Related papers: Optimal Coordinate as a General Method in Stochast…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
We study a class of stochastic target games where one player tries to find a strategy such that the state process almost-surely reaches a given target, no matter which action is chosen by the opponent. Our main result is a geometric dynamic…
The convex analytic method has proved to be a very versatile method for the study of infinite horizon average cost optimal stochastic control problems. In this paper, we revisit the convex analytic method and make three primary…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
Moment optimization techniques have been recently proposed to solve globally various classes of optimal control problems. As those methods return truncated moment sequences of occupation measures, this paper explores a numeric method for…
The problem of finding a solution to the linear system $Ax = b$ with certain minimization properties arises in numerous scientific and engineering areas. In the era of big data, the stochastic optimization algorithms become increasingly…
Momentum methods play a significant role in optimization. Examples include Nesterov's accelerated gradient method and the conditional gradient algorithm. Several momentum methods are provably optimal under standard oracle models, and all…
This work deals with the one-dimensional Stefan problem with a general time-dependent boundary condition at the fixed boundary. Stochastic solutions are obtained using discrete random walks, and the results are compared with analytic…
In order to solve complex, long-horizon tasks, intelligent robots need to carry out high-level, abstract planning and reasoning in conjunction with motion planning. However, abstract models are typically lossy and plans or policies computed…
This paper describes a new approach to solving some stochastic optimization problems for linear dynamic system with various parametric uncertainties. Proposed approach is based on application of tensor formalism for creation the…
Automated synthesis of correct-by-construction controllers for autonomous systems is crucial for their deployment in safety-critical scenarios. Such autonomous systems are naturally modeled as stochastic dynamical models. The general…
Finding the stochastic equilibria for finite-state stochastic matrices amounts to solving an eigen\-vector problem $\pi = \pi P$. Various techniques for doing so are known, some extremely computationally intensive. Herein we shall aim to…
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
A typical manipulation task consists of a manipulator equipped with a gripper to grasp and move an object with constraints on the motion of the hand-held object, which may be due to the nature of the task itself or from object-environment…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
Optimal control synthesis in stochastic systems with respect to quantitative temporal logic constraints can be formulated as linear programming problems. However, centralized synthesis algorithms do not scale to many practical systems. To…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…