived using the Clohessy–Wiltshire (CW) equation. Third, the time-optimal control output under the constant thrust is provided leveraging Pontryagin’s minimum principle (PMP). Meanwhile, an indirect solution equation is established with the constraints of relative position and velocity for the flyover waypoint during the rendezvous process. Finally, a computational methodology for solving this time-optimal problem is proposed, integrating the initial guess for the unspecified time, multi-objective particle swarm optimization using multiple search strategies (MMOPSO) and Newton–Raphson method (NRM). Simulation results demonstrate that the method can effectively and practically solve the time-optimal rendezvous trajectory planning under a constant thrust, while satisfying the constraints of the flyover waypoint. Moreover, Monte Carlo simulations are performed, the results of which indicate that the proposed methodology exhibits strong robustness and fidelity. Full article

Numerous studies have shown that overweight and obesity significantly increase the risk of severe illnesses, including type 2 diabetes, hypertension, and knee osteoarthritis. This study aims to develop a generalized mathematical model to manage the growing prevalence of overweight and obesity. We first demonstrate that the model’s solution remains positive and bounded under specific conditions. To determine optimal intervention strategies, we apply Pontryagin’s minimum principle (PMP) to establish necessary optimality conditions. The Forward–Backward Sweeping Method (FBSM) is then used to obtain numerically optimal controls and to demonstrate their effect over a fixed time interval. The results indicate that the proposed approach effectively reduces overweight and obesity while ensuring cost-effectiveness. Full article

We establish a version of Pontryagin’s maximum principle for optimal control problems with impulses and phase constraints. Using the Dubovitskii–Milyutin theory, we construct a conic variational framework that handles impulsive dynamics and general state constraints. The main difficulty lies in working with piecewise continuous functions, required by the impulsive nature of the system. This setting also demands an extension of the classical result on the existence of non-negative Borel measures, which leads to an adjoint equation formulated as a Stieltjes integral. Theoretical results are illustrated with examples, and key results by I. Girsanov are extended to the impulsive context. Full article

Dental caries is an example of an oral infectious disease that affects many people worldwide, but it is not well studied in deterministic mathematical modeling. Therefore, we are interested in studying the dynamics of tooth cavity disease using a deterministic modeling approach. We propose a delay differential equation system (DDEs) to describe the phenomenon. The breakthrough of the constructed model is the formulation of the recovery rate as a saturation function constrained by healthcare capacity and the plausibility of caries reformation. In addition, we consider two controls, such as a health campaign and a post-treatment intervention. The mathematical analysis yields equilibrium solutions and their stability, which is determined by the basic reproduction number $\left({\mathfrak{R}}_0\right)$. Furthermore, backward bifurcation occurs as the medical facility’s capacity decreases, driven by an increasing infectious population. The sensitivity analysis results indicate that both considered controls are the most influential parameters. The optimal control problem is formulated using the Pontryagin Maximum Principle to obtain an optimal solution in suppressing the number of caries formation cases. At the end, a numerical simulation shows that interventions reduce the risk of transmission and suppress the number of infectious individuals. The constructed model has excellent future potential, such as generating a function for relapse cases or other preventive actions into an optimal control problem. Full article

Evolutionary changes can significantly impact interactions among populations and disrupt ecosystems by driving extinctions or collapsing population oscillations, posing substantial challenges to biodiversity conservation. This study addresses the ecological rescue of a predator population threatened by a mutant prey population using the optimal control method. To study this, we study a model that incorporates a genotypically structured prey population comprising wild-type, heterozygous, and mutant prey types, as well as the predator population. We prove that this model has both local and global existence and uniqueness of solutions, ensuring the model’s robustness. Then, we applied the optimal control method, incorporating Pontryagin’s Maximum Principle, to introduce a control input into the model and minimize the mutant population, thereby stabilizing the ecosystem. We utilize a reproduction number and a control efficacy measure to numerically demonstrate that the undesired dynamics of the model can be controlled, leading to the suppression of the mutant and the restoration of the oscillatory dynamics of the system. These findings demonstrate the applicability of optimal control strategies and provide a mathematical framework for managing such ecological disruptions. Full article

