Search Results (72)

One of the main obstacles in rice cultivation is tungro disease, caused by Rice Tungro Spherical Virus (RTSV) and Rice Tungro Bacilliform Virus (RTBV), which are transmitted by green leafhopper vectors (Nephotettix virescens). This disease can be controlled by using pesticides and refugia plants. Excessive use of pesticides can have negative impacts and high costs, so it is necessary to control the use of pesticides. In this study, a mathematical model of the spread of tungro virus disease in rice plants was developed by considering the characteristics of the virus, the presence of green leafhoppers and natural enemies, refugia planting, and pesticide use. From this model, dynamic and sensitivity analyses were carried out, and the optimal control theory was searched using the Pontryagin minimum principle. The analysis results showed three equilibriums: two non-endemic equilibriums (when plant and vector populations exist and when plant, vector, and natural enemy populations exist) and one endemic equilibrium. The non-endemic equilibrium will be asymptotically stable locally if $R_0<1$. At the same time, the parameters that greatly influence the spread of this disease are parameters $\mu , {\mu }_2$, and $\varphi$ for local sensitivity analysis and $\alpha , a, \beta , b, \varphi ,$ and ${\mu }_2$ for global sensitivity analysis. The results of the numerical simulation show that control using combined control is more effective in reducing the intensity of the spread of tungro disease in rice plants than control in the form of planting refugia plants as a source of food for natural enemies. The use of pesticides is sufficient for only four days, so the costs incurred are quite effective in controlling the spread of this disease. Full article

With increasingly stringent emission regulations, various clean fuel engines, electric propulsion systems, and renewable energy sources have been demonstratively applied in marine power systems. The development of control strategies that can effectively and efficiently coordinate the operation of multiple energy sources has become a key research focus. This study uses a modular modeling method to establish a system simulation model for a parallel hybrid ship with a natural gas engine (NGE) as the prime mover, and designs an energy management control strategy that can run in real time. The strategy is based on Pontryagin’s minimum principle (PMP) for power allocation, and is supplemented by a hybrid model predictive control (HMPC) method for speed-tracking control of the power system. Finally, the designed strategy is evaluated. Through simulation and hardware-in-the-loop (HIL) experimental validation, results compared with the Rule-based strategy indicate that under the given conditions, the SOC final value deviation from the initial value is reduced from 11.5% (in the reference strategy) to 0.39%. The system speed error integral is significantly lower at 39.06, compared to 2264.67 in the reference strategy. While gas consumption increased slightly by 2.4%, emissions were reduced by 3.2%. Full article

Cancer cells typically divide with weaker synchronisation with the circadian clock than normal cells, with the degree of decoupling increasing with tumour maturity. Chronotherapy exploits this loss of synchronisation, using drugs with circadian-clock-dependent activity and timed infusion to balance the competing demands of reducing toxicity toward normal cells that display physiological circadian rhythms and of efficacy against the tumour. We analysed optimal chronotherapy for one-compartment nonlinear tumour growth models that were no longer synchronised with the circadian clock, minimising a cost function with a periodically driven running cost accounting for the circadian drug tolerability of normal cells. Using Pontryagin’s Minimum Principle (PMP), we show, for drugs that either increase the cell death rate or kill dividing cells, that optimal solutions are aperiodic bang–bang solutions with two switches per day, with the duration of the daily drug administration increasing as treatment progresses; for large tumours, optimal therapy can in fact switch mid treatment from aperiodic to continuous treatment. We illustrate this with tumours grown under logistic and Gompertz dynamics conditions; for logistic growth, we categorise the different types of solutions. Singular solutions can be applicable for some nonlinear tumour growth models if the per capita growth rate is convex. Direct comparison of the optimal aperiodic solution with the optimal periodic solution shows the former presents reduced toxicity whilst retaining similar efficacy against the tumour. We only found periodic solutions with a daily period in one-compartment exponential growth models, whilst models incorporating nonlinear growth had generic aperiodic solutions, and linear multi-compartments appeared to have long-period (weeks) periodic solutions. Our results suggest that chronotherapy-based optimal solutions under a harmonic running cost are not typically periodic infusion schedules with a 24 h period. Full article

To enhance the fuel efficiency of fuel cell hybrid electric vehicles (FCHEVs), we propose a hierarchical energy management strategy (HEMS) to efficiently allocate power to a hybrid system comprising a fuel cell and a battery. Firstly, the upper-layer supervisor employs a fuzzy fault-tolerant control and prediction strategy for the battery and fuel cell management system, ensuring vehicle stability and maintaining a healthy state of charge for both the battery and fuel cell, even during faults. Secondly, in the lower layer, dynamic programming and Pontryagin’s minimum principle are utilized to distribute the necessary power between the fuel cell system and the battery. This layer also incorporates an optimized proportional-integral controller for precise tracking of vehicle subsystem set-points. Finally, we compare the economic and dynamic performance of the vehicle using HEMS with other strategies, such as the equivalent consumption minimization strategy and fuzzy logic control strategy. Simulation results demonstrate that HEMS reduces hydrogen consumption and enhances overall vehicle energy efficiency across all operating conditions, indicating superior economic performance. Additionally, the dynamic performance of the vehicle shows significant improvement. Full article

