相关论文: Infinite Dimensional Multipliers and Pontryagin Pr…

In this paper, infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noises are studied. The main difficulty comes from fractional noises on infinite horizon. Motivated by…

Through the Pontryagin maximum principle, we solve a minimal-time problem for a linear control system on a cylinder, considered as a homogeneous space of the solvable Lie group of dimension two. The main result explicitly shows the…

Motivated by infinite-dimensional optimal control problems with endpoint state constraints, in this Note, we introduce the notion of finite codimensional exact controllability for evolution equations. It is shown that this new…

In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…

This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite…

We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…

This paper considers the problem of finding a solution to the finite horizon constrained Markov decision processes (CMDP) where the objective as well as constraints are sum of additive and multiplicative utilities. Towards solving this, we…

This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building…

Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and…

This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time.…

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…

Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value…

We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c)…

The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a…

This article considers a discrete-time robust optimal control problem on matrix Lie groups. The underlying system is assumed to be perturbed by exogenous unmeasured bounded disturbances, and the control problem is posed as a min-max optimal…

The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…

Pontryagin type maximum principle and Bellman's dynamic programming principle serve as two of the most important tools in solving optimal control problems. There is a huge literature on the study of relationship between them. The main…

This paper develops a theory of symplectic reduction in the infinite-dimensional setting, covering both the regular and singular case. Extending the classical work of Marsden, Weinstein, Sjamaar and Lerman, we address challenges unique to…

In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…

This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…