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 mathematical model of relative motion between the active and passive spacecraft is employed, which is formulated in dimensionless variables that characterize secular, periodic, and lateral motion components of the relative motion. By applying Pontryagin’s Maximum Principle, the equations governing the optimal relative motion of the spacecraft are derived. To address the discontinuities associated with the bang–bang switching function inherent in the motor-time-optimal problem, and the lack of a suitable initial guess, a homotopy method is adopted, in which the solution to the rendezvous time-optimal problem is used as an initial guess and is gradually deformed into the motor-time-optimal control. Considering the errors introduced by the linearization of the relative motion model, the obtained control law is validated via numerical simulations based on the original nonlinear dynamics of the system. Simulation results demonstrate that the proposed trajectory optimization methodology achieves high success rates and rapid convergence, providing valuable theoretical support and practical guidance for mission scenarios with similar trajectory design requirements. Full article

This study develops a mathematical model to investigate the transmission dynamics of HSV-II within the framework of symmetry in dynamical systems. The basic reproduction number ($R_0^{HSV}<1$) of the model was determined using the next generation method (NGM). The stability of the disease-free equilibrium point was also investigated using the Routh–Hurwitz Criterion and was found to be locally asymptotically stable (LAS) when $R_0^{HSV}<1$ but not globally asymptotically stable (GAS). To help ensure that the control variables were included correctly, sensitivity analysis was performed on the fundamental reproduction number parameters. Four control variables were applied for the model: HSV-II vaccination, effective condom use, laboratory test, and treatment. The optimality system was solved using Pontryagin’s maximum principle (PMP) to establish the optimal control strategy for combating the spread of the disease. Numerical solution was obtained by using the forward-backward Runge–Kutta fourth-order approach. The most effective approach to help eradicate HSV-II disease in the system is to combine the HSV-II vaccine, effective condom use, laboratory testing, and HSV therapy (strategy D). Full article

This paper focuses on finite-horizon optimum state feedback control problems for interconnected systems of two players involved with asymmetric one-step delay information. For the finite horizon optimum decentralized control problem, a crucial and adequate condition is derived by using Pontryagin’s maximum principle. Under this framework, player 1 transmits its state and control input data with a one-step delay to the controller of player 2, while player 1’s controller does not have access to the real-time or delayed states and control inputs of player 2, resulting in an asymmetric information structure characterized by a one-step delay Then, the solutions to the forward and backward stochastic difference equations are derived. A target tracking system is given in numerical examples to verify the proposed algorithm. Full article

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 a given initial state to a prescribed terminal state in the shortest possible time. Our approach combines Pontryagin’s maximum principle with Bellman’s principle of optimality. First, we decompose the original problem into a sequence of auxiliary problems, each corresponding to a single semi-oscillation. For every such subproblem, we obtain a complete analytical solution by applying Pontryagin’s maximum principle. These results allow us to reduce the global problem of minimizing the transfer time between the prescribed states to a finite-dimensional optimization problem over a sequence of intermediate amplitudes, which is then solved numerically by dynamic programming. Numerical experiments reveal characteristic features of optimal trajectories in the nonlinear regime, including a non-periodic switching structure, non-uniform semi-oscillation durations, and significant deviations from the behavior of the corresponding linearized system. The proposed framework provides a basis for the synthesis of fast oscillatory regimes in systems with controllable frequency, such as pendulum and crane systems and robotic manipulators. Full article

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 establishes a Pontryagin-type maximum principle for Volterra optimal control with general control and state constraints (fixed terminal constraints and time-dependent state bounds), where the cost combines a terminal term with a state-dependent and integral term. Using the Dubovitskii–Milyutin framework, we construct conic approximations for the cost, dynamics, and constraints and derive necessary optimality conditions under mild regularity: (i) a classical adjoint system when only terminal constraints are present and (ii) a Stieltjes-type adjoint with a non-negative Borel measure when pathwise state constraints are active. Furthermore, under convexity of the cost functional and linear Volterra dynamics, the maximum principle becomes a sufficient criterion for global optimality (recovering the classical sufficiency in the differential case). The differential case recovers the classical PMP, and an SIR example illustrates the results. A key theme is symmetry/duality: the adjoint differentiates in the state while the maximum condition differentiates in the control, reflecting operator transposition and the primal–dual geometry of Dubovitskii–Milyutin cones. Full article

