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Thematische Bibliographien / Optimization Calculus of Variations and Optimal Control / Zeitschriftenartikel

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Zeitschriftenartikel zum Thema „Optimization Calculus of Variations and Optimal Control“

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Veröffentlicht am 28. Juli 2024

Zuletzt aktualisiert am 31. Juli 2025

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1

Lan, Tian-Syung. "Dynamic MRR Function Optimization Using Calculus of Variations." Mathematical Problems in Engineering 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/671062.

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A dynamic machining model to optimize the control of material removal rate (MRR) for a cutting tool undergoing the considerations of fixed tool life and maximum machining rate is established in this paper. This study not only applies material removal rate mathematically into the objective function, but also implements Calculus of Variations to comprehensively optimize the control of material removal rate. In addition, the optimal solution for the dynamic machining model to gain the maximum profit is provided, and the decision criteria for selecting the optimal solution of the dynamic machining

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McShane, E. J. "The Calculus of Variations from the Beginning Through Optimal Control Theory." SIAM Journal on Control and Optimization 27, no. 5 (1989): 916–39. http://dx.doi.org/10.1137/0327049.

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3

Carlier, G., and A. Lachapelle. "A Planning Problem Combining Calculus of Variations and Optimal Transport." Applied Mathematics & Optimization 63, no. 1 (2010): 1–9. http://dx.doi.org/10.1007/s00245-010-9107-8.

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4

Krastanov, Mikhail, and Nadezhda Ribarska. "Lagrange multipliers in dynamic optimization." Mathematics and Education in Mathematics 54 (March 27, 2025): 009–17. https://doi.org/10.55630/mem.2025.54.009-017.

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An approach for studying optimization problems in abstract setting is presented and a general Lagrange multiplier rule is formulated. It is described how to apply this result to the basic problem of calculus of variations with pure state constraints of equality- type, as well as to a Mayer optimal control problem with pure state constraints.

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Petit, Maria Luisa. "Dynamic optimization. The calculus of variations and optimal control in economics and management." International Review of Economics & Finance 3, no. 2 (1994): 245–47. http://dx.doi.org/10.1016/1059-0560(94)90037-x.

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6

Dolgopolik, Maksim. "Constrained nonsmooth problems of the calculus of variations." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 79. http://dx.doi.org/10.1051/cocv/2021074.

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The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric constraints. To derive optimality conditions, we study generalised concepts of differentiability of nonsmooth functions called codifferentiability and quasidifferentiability. Under some natural and easily verifiable assumptions we prove that a nonsmooth integral functional defined on the Sobolev space is continuously codifferentiable and compute its codifferential an

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Lei, Yang, Shurong Li, Xiaodong Zhang, Qiang Zhang, and Lanlei Guo. "Dynamic Optimization of a Polymer Flooding Process Based on Implicit Discrete Maximum Principle." Mathematical Problems in Engineering 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/281567.

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Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and some inequality constraints as polymer concentration and injection amount limitation. The optimal control model is discretized by full implicit finite-difference method. To cope with the discrete optimal control problem (OCP), the necessar

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Murray, J. M. "Existence Theorems for Optimal Control and Calculus of Variations Problems Where the States Can Jump." SIAM Journal on Control and Optimization 24, no. 3 (1986): 412–38. http://dx.doi.org/10.1137/0324024.

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9

Drivotin, Oleg I. "Оn momentum flow density of the gravitational field". Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 17, № 2 (2021): 137–47. http://dx.doi.org/10.21638/11701/spbu10.2021.204.

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Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution repr

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Bouzaouache, Hajer. "Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching." Complexity 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/5308013.

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This paper investigates the optimal control problem of a particular class of hybrid dynamical systems with controlled switching. Given a prespecified sequence of active subsystems, the objective is to seek both the continuous control input and the discrete switching instants that minimize a performance index over a finite time horizon. Based on the use of the calculus of variations, necessary conditions for optimality are derived. An efficient algorithm, based on nonlinear optimization techniques and numerical methods, is proposed to solve the boundary-value ordinary differential equations. In

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Hull, D. G. "Variational Calculus and Approximate Solution of Optimal Control Problems." Journal of Optimization Theory and Applications 108, no. 3 (2001): 483–97. http://dx.doi.org/10.1023/a:1017527222995.

