Related papers: A Time Consistent Formulation of Risk Constrained …
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…
Most interesting problems in robotics (e.g., locomotion and manipulation) are realized through intermittent contact with the environment. Due to the perception and modeling errors, assuming an exact time for establishing contact with the…
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a…
This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a L\'evy noise time-changed by an inverse subordinator. We establish a maximum principle theory for the time-changed stochastic control…
An off policy reinforcement learning based control strategy is developed for the optimal tracking control problem to achieve the prescribed performance of full states during the learning process. The optimal tracking control problem is…
For time inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by the sophisticated agents. In this short note we construct a deterministic continuous time example where the unique equilibrium is…
This paper studies a risk-sensitive decision-making problem under uncertainty. It considers a decision-making process that unfolds over a fixed number of stages, in which a decision-maker chooses among multiple alternatives, some of which…
In this paper we present a framework for risk-averse model predictive control (MPC) of linear systems affected by multiplicative uncertainty. Our key innovation is to consider time-consistent, dynamic risk metrics as objective functions to…
This paper shows how the theory of dynamic risk measures provides viscosity solutions to a family of second-order parabolic partial differential equations, even in the degenerate case. First, motivated by the martingale problem approach of…
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable…
In this paper we present a Learning Model Predictive Control (LMPC) strategy for linear and nonlinear time optimal control problems. Our work builds on existing LMPC methodologies and it guarantees finite time convergence properties for the…
For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Bj\"ork and Murgoci (Finance Stoch, 2014) is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium…
Stochastic models such as Continuous-Time Markov Chains (CTMC) and Stochastic Hybrid Automata (SHA) are powerful formalisms to model and to reason about the dynamics of biological systems, due to their ability to capture the stochasticity…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typically solving a regularized…
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…