Related papers: Linear and dynamic programs for risk-sensitive cos…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
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…
In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
We study infinite horizon control of continuous-time non-linear branching processes with almost sure extinction for general (positive or negative) discount. Our main goal is to study the link between infinite horizon control of these…
This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the…
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal…
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…
We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the…