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On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems
AbstractWe consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a...
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Application of Hamilton–Jacobi–Bellman Equation/Pontryagin’s Principle for Constrained Optimal Control
This article applies novel results for infinite- and finite-horizon optimal control problems with nonlinear dynamics and constraints. We use the...
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The turnpike property and the longtime behavior of the Hamilton–Jacobi–Bellman equation for finite-dimensional LQ control problems
We analyze the consequences that the so-called turnpike property has on the longtime behavior of the value function corresponding to a...
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Application of maximal monotone operator method for solving Hamilton–Jacobi–Bellman equation arising from optimal portfolio selection problem
In this paper, we investigate a fully nonlinear evolutionary Hamilton–Jacobi–Bellman (HJB) parabolic equation utilizing the monotone operator...
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A class of backward stochastic Bellman–Bihari’s inequality and its applications
In this paper, we propose and prove several different forms of backward stochastic Bellman–Bihari’s inequality. Then, as two applications, two...
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Abstract McKean–Vlasov and Hamilton–Jacobi–Bellman Equations, Their Fractional Versions and Related Forward–Backward Systems on Riemannian Manifolds
AbstractWe introduce a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the McKean–Vlasov...
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Fractional McKean–Vlasov and Hamilton–Jacobi–Bellman–Isaacs Equations
We study a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the McKean–Vlasov type equations...
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A Fast Single-Pass Method for Solving the Generalized Eikonal Equation in a Moving Medium
AbstractWe develop a fast method for approximating the solution to the generalized eikonal equation in a moving medium. Our approach consists of the...
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Gårding Cones and Bellman Equations in the Theory of Hessian Operators and Equations
In this work, we continue the investigation of algebraic properties of Gårding cones in the space of symmetric matrices. Based on this theory, we...
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Optimal Controls of Stochastic Differential Equations with Jumps and Random Coefficients: Stochastic Hamilton–Jacobi–Bellman Equations with Jumps
We study the stochastic Hamilton–Jacobi–Bellman (HJB) equation with jump, which arises from a non-Markovian optimal control problem with a recursive...
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Newton’s Method, Bellman Recursion and Differential Dynamic Programming for Unconstrained Nonlinear Dynamic Games
Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics,...
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Dynamic Programming of the Stochastic Burgers Equation Driven by Lévy Noise
In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Lévy-type noises with distributed control process...
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The large time profile for Hamilton–Jacobi–Bellman equations
Here, we study the large-time limit of viscosity solutions of the Cauchy problem for second-order Hamilton–Jacobi–Bellman equations with convex...
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Some new dynamic Gronwall–Bellman–Pachpatte type inequalities with delay on time scales and certain applications
The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall–Bellman–Pachpatte type on time...
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Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations
We consider the optimal control problem for stochastic differential equations (SDEs) with random coefficients under the recursive-type objective...
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Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control...
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A semi-Lagrangian scheme for Hamilton–Jacobi–Bellman equations with oblique derivatives boundary conditions
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton–Jacobi–Bellman (HJB)...
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Numerical Approximation of a System of Hamilton–Jacobi–Bellman Equations Arising in Innovation Dynamics
We consider a system of fully nonlinear partial differential equations that corresponds to the Hamilton–Jacobi–Bellman equations for the value...
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A comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton–Jacobi equations in the space of probability...
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