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12

Šimon Hilscher, Roman, and Vera M. Zeidan. "Transformation preserving controllability for nonlinear optimal control problems with joint boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 75. http://dx.doi.org/10.1051/cocv/2021068.

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In this paper we develop a new approach for optimal control problems with general jointly varying state endpoints (also called coupled endpoints). We present a new transformation of a nonlinear optimal control problem with jointly varying state endpoints and pointwise equality control constraints into an equivalent optimal control problem of the same type but with separately varying state endpoints in double dimension. Our new transformation preserves among other properties the controllability (normality) of the considered optimal control problems. At the same time it is well suited even for t

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Horla, Dariusz, and Jacek Cieślak. "On Obtaining Energy-Optimal Trajectories for Landing of UAVs." Energies 13, no. 8 (2020): 2062. http://dx.doi.org/10.3390/en13082062.

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The optimization issues connected to a landing task of an unmanned aerial vehicle are discussed in the paper, based on a model of a mini-class drone. Three landing scenarios are considered, including minimum-time landing, landing with minimum energy consumption, and planned landing. With the use of classical dynamic programming techniques, including the minimum principle of Pontryagin, as well as the calculus of variations, the optimal altitude reference trajectories are found, to form the altitude control system in such a way as to mimic the profile of the reference trajectory by the actual a

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Tourajizadeh, H., and O. Gholami. "Optimal Control and Path Planning of a 3PRS Robot Using Indirect Variation Algorithm." Robotica 38, no. 5 (2019): 903–24. http://dx.doi.org/10.1017/s0263574719001152.

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SUMMARYIn this paper, optimal control of a 3PRS robot is performed, and its related optimal path is extracted accordingly. This robot is a kind of parallel spatial robot with six DOFs which can be controlled using three active prismatic joints and three passive rotary ones. Carrying a load between two initial and final positions is the main application of this robot. Therefore, extracting the optimal path is a valuable study for maximizing the load capacity of the robot. First of all, the complete kinematic and kinetic modeling of the robot is extracted to control and optimize the robot. As th

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Ribeiro, Marcelo Perencin de Arruda, and Roberto de Campos Giordano. "Variational calculus (optimal control) applied to the optimization of the enzymatic synthesis of ampicillin." Brazilian Archives of Biology and Technology 48, spe (2005): 19–28. http://dx.doi.org/10.1590/s1516-89132005000400003.

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In this work, optimal control techniques were used to optimize the feed of reactants during the enzymatic synthesis of ampicillin in a semi-batch reactor. Simulation results showed that a semi-batch integrated reactor (with product crystallization) might achieve 88% 6-APA (6-aminepenicillanic acid) conversion and 92% of PGME (phenylglycine methyl ester) yield, with a productivity between 3.5 and 5.5 mM min-1.

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Kumar, Avinash, and Tushar Jain. "Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions." Mathematical Problems in Engineering 2019 (October 13, 2019): 1–17. http://dx.doi.org/10.1155/2019/9490512.

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This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost. For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches. To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to o

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Abbasov, Majid E., and Artyom S. Sharlay. "Searching for the cost-optimal road trajectory on the relief of the terrain." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 17, no. 1 (2021): 4–12. http://dx.doi.org/10.21638/11701/spbu10.2021.101.

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The article analyzes the problem of obtaining the cost-optimal trajectory for building a road. Using the apparatus of mathematical modelling, the authors derive the cost functional, the argument of which is the function that describes the path trajectory. The resulting functional after some additional transformations is written in a simpler form. For the problem of the calculus of variations obtained in this manner, an optimality condition is derived. This condition takes into account the specifics of the constructed functional. Unlike the classical Euler—Lagrange condition, it leads not to a

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Tahere Morowati, Seyed Kamaleddin Mousavi Mashhadi, and Mohammad Fiuzy. "Optimal Time Trajectory Planning and Control of Space Cable Robot based on " Brachistochrone " Theory." International Journal of Scholarly Research in Engineering and Technology 1, no. 1 (2022): 033–43. http://dx.doi.org/10.56781/ijsret.2022.1.1.0023.

