We consider a finite horizon multi-model linear-quadratic optimal control problem. For this problem, we treat the case where the problem’s functional does not contain a control function. The latter means that the problem under consideration is...
This paper focuses on addressing the linear quadratic (LQ) optimal control problem on an infinite time horizon for stochastic systems controlled by impulses. No constraint regarding the sign of the quadratic functional is applied. That is why our fir...
This paper presents the optimal control approach to solve both Lambert’s problem and Gibbs’ method, which are commonly used for preliminary orbit determination. Lambert’s problem is reinterpreted with Hamilton’s principle and...
This paper investigates the well-posedness of the inverse problem for the time-fractional Burgers equation, which aims to reconstruct initial conditions from terminal observations. Such equations are crucial for the modeling of hydrodynamic phenomena...
This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations...
In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary...
Optimal control problems governed by stochastic partial differential equations have become an important field in applied mathematics. In this article, we investigate one such important optimization problem, that is, the stochastic Stokes control prob...
In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. W...
We consider a discrete-time susceptible-infected-removed-susceptible “again” (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible...
In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the...
A multilevel Monte Carlo (MLMC) method is applied to simulate a stochastic optimal problem based on the gradient projection method. In the numerical simulation of the stochastic optimal control problem, the approximation of expected value is involved...
This paper is devoted to proposing an approximate numerical algorithm based on the use of the state parameterization technique in order to find the solution to the optimal control problem (OCP). An explicit formula for new shifted wavelet (NSW) funct...
A numerical method based on the Pontryagin maximum principle for solving an optimal control problem with static and dynamic phase constraints for a group of objects is considered. Dynamic phase constraints are introduced to avoid collisions between o...
This study establishes a fractional-order model (FOM) to describe the rumor spreading process. Members of society in this FOM are classified into three categories that change with time—the population that is ignorant of the rumors and does not...
This study focuses on improving the application of the quadratic penalty smoothing technique for solving the fuel-optimal problem of low-thrust trajectory. Some practical techniques, including the Particle Swarm Optimization algorithm (PSO), the co-s...
In this paper, optimality conditions are studied for a new class of PDE and PDI-constrained scalar variational control problems governed by path-independent curvilinear integral functionals. More precisely, we formulate and prove a minimal criterion...
In this paper we investigate the optimal control problem for set-valued quasivariational inequality with unilateral constraints. Under suitable conditions, we prove that the solution to the current optimal control problem converges to a solution to o...
The development of artificial intelligence systems assumes that a machine can independently generate an algorithm of actions or a control system to solve the tasks. To do this, the machine must have a formal description of the problem and possess com...
Optimal control problems arise in many applications and need suitable numerical methods to obtain a solution. The indirect methods are an interesting class of methods based on the Pontryagin’s minimum principle that generates Hamiltonian Boundary Val...
In this paper, we consider the problem of selecting the most efficient optimization algorithm for neural network approximation—solving optimal control problems with mixed constraints. The original optimal control problem is reduced to a finite-dimens...
We establish a generalization of the Noether theorem for stochastic optimal control problems. Exploiting the tools of jet bundles and contact geometry, we prove that from any (contact) symmetry of the Hamilton–Jacobi–Bellman equation associated with...
The optimal control theory in mathematics aims to study the finding of control for a dynamic system over time, where an objective function is optimized. It has a broad range of applications in engineering, operations research, and science. The main p...
In this paper, we analyze an optimal control problem with a mixed cost function, which combines a terminal cost at the final state and an integral term involving the state and control variables. The problem includes both state and control constraints...
In this paper, we consider a discrete-time optimal control problem related to the model of Robinson, Solow and Srinivasan. We analyze this optimal control problem without concavity assumptions on a non-concave utility function which represents the pr...
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...
This paper presents an enhanced inertial Tseng’s extragradient method designed to address variational inequality problems involving pseudomonotone operators, along with fixed point problems governed by quasi-nonexpansive operators in real Hilbe...
