Related papers: A numerical approach for solving fractional optima…
We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order…
Distributed-order fractional non-local operators have been introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted…
Fractional operators (derivatives/integrals) are defined via the integration of the functions. When the function is produced by a spanning set of fractional power functions, traditional quadrature rules often need to be revised, failing to…
- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…
We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
We investigate the exact enlarged controllability and optimal control of a fractional diffusion equation in Caputo sense. This is done through a new definition of enlarged controllability that allows us to extend available contributions.…
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary value…
This paper derives the Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems for cost functions with fractional discount rate from the Bellman's principle of optimality. The fractional discount rate is described by…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit…
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…
Fractional control systems with the Caputo derivative are considered. The modified controllability Gramian and the minimum energy optimal control problem are investigated. Construction of minimizing steering controls for the modified energy…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…
This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…