Huanglongbing (HLB), also known as citrus greening disease, represents a severe and imminent threat to the global citrus industry. With no complete cure currently available, effective control strategies are crucial. This article presents a transmission model of HLB, both with and without nutrient injection, to explore methods for controlling disease spread. By calculating the basic reproduction number ($R_0$) and analyzing threshold dynamics, we demonstrate that the system remains globally stable when $R_0<1$, but persists when $R_0>1$. Sensitivity analyses reveal factors that significantly impact HLB spread on both global and local scales. We also propose a comprehensive optimal control model using the pontryagin minimum principle and validate its feasibility through numerical simulations. Results show that while removing infected trees and spraying insecticides can significantly reduce disease spread, a combination of measures, including the production of disease-free budwood and nursery trees, nutrient solution injection, removal of infected trees, and insecticide application, provides superior control and meets the desired control targets. These findings offer valuable insights for policymakers in understanding and managing HLB outbreaks. Full article

Optimization studies for the energy management systems of hybrid electric powertrains have critical importance as an effective measure for vehicle manufacturers to reduce greenhouse gas emissions and fuel consumption due to increasingly stringent emission regulations in the automotive industry, strict fuel economy legislation, continuously rising oil prices, and increasing consumer awareness of global warming and environmental pollution. In this study, firstly, the mathematical model of the powertrain and the rule-based energy management system of the vehicle with a power-split hybrid electric vehicle configuration are developed in the Matlab/Simulink environment and verified with real test data from the vehicle dynamometer for the UDDS drive cycle. In this way, a realistic virtual test platform has been developed where the simulation results of the energy management systems based on discrete dynamic programming and Pontryagin’s minimum principle optimization can be used to train the artificial neural network-based energy management algorithms for hybrid electric vehicles. The average fuel consumption in relation to the break specific fuel consumption of the internal combustion engine and the total electrical energy consumption of the battery in relation to the operating efficiency of the electrical machines, obtained by comparing the simulation results at the initial battery charging conditions of the vehicle using different driving cycles, will be analyzed and the advantages of the different energy management techniques used will be evaluated. Full article

This paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control problems through indirect methods. Specifically, PoNNs learn to solve the Two-Point Boundary Value Problem derived from the application of the Pontryagin Minimum Principle to the problem’s Hamiltonian. Within PoNNs, the Extreme Theory of Functional Connections (X-TFC) is leveraged to approximate states and costates using constrained expressions (CEs). These CEs comprise a free function, modeled by a shallow neural network trained via Extreme Learning Machine, and a functional component that consistently satisfies boundary conditions analytically. Addressing discontinuous control, a smoothing technique is employed, substituting the sign function with a hyperbolic tangent function and implementing a continuation procedure on the smoothing parameter. The proposed methodology is applied to scenarios involving fuel-optimal Earth−Mars interplanetary transfers and Mars landing trajectories. Remarkably, PoNNs exhibit convergence to solutions even with randomly initialized parameters, determining the number and timing of control switches without prior information. Additionally, an analytical approximation of the solution allows for optimal control computation at unencountered points during training. Comparative analysis reveals the efficacy of the proposed approach, which rivals state-of-the-art methods such as the shooting technique and the adaptive Gaussian quadrature collocation method. Full article

In order to study the energy distribution of the tandem hybrid tractor and achieve optimal fuel economy under the whole operating condition, an energy distribution strategy based on PMP (Pontryagin minimum principle) is proposed. The performance parameters of the relevant power components are obtained by constructing the test bench of the tandem hybrid tractor. At the same time, the mathematical model of energy distribution is established from the aspects of energy distribution objective function, state variable, and variable constraint. Based on the external characteristic test of the hub motor and the resistance analysis, the transport operation condition of the tractor is selected as the simulation target condition. The ADVISOR2002 and Simulink software are used to jointly simulate the three energy distribution strategies: the thermostat type, the power-following type, and the PMP type. The simulation results show that, compared with the other two, the fuel economy and battery power loss of the PMP-based energy distribution strategy are significantly improved. The fuel consumption per 100 km is decreased by 32.91% and 26.10%, respectively, which verifies the feasibility of the strategy. This study is of great significance for improving the production efficiency and reducing fuel consumption of hybrid tractors. Full article

Wave Energy Converters (WECs) are designed to be deployed in arrays, usually in a limited space, to minimize the cost of installation, mooring, and maintenance. Control methods that attempt to maximize the harvested power often lead to power flow from the WEC to the ocean, at times, to maximize the overall harvested power from the ocean over a longer period. The Power Take-Off (PTO) units that can provide power to the ocean (reactive power) are usually more expensive and complex. In this work, an optimal control formulation is presented using Pontryagin’s minimum principle that aims to maximize the harvested energy subject to constraints on the maximum PTO force and power flow direction. An analytical formulation is presented for the optimal control of an array of WECs, assuming irregular wave input. Three variations of the developed control are tested: a formulation without power constraints, a formulation that only allows for positive power, and finally, a formulation that allows for finite reactive power. The control is compared with optimally tuned damping and bang–bang control. Full article

