Related papers: Dynamic programming for infinite horizon boundary …
We present a receding-horizon optimal control for nonlinear continuous-time systems subject to state constraints. The cost is a quadratic finite-horizon integral. The key enabling technique is a new constrained approximate dynamic…
We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…
We consider a two-player zero-sum deterministic differential game where each player uses both continuous and impulse controls in infinite-time horizon. We assume that the impulses supposed to be of general term and the costs depend on the…
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 $\alpha \in (0, 1)$. The value of this problem is introduced as a functional in a…
This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation…
This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or…
In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose…
We present methods for locally solving the Dynamic Programming Equations (DPE) and the Hamilton Jacobi Bellman (HJB) PDE that arise in the infinite horizon optimal control problem. The method for solving the DPE is the discrete time version…
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear…
We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value…
In the Dynamic Programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this…
We consider the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift. We only impose a structural assumption on the running cost function, namely…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of…