Related papers: Piecewise-Deterministic Optimal Path Planning
Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space…
We propose a model predictive control approach for autonomous vehicles that exploits learned Gaussian processes for predicting human driving behavior. The proposed approach employs the uncertainty about the GP's prediction to achieve…
This paper presents an adaptive online distributed optimal control approach that is applicable to optimal planning for very-large-scale robotics systems in highly uncertain environments. This approach is developed based on the optimal mass…
We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by Partial Differential Equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…
The paper introduces an asymptotically optimal lifelong sampling-based path planning algorithm that combines the merits of lifelong planning algorithms and lazy search algorithms for rapid replanning in dynamic environments where edge…
We introduce a new method, stepwise method for solving optimal con- trol problems. Our first motivation for new approach emanate from limi- tations on continuous time control functions in PMP. Practically in most of the real world models,…
Navigation in complex and noisy environments is a key issue in diverse fields from biology to engineering. Despite extensive progress in numerical optimization methods for computing navigation policies, insights into how disorder reshapes…
In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…
We explore the probabilistic foundations of shared control in complex dynamic environments. In order to do this, we formulate shared control as a random process and describe the joint distribution that governs its behavior. For…
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…
The Dynamic Programming approach allows to compute a feedback control for nonlinear problems, but suffers from the curse of dimensionality. The computation of the control relies on the resolution of a nonlinear PDE, the…
We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (inspired by traffic models). We adapt the results in [H. M.…
In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics…
We report a globally-optimal approach to robotic path planning under uncertainty, based on the theory of quantitative measures of formal languages. A significant generalization to the language-measure-theoretic path planning algorithm…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…