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We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases…
We consider the numerical approximation of a generalized fractional Oldroyd-B fluid problem involving two Riemann-Liouville fractional derivatives in time. We establish regularity results for the exact solution which play an important role…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving…
Operator fractional Brownian motion (OFBM) is the natural vector-valued extension of the univariate fractional Brownian motion. Instead of a scalar parameter, the law of an OFBM scales according to a Hurst matrix that affects every…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
In this paper, we consider a special class of nonlinear optimal control problems, where the control variables are box-constrained and the objective functional is strongly convex corresponding to control variables and separable with respect…
Optimal control theory aims to find an optimal protocol to steer a system between assigned boundary conditions while minimizing a given cost functional in finite time. Equations arising from these types of problems are often non-linear and…
This paper presents a sensor-control method for choosing the best next state of the sensor(s), that provide(s) accurate estimation results in a multi-target tracking application. The proposed solution is formulated for a multi-Bernoulli…
The fractional order system, which is described by the fractional order derivative and integral, has been studied in many engineering areas. Recently, the concept of fractional order has been generalized to the distributed order concept,…
One of the most often used methods of summing divergent series in physics is the Borel-type summation with control parameters improving convergence, which are defined by some optimization conditions. The well known annoying problem in this…
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the…
This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\varepsilon$. The small parameter $\varepsilon>0$ denotes the…
On the 3-dimensional fractional-order Toda lattice with two controls The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to 3-dimensional Toda lattice with two controls. For this…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
We propose and study an optimal control model for malaria infection described by system of fractional differential equations. The model is formulated in terms of the left and right Caputo fractional derivatives. We determine the necessary…