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This paper investigates the optimal control problem for a class of discrete-time stochastic systems subject to additive and multiplicative noises. A stochastic Lyapunov equation and a stochastic algebra Riccati equation are established for…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the…
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly non-convex risk…
We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it…
We consider a discrete-time bipartite matching model with random arrivals of units of supply and demand that can wait in queues located at the nodes in the network. A control policy determines which are matched at each time. The focus is on…
We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
In this paper we study a class of risk-sensitive Markovian control problems in discrete time subject to model uncertainty. We consider a risk-sensitive discounted cost criterion with finite time horizon. The used methodology is the one of…
In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under…
When sales of a product are affected by randomness in demand, retailers can use dynamic pricing strategies to maximise their profits. In this article the pricing problem is formulated as a stochastic optimal control problem, where the…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
We consider infinite horizon dynamic programming problems, where the control at each stage consists of several distinct decisions, each one made by one of several agents. In an earlier work we introduced a policy iteration algorithm, where…
Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to…
An adaptive controller is proposed and analyzed for the class of infinite-horizon optimal control problems in positive linear systems presented in (Ohlin et al., 2024b). This controller is derived from the solution of a "data-driven…
Time-consistency is an essential requirement in risk sensitive optimal control problems to make rational decisions. An optimization problem is time consistent if its solution policy does not depend on the time sequence of solving the…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…