57 citations · 156 across the 15 of their papers we have counts for
16 papers
Path-dependent Hamilton--Jacobi equations: Uniqueness results for viscosity solutions defined via families of compact sets
Mikhail I. Gomoyunov
We consider a path-dependent Hamilton--Jacobi equation with coinvariant derivatives over the space of continuous functions. We prove two uniqueness results for viscosity (generaliz…
Minimax solutions of path-dependent Hamilton--Jacobi equations under weakened assumptions with application to differential games
Mikhail Gomoyunov
We study minimax (generalized) solutions of a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with co-invariant derivatives under a right-end boundary c…
Viscosity and minimax solutions for path-dependent Hamilton-Jacobi equations in infinite dimensions and related differential games
Erhan Bayraktar, Mikhail Gomoyunov, Christian Keller
We establish new results for path-dependent Hamilton-Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar an…
Lipschitz Continuity Results for Minimax Solutions of Path-Dependent Hamilton--Jacobi Equations
Mikhail I. Gomoyunov
We consider a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with coinvariant derivatives and a right-end boundary condition. Such problems arise natur…
Zero-Sum Games for Volterra Integral Equations and Viscosity Solutions of Path-Dependent Hamilton-Jacobi Equations
Mikhail I. Gomoyunov
We consider a game, in which the dynamics is described by a non-linear Volterra integral equation of Hammerstein type with a weakly-singular kernel and the goals of the first and s…
Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system
Mikhail I. Gomoyunov
In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional i…
Equivalence of minimax and viscosity solutions of path-dependent Hamilton-Jacobi equations
Mikhail Gomoyunov, Anton Plaksin
In the paper, we consider a path-dependent Hamilton-Jacobi equation with coinvariant derivatives over the space of continuous functions. Such equations arise from optimal control p…
On differentiability of solutions of fractional differential equations with respect to initial data
Mikhail I. Gomoyunov
In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order . As initial data, we consider a pair…
On viscosity solutions of path-dependent Hamilton--Jacobi--Bellman--Isaacs equations for fractional-order systems
Mikhail I. Gomoyunov
This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order and a Bolza cost…
Minimax Solutions of Hamilton--Jacobi Equations with Fractional Coinvariant Derivatives
Mikhail Gomoyunov
We consider a Cauchy problem for a Hamilton--Jacobi equation with coinvariant derivatives of an order . Such problems arise naturally in optimal control problems for d…
Optimal Control Problems with a Fixed Terminal Time in Linear Fractional-Order Systems
Mikhail Gomoyunov
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to m…
On representation formulas for solutions of linear differential equations with Caputo fractional derivatives
Mikhail Gomoyunov
In the paper, a linear differential equation with variable coefficients and a Caputo fractional derivative is considered. For this equation, a Cauchy problem is studied, when an in…
Dynamic programming principle and Hamilton-Jacobi-Bellman equations for fractional-order systems
Mikhail I. Gomoyunov
We consider a Bolza-type optimal control problem for a dynamical system described by a fractional differential equation with the Caputo derivative of an order . The va…
Solution to Zero-Sum Differential Game with Fractional Dynamics via Approximations
Mikhail Gomoyunov
The paper deals with a zero-sum differential game in which the dynamical system is described by a fractional differential equation with the Caputo derivative of an order $α\in (0,…
Approximation of Fractional Order Conflict-Controlled Systems
Mikhail Gomoyunov
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order Basing o…
Fractional Derivatives of Convex Lyapunov Functions and Control Problems in Fractional Order Systems
Mikhail Gomoyunov
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with th…