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This paper presents optimal-time trajectory planning of Samen cable robot using optimal control theory. The optimal-time trajectory planning solution method is based on the calculus of variations method. This issue can be solved by the Pontryagin’s Minimum Principle using the Bang-Bang control. To do so, a time-cost function is considered. By turning optimal-time trajectory planning into a problem-solving procedure with a two-point boundary value problem, the solving stages begin. In addition, the beginning and the end of the path are certain, which can be solved with numerical algorithms. One

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Ebenbeck, Matthias, and Patrik Knopf. "Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 71. http://dx.doi.org/10.1051/cocv/2019059.

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We investigate a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn–Hilliard type equation for the phase field variable, a reaction diffusion equation for the nutrient concentration and a Brinkman type equation for the velocity field. These PDEs are endowed with homogeneous Neumann boundary conditions for the phase field variable, the chemical potential and the nutrient as well as a “no-friction” boundary condition for the velocity. The control represents a medication by cytotoxic drugs and enters the phase field equation. The aim i

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Zine, Houssine, El Mehdi Lotfi, Delfim F. M. Torres, and Noura Yousfi. "Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation." Axioms 11, no. 4 (2022): 178. http://dx.doi.org/10.3390/axioms11040178.

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Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fractional derivative in the Riemann–Liouville sense with its associated integral for the recently introduced weighted generalized fractional derivative with Mittag–Leffler kernel. We rewrite these operators equivalently in effective series, proving some interesting properties relating to the left and the right fractional operators. These results per

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Gonopolsky, Аdam М., and Тatyana V. Zinets. "Optimization problems for ensuring ecological safety of main oil pipelines." SCIENCE & TECHNOLOGIES OIL AND OIL PRODUCTS PIPELINE TRANSPORTATION 10, no. 3 (2020): 293–99. http://dx.doi.org/10.28999/2541-9595-2020-10-3-293-299.

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This article is devoted to the search for optimal conditions for environmental and economic security of oil main pipelines using classical calculus of variations. The goal functions here are either stochastic reliability criteria for deterministic parametric criteria, or parametric criteria for specified reliability criteria. The functions of the optimization process are environmental and technological indicators of the system, taking into account the characteristics of oil pipelines or a set of measures to improve their reliability. The arguments are environmental and economic indicators that

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Tabunshchikov, Yuri, and Marianna Brodach. "OPTIMIZATION PROBLEMS OF MATHEMATICAL MODELLING OF A BUILDING AS A UNIFIED HEAT AND POWER SYSTEM." International Journal for Computational Civil and Structural Engineering 16, no. 1 (2020): 156–61. http://dx.doi.org/10.22337/2587-9618-2020-16-1-156-161.

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The mathematical model of a building as a single heat energy system by the decomposition method is represented by three interconnected mathematical models: the first is a mathematical model of the energy interaction of a building’s shell with an outdoor climate; the second is a mathematical model of energy flows through the shell of a building; the third is a mathematical model of optimal control of energy consumption to ensure the required microclimate. Optimization problems for three mathematical models with objective functions are formulated. Methods for solving these problems are determine

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Mahmudov, Elimhan. "Optimization of Lagrange problem with higher order differential inclusions and endpoint constraints." Filomat 32, no. 7 (2018): 2367–82. http://dx.doi.org/10.2298/fil1807367m.

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In the paper minimization of a Lagrange type cost functional over the feasible set of solutions of higher order differential inclusions with endpoint constraints is studied. Our aim is to derive sufficient conditions of optimality for m th-order convex and non-convex differential inclusions. The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called ?endpoint? conditions. Here the basic apparatus of locally adjoint mappings is suggested. An application from the calculus of variations is

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Asgari, Mohsen, and Amin Nikoobin. "A variational approach to determination of maximum throw-able workspace of robotic manipulators in optimal ball pitching motion." Transactions of the Institute of Measurement and Control 43, no. 10 (2021): 2378–91. http://dx.doi.org/10.1177/01423312211001694.

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This study is aimed at finding the entire points that a manipulator can launch an object onto by an optimal motion. These points are called throw-able workspace, which are located outside the reachable workspace of the robot. From an optimization point of view, some throwing parameters can be found to decrease motion cost. In this paper, by using this concept, the best combination of throwing and trajectory planning is attempted. The proposed method consists of two basic ideas: first, defining the optimal throwing problem as the optimal control problem (OCP) and solving it using the indirect s

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Josef Pesch, Hans. "Carath&#233odory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory." Numerical Algebra, Control & Optimization 3, no. 1 (2013): 161–73. http://dx.doi.org/10.3934/naco.2013.3.161.

