Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs

• URL: http://arxiv.org/abs/2009.01196v1
• Date: Wed, 2 Sep 2020 17:10:07 GMT
• Title: Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs
• Authors: Marcus Aloysius Pereira and Ziyi Wang and Ioannis Exarchos and Evangelos A. Theodorou
• Abstract summary: This paper introduces a new formulation for optimal control and dynamic optimization. A Neural Network architecture is designed for safe trajectory optimization in which learning can be performed in an end-to-end fashion.
• Score: 23.554700972887375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as Forward-Backward Stochastic Differential Equations, Stochastic Barrier Functions, Differentiable Convex Optimization and Deep Learning. Using the aforementioned concepts, a Neural Network architecture is designed for safe trajectory optimization in which learning can be performed in an end-to-end fashion. Simulations are performed on three systems to show the efficacy of the proposed methodology.

Related papers

• A Simulation-Free Deep Learning Approach to Stochastic Optimal Control [12.699529713351287]
  We propose a simulation-free algorithm for the solution of generic problems in optimal control (SOC) Unlike existing methods, our approach does not require the solution of an adjoint problem.
  arXiv  Detail & Related papers  (2024-10-07T16:16:53Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Optimal Control of Nonlinear Systems with Unknown Dynamics [4.551160285910024]
  This paper presents a data-driven method for finding a closed-loop optimal controller.<n>It minimizes a specified infinite-horizon cost function for systems with unknown dynamics given any arbitrary initial state.
  arXiv  Detail & Related papers  (2023-05-24T14:27:22Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Introduction to Online Nonstochastic Control [34.77535508151501]
  In online nonstochastic control, both the cost functions as well as the perturbations from the assumed dynamical model are chosen by an adversary. The target is to attain low regret against the best policy in hindsight from a benchmark class of policies.
  arXiv  Detail & Related papers  (2022-11-17T16:12:45Z)
• Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics [96.9177297872723]
  We present a novel method for guaranteeing linear momentum in learned physics simulations. We enforce conservation of momentum with a hard constraint, which we realize via antisymmetrical continuous convolutional layers. In combination, the proposed method allows us to increase the physical accuracy of the learned simulator substantially.
  arXiv  Detail & Related papers  (2022-10-12T09:12:59Z)
• Chance-Constrained Optimization in Contact-Rich Systems for Robust Manipulation [13.687891070512828]
  We present a chance-constrained optimization for Discrete-