Sandflies spread the neglected vector-borne disease anthroponotic cutaneous leishmaniasis (ACL), which only affects humans. Despite decades of control, asymptomatic carriers, vector pesticide resistance, and low public awareness prevent eradication. This study proposes a fractional-order optimal control model that integrates biological and behavioral aspects of ACL transmission to better understand its complex dynamics and intervention responses. We model asymptomatic human illnesses, insecticide-resistant sandflies, and a dynamic awareness function under public health campaigns and collective behavioral memory. Four time-dependent control variables—symptomatic treatment, pesticide spraying, bed net use, and awareness promotion—are introduced under a shared budget constraint to reflect public health resource constraints. In addition, Caputo fractional derivatives incorporate memory-dependent processes and hereditary effects, allowing for epidemic and behavioral states to depend on prior infections and interventions; on the other hand, standard integer-order frameworks miss temporal smoothness, delayed responses, and persistence effects from this memory feature, which affect optimal control trajectories. Next, we determine the optimality conditions for fractional-order systems using a generalized Pontryagin’s maximum principle, then solve the state–adjoint equations numerically with an efficient forward–backward sweep approach. Simulations show that fractional (memory-based) dynamics capture behavioral inertia and cumulative public response, improving awareness and treatment efforts. Furthermore, sensitivity tests indicate that integer-order models do not predict the optimal allocation of limited resources, highlighting memory effects in epidemiological decision-making. Consequently, the proposed method provides a realistic and flexible mathematical basis for cost-effective and sustainable ACL control plans in endemic settings, revealing how memory-dependent dynamics may affect disease development and intervention efficiency. Full article

This study constructs a Stackelberg differential game model for green technology invest-ment in the food industry under a governmental coordination mechanism. The optimal dynamic strategies for local governments and enterprises are derived using Pontryagin’s maximum principle. The backward differential equation method is employed in this study. It is used to analyze the impact of shadow prices on the optimal decisions of both parties. Furthermore, the study examines how social welfare benefits influence the food quality levels within the jurisdiction of local governments. Based on these findings, optimal strategy pathways are proposed to achieve social welfare and enterprise profit maximization in the green transition process of both government and enterprises. The results indicate that a local government’s investment in food quality improvement significantly enhances the food quality levels within their jurisdictions—greater government investment leads to higher food quality. At the same time, food quality levels are positively correlated with the enterprises’ green technology capital investment. Additionally, consumer price sensitivity and sensitivity to price differences have a notable impact on product pricing. As consumers become more price-sensitive, product prices decrease accordingly, which, in turn, helps increase the market share of the enterprises’ products. Full article

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 Lyapunov functions, and the derivation of optimal control laws based on Pontryagin’s Maximum Principle. Our methodology not only ensures theoretical soundness but also offers practical effectiveness. To demonstrate its applicability, we conduct simulations using real-world data from the AAPL stock database. The proposed RNN-based control framework significantly reduces the deviation between predicted system outputs and actual observations. We further enhance performance through two complementary strategies, a direct control method and a parameter optimization approach, both of which contribute to the accuracy and adaptability of the control system. These results confirm the potential of neural network-based control in managing complex nonlinear dynamics Full article

The challenge of optimally controlling energy storage systems under uncertainty conditions, whether due to uncertain storage device dynamics or load signal variability, is well established. Recent research works tackle this problem using two primary approaches: optimal control methods, such as stochastic dynamic programming, and data-driven techniques. This work’s objective is to quantify the inherent trade-offs between these methodologies and identify their respective strengths and weaknesses across different scenarios. We evaluate the degradation of performance, measured by increased operational costs, when a reinforcement learning policy is adopted instead of an optimal control policy, such as dynamic programming, Pontryagin’s minimum principle, or the Shortest-Path method. Our study examines three increasingly intricate use cases: ideal storage units, storage units with losses, and lossy storage units integrated with transmission line losses. For each scenario, we compare the performance of a representative optimal control technique against a reinforcement learning approach, seeking to establish broader comparative insights. Full article