In the grid-connected operation dynamics of brushless doubly fed generators (BDFGs), a dip in the grid voltage is equivalent to suddenly adding a reverse voltage source at the parallel node. By deriving the expressions of the transient current of power winding (PW), control winding (CW), and rotor winding (RW) of a BDFG in the complex frequency domain under a natural state, it was concluded that the overshoot and oscillation time are affected by the CW voltage, the drop degree and phase of the grid voltage, and the rotor speed. Therefore, an optimal control strategy is proposed. A state model with the CW current as the state variable was constructed using the Pontryagin minimum principle. The finite-time integral value of the square of the electromagnetic torque was set as the objective function to achieve the minimum value that could suppress the overshoot and oscillation of the electromagnetic torque, and the optimal CW voltage command value was directly solved to accelerate the convergence of the BDFG’s physical quantities, thereby reducing the amplitude. Finally, the feasibility of the optimal control algorithm was verified using tests on an experimental platform. Full article

Energy savings in electric rail transport are important in order to increase energy efficiency and reduce its carbon footprint. This can be achieved by storing and using the energy generated during regenerative braking. The system described in this paper consists of a supercapacitor energy storage system (SC ESS), a bidirectional DC/DC converter, and an algorithm to control the energy flow. The proper design of the algorithm is critical for maximizing energy savings and stabilizing the power grid, and it affects the lifetime of the SC ESS. This paper presents an energy flow control algorithm based on Pontryagin’s minimum principle that balances maximum energy savings with maximum SC ESS lifetime. The algorithm also performs SC ESS recharging while the rail vehicle stops on inclines to reduce the impact of its next acceleration on the power grid. To validate the algorithm, offline simulations are performed using real tram speed measurements. The results are then verified with a real-time laboratory emulation setup with HIL simulation. The tram and power grid are emulated with LiFePO4 batteries, while the SC ESS is emulated with a supercapacitor. The proposed algorithm controls a three-phase converter that enables energy exchange between the batteries and the supercapacitor. The results show that the proposed algorithm is feasible in real time and that it can be used under real operating conditions. Full article

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 maximum principle can be used. Our optimisation approach is based on an algorithm presented by Khmelnitsky that considers electric trains equipped with regenerative braking. A derivation of Khmelnitsky’s theory from a more general formulation of the maximum principle is given in this article, and a complete list of switching cases between different driving regimes is included that is essential for practical application. A number of numerical examples are added to visualise the various switching cases. Energy consumption data from real-life operation of passenger trains are compared to the calculated energy minimum. In the presented study, the optimised strategy was able to save 37 percent of the average energy demand of the train in operation. The sensitivity of the energy consumption to deviations of the train speed from the optimum speed profile is studied in an example. Another example illustrates that the efficiency of regenerative braking has an effect on the optimum speed profile. Full article

We study a time-optimal problem in the roto-translation group with admissible control in a circular sector. The problem reveals the trajectories of a car model that can move forward on a plane and turn with a given minimum turning radius. Our work generalizes the sub-Riemannian problem by adding a restriction on the velocity vector to lie in a circular sector. The sub-Riemannian problem is given by a special case when the sector is the full disc. The trajectories of the system are applicable in image processing to detect salient lines. We study the local and global controllability of the system and the existence of a solution for given arbitrary boundary conditions. In a general case of the sector opening angle, the system is globally but not small-time locally controllable. We show that when the angle is obtuse, a solution exists for any boundary conditions, and when the angle is reflex, a solution does not exist for some boundary conditions. We apply the Pontryagin maximum principle and derive a Hamiltonian system for extremals. Analyzing a phase portrait of the Hamiltonian system, we introduce the rectified coordinates and obtain an explicit expression for the extremals in Jacobi elliptic functions. We show that abnormal extremals are of circular type, and they correspond to motions of a car along circular arcs of minimal possible radius. The normal extremals in a general case are given by concatenation of segments of sub-Riemannian geodesics in ${SE}_2$ and arcs of circular extremals. We show that, in a general case, the vertical (momentum) part of the extremals is periodic. We partially study the optimality of the extremals and provide estimates for the cut time in terms of the period of the vertical part. Full article

We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of anesthesia relies on a pharmacokinetic/pharmacodynamic (PK/PD) model proposed by Bailey and Haddad in 2005 to regulate the infusion of propofol. In order to evaluate our approach and compare it with existing results in the literature, we examine a minimum-time problem for anesthetizing a patient. By applying the Pontryagin minimum principle, we introduce the shooting method as a means to solve the problem at hand. Additionally, we conducted numerical simulations using the MATLAB computing environment. We solve the time-optimal control problem using our newly proposed analytical method and discover that the optimal continuous infusion rate of the anesthetic and the minimum required time for transition from the awake state to an anesthetized state exhibit similarity between the two methods. However, the advantage of our new analytic method lies in its independence from unknown initial conditions for the adjoint variables. Full article

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. Furthermore, the novel technique offers an alternative solution to the classic example of the time-optimal control of a double integrator system. Full article