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Hinterberger, W., O. Scherzer, C. Schnörr, and J. Weickert. "ANALYSIS OF OPTICAL FLOW MODELS IN THE FRAMEWORK OF THE CALCULUS OF VARIATIONS." Numerical Functional Analysis and Optimization 23, no. 1-2 (2002): 69–89. http://dx.doi.org/10.1081/nfa-120004011.

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Ferrentino, Enrico, Federico Salvioli, and Pasquale Chiacchio. "Globally Optimal Redundancy Resolution with Dynamic Programming for Robot Planning: A ROS Implementation." Robotics 10, no. 1 (2021): 42. http://dx.doi.org/10.3390/robotics10010042.

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Dynamic programming techniques have proven much more flexible than calculus of variations and other techniques in performing redundancy resolution through global optimization of performance indices. When the state and input spaces are discrete, and the time horizon is finite, they can easily accommodate generic constraints and objective functions and find Pareto-optimal sets. Several implementations have been proposed in previous works, but either they do not ensure the achievement of the globally optimal solution, or they have not been demonstrated on robots of practical relevance. In this co

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Aribowo, Widi, Bambang Suprianto, Reza Rahmadian, Mahendra Widyartono, Ayusta Lukita Wardani, and Aditya Prapanca. "Optimal tuning fractional order PID based on marine predator algorithm for DC motor." International Journal of Power Electronics and Drive Systems (IJPEDS) 14, no. 2 (2023): 762. http://dx.doi.org/10.11591/ijpeds.v14.i2.pp762-770.

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DC motors are a popular topic because they are widely applied in various electronic equipment. So, this requires a control that is fast and reliable. The development of optimized control methods is growing rapidly with the discovery of several new methods. Marine predator algorithm (MPA) is an optimization method based on marine life between living things. This article discusses the application of the MPA method for optimizing fractional order PID (FOPID) control on DC motors. The implementation of the FOPID controller is also difficult because the fractional calculus operators of the FOPID co

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Widi, Aribowo, Suprianto Bambang, Rahmadian Reza, Widyartono Mahendra, Lukita Wardani Ayusta, and Prapanca Aditya. "Optimal tuning fractional order PID based on marine predator algorithm for DC motor." International Journal of Power Electronics and Drive Systems 14, no. 02 (2023): 762~770. https://doi.org/10.11591/ijpeds.v14.i2.pp762-770.

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DC motors are a popular topic because they are widely applied in various electronic equipment. So, this requires a control that is fast and reliable. The development of optimized control methods is growing rapidly with the discovery of several new methods. Marine predator algorithm (MPA) is an optimization method based on marine life between living things. This article discusses the application of the MPA method for optimizing fractional order PID (FOPID) control on DC motors. The implementation of the FOPID controller is also difficult because the fractional calculus operators of the FOPID co

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Ignatkin, V. U., V. S. Dudnikov, Y. O. Shulzhyk, and O. P. Yushkevich. "BASIC PRINCIPLES AND ANALOGIES IN SOLVING THE PROBLEMS OF ADAPTATION, LEARNING, PATTERN RECOGNITION, OPTIMIZATION AND SIMILAR PROBLEMS OF FLIGHT CONTROL." System design and analysis of aerospace technique characteristics 35, no. 2 (2024): 35–48. https://doi.org/10.15421/472412.

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Using the method of mathematical programming and stochastic approximation, the development of algorithms for solving the problems of adaptation, learning, pattern recognition, identification and other similar problems of aircraft control is shown. In control theory, the optimization task is reduced to determining the extrema of various quality functionals, and with the help of calculus of variations, this task is simplified to finding the extrema of some functions. In the general case, the quality functional is given by the mathematical expectation for some arguments of some functions of these

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GREGORY, JOHN. "A NEW SYSTEMATIC METHOD FOR EFFICIENTLY SOLVING HOLONOMIC (AND NONHOLONOMIC) CONSTRAINT PROBLEMS." Analysis and Applications 08, no. 01 (2010): 85–98. http://dx.doi.org/10.1142/s0219530510001527.

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A new systematic approach to holonomic constraint is presented. By holonomic we mean a constraint problem in the calculus of variations/optimal control theory where the constraints are independent of the derivative of the dependent variable. It is seen that these new methods follow from a general theory of constraint optimization previously given by the author. A major, new emphasis of this work is the necessity of properly handling the boundary values of our introduced variables. The author's previous theory allows the solution of a wide variety of general or anholonomic problems which includ

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Barrios, Melani, Gabriela Reyero, and Mabel Tidball. "Necessary Conditions to A Fractional Variational Problem." Statistics, Optimization & Information Computing 10, no. 2 (2022): 426–38. http://dx.doi.org/10.19139/soic-2310-5070-1047.

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The fractional variational calculus is a recent fifield, where classical variational problems are considered, but in the presence of fractional derivatives. Since there are several defifinitions of fractional derivatives, it is logical to think of different types of optimality conditions. For this reason, in order to solve fractional variational problems, two theorems of necessary conditions are well known: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that involves only Caputo derivatives. However, it is undeci

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Forster, Bruce A. "Dynamic Optimization: The calculus of variations and optimal control in Economics and Management, Morton S. Kamien and Nancy L. Scwartz, Elsevier North-Holland, New York, 1981. No. of pages: 331. Price: U.S. and Canada, $32.95; Elsewhere,$44.00/Dfl. 90.00." Optimal Control Applications and Methods 3, no. 3 (2007): 299–300. http://dx.doi.org/10.1002/oca.4660030308.

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Loveykin, Viacheslav, Dmytro Mishchuk, and Yevhen Mishchuk. "Optimization of manipulator's motion mode on elastic base according to the criteria of the minimum central square value of drive torque." Strength of Materials and Theory of Structures, no. 109 (November 11, 2022): 403–15. http://dx.doi.org/10.32347/2410-2547.2022.109.403-415.

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The results of studies of optimizing the mode of movement of the manipulator boom, mounted on an elastic base with a known stiffness the paper presents. The purpose of this scientific research is to reduce the oscillations of the manipulator turnout system, which will increase the overall efficiency of the manipulator, durability and reliability of the metal structure elements. The implementation of this goal have achieved by applying a controlled mode of operation of the drive with dynamic balancing of the drive mechanism. Using the Lagrange equation of the second kind, the equation of motion

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Zjavka, Ladislav. "Photovoltaic Energy All-Day and Intra-Day Forecasting Using Node by Node Developed Polynomial Networks Forming PDE Models Based on the L-Transformation." Energies 14, no. 22 (2021): 7581. http://dx.doi.org/10.3390/en14227581.

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Forecasting Photovoltaic (PV) energy production, based on the last weather and power data only, can obtain acceptable prediction accuracy in short-time horizons. Numerical Weather Prediction (NWP) systems usually produce free forecasts of the local cloud amount each 6 h. These are considerably delayed by several hours and do not provide sufficient quality. A Differential Polynomial Neural Network (D-PNN) is a recent unconventional soft-computing technique that can model complex weather patterns. D-PNN expands the n-variable kth order Partial Differential Equation (PDE) into selected two-variab

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Volkov, V. "MINIMIZATION OF ELECTRICAL CONSUMPTION OF A FREQUENCY-REGULATION INDUCTION MOTOR WITH A FAN LOAD IN START-BRAKING REGIMES." Electromechanical and energy saving systems 4, no. 56 (2021): 8–24. http://dx.doi.org/10.30929/2072-2052.2021.4.56.8-24.

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Purpuse. To minimize the total power consumption in start-braking regimes by a three-phase squirrel-cage frequency-regulated induction motor, loaded a centrifugal fan (or smoke exhauster), and also to obtain analytical dependencies for calculating the optimal durations of acceleration and deceleration times, corresponding to minimizing the total energy consumption of this motor in start-braking regimes with the indicated type of load. Metodology. Based on the methods of calculus of variations and numerical solution of non-linear differential equations, the quasi-optimal type of trajectories of

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Naumann, J. "Troutman, J. L.: Variational Calculus and Optimal Control. Optimization with Elementary Convexity. Second Edition. New York etc., Springer-Verlag 1996. XV, 461 pp., 87 figs., DM 84,00. ISBN 0-387-94511-3 (Undergraduate Texts in Mathematics)." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 77, no. 4 (1997): 316. http://dx.doi.org/10.1002/zamm.19970770421.

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Bronsard, Lia, Maria Colombo, László Székelyhidi Jr., and Yoshihiro Tonegawa. "Calculus of Variations." Oberwolfach Reports 21, no. 3 (2025): 2113–78. https://doi.org/10.4171/owr/2024/37.

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The Calculus of Variations is at the same time a classical subject, with long-standing open questions which have generated exciting discoveries in recent decades, and a modern subject in which new types of questions arise, driven by mathematical developments and emergent applications. It is also a subject with a very wide scope, touching on interrelated areas that include geometric variational problems, optimal transportation, geometric inequalities and domain optimization problems, elliptic regularity, geometric measure theory, harmonic analysis, physics, free boundary problems, etc. The work

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Grigorieva, Ellina. "Optimal Control Theory: Introduction to the Special Issue." Games 12, no. 1 (2021): 29. http://dx.doi.org/10.3390/g12010029.

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Benharrat, Mohammed, and Delfim F. M. Torres. "Optimal Control with Time Delays via the Penalty Method." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/250419.

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We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

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41

Barron, E. N., and W. Liu. "Calculus of variations inL ∞." Applied Mathematics & Optimization 35, no. 3 (1997): 237–63. http://dx.doi.org/10.1007/bf02683330.

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42

Frederico, Gastão S. F., Paolo Giordano, Alexandr A. Bryzgalov, and Matheus J. Lazo. "Calculus of variations and optimal control for generalized functions." Nonlinear Analysis 216 (March 2022): 112718. http://dx.doi.org/10.1016/j.na.2021.112718.

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43

Barron, E. N., and W. Liu. "Calculus of Variations in L ∞." Applied Mathematics and Optimization 35, no. 3 (1997): 237–63. http://dx.doi.org/10.1007/s002459900047.

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44

AL BADR, A., A. A. ANDRONOVA, R. R. HUSAINOV, and S. I. SAVIN. "ANALYSIS OF HIGH-LEVEL CONTROL METHODS FOR WALKING ROBOTS." IZVESTIA VOLGOGRAD STATE TECHNICAL UNIVERSITY 9 (292) (September 2024): 6–10. http://dx.doi.org/10.35211/1990-5297-2024-9-292-6-10.

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The review critically evaluates and summarizes state-of-the-art path planning methods designed for walking robots. Methods based on optimization including mixed-integer optimization, neural networks, graphs, calculus of variations, and random sampling are compared.

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45

Baláž, Vladimír, Maria Rita Iacò, Oto Strauch, Stefan Thonhauser, and Robert F. Tichy. "An Extremal Problem in Uniform Distribution Theory." Uniform distribution theory 11, no. 2 (2016): 1–21. http://dx.doi.org/10.1515/udt-2016-0012.

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Abstract In this paper we consider an optimization problem for Cesàro means of bivariate functions. We apply methods from uniform distribution theory, calculus of variations and ideas from the theory of optimal transport.

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46

Zaslavski, Alexander J. "Generic existence of solutions of nonconvex optimal control problems." Abstract and Applied Analysis 2005, no. 4 (2005): 375–421. http://dx.doi.org/10.1155/aaa.2005.375.

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The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrandsfwhich satisfy convexity and growth conditions. In 1996, the author obtained a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we survey this result and its recent extensions, and establish several new results in this direction.

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47

Marinković, Boban. "Optimality conditions for discrete calculus of variations problems." Optimization Letters 2, no. 3 (2007): 309–18. http://dx.doi.org/10.1007/s11590-007-0059-0.

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48

Malinowska, Agnieszka B., and Delfim F. M. Torres. "A general backwards calculus of variations via duality." Optimization Letters 5, no. 4 (2010): 587–99. http://dx.doi.org/10.1007/s11590-010-0222-x.

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49

Jajarmi, Amin, and Dumitru Baleanu. "Suboptimal control of fractional-order dynamic systems with delay argument." Journal of Vibration and Control 24, no. 12 (2017): 2430–46. http://dx.doi.org/10.1177/1077546316687936.

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In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new t

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50

Martins, Natália, Ricardo Almeida, Cristiana J. Silva, and Moulay Rchid Sidi Ammi. "Editorial for the Special Issue of Axioms “Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday”." Axioms 12, no. 2 (2023): 110. http://dx.doi.org/10.3390/axioms12020110.

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