In this paper, we consider the time-optimal control problem about a kind of Petrowsky system and its bang-bang property. To solve this problem, we first construct another control problem, whose null controllability is equivalent to the controllabilit...
In this paper, elliptic optimal control problems with
An adaptive moving mesh method for optimal control problems in viscous incompressible fluid is proposed with the incompressible Navier–Stokes system used to describe the motion of the fluid. The moving distance of nodes in the adopted mesh movi...
In response to the problem of low optimization efficiency and low tracking accuracy in vehicle path tracking, a comprehensive optimization method is established based on the 3-DOF vehicle motion model. The outer layer adopts the adaptive particle swa...
This paper studies an averaged Linear Quadratic Regulator (LQR) problem for a parabolic partial differential equation (PDE), where the system dynamics are affected by uncertain parameters. Instead of assuming a deterministic operator, we model the un...
In this work, a new approach to solving problems of optimal control of manufacture procedures for the production of silica optical fiber are proposed. The procedure of silica tubes alloying by the Modified Chemical Vapor Deposition (MCVD) method and...
We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann–Liouville integral...
This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins whe...
This paper is devoted to the solution of the optimal control problem. The obtained control should be optimal in terms of quality criteria and, at the same time, feasible when implemented in the control object. To solve the optimal control problem in...
This article proposes a method to solve nonlinear optimal control problems with arbitrary performance indices and terminal constraints, which is based on the neighboring extremal method and Gauss pseudospectral collocation. Firstly, a quadratic perfo...
In this paper, we consider the numerical solution of the optimal control problems of the elliptic partial differential equation. Numerically tackling these problems using the finite element method produces a large block coupled algebraic system of eq...
The optimal control currently decides the minimum energy consumption within the problems attached to subways. Among other things, we formulate and solve an optimal bi-control problem, the two controls being the acceleration and the feed-back of a Rie...
This paper investigates some duality results of a mixed type for a class of multiple objective fractional optimal control problems. More precisely, by considering the Wolfe- and Mond–Weir-type dualities, we formulate a robust mixed-type dual pr...
Aiming at the problem of multiple constraints and low solving efficiency in the process of vehicle path tracking, an improved hp-adaptive Radau pseudospectral method (I-hp-ARPM) which uses a double-layer optimization iteration strategy and the residu...
In this paper, a linear Chebyshev pseudospectral method (LCPM) is proposed to solve the nonlinear optimal control problems (OCPs) with hard terminal constraints and unspecified final time, which uses Chebyshev collocation scheme and quasi-linearizati...
This paper tackles the ill-posed inversion of initial conditions and diffusion coefficient for Burgers’ equation with a source term. Using optimal control theory combined with a finite difference discretization scheme and a dual-functional desc...
This paper considers the difficulties that arise in the implementation of solutions to the optimal control problem. When implemented in real systems, as a rule, the object is subject to some perturbations, and the control obtained as a function of ti...
Two approaches to the numerical solution of the optimal control problem are studied. The direct approach is based on the reduction of the optimal control problem to a nonlinear programming problem. Another approach is so-called synthesized optimal co...
In the area of production planning and control, the aggregate production planning (APP) problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To addr...
The study of the existence of an optimal feedback control problem for the initial-boundary value problem that describes the motion of the fractional Voigt-
The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator is controlled with a shared limited scalar control. The objective of the control is to accelerate the oscillatory system to a g...
We research a control problem for an ecological model given by a reaction–diffusion system. The ecological model is given by a nonlinear parabolic PDE system of three equations modelling the interaction of three species by considering the standard Lo...
In this study, we consider the extended optimal control problem and search for a control function in the class of feasible functions for a real control object. Unlike the classical optimal control problem, the control function should depend on the st...
Uncertain singular non-causal systems represent a class of singular systems distinguished by the presence of regularity constraints and the involvement of uncertain variables. This paper considers optimal control problems for such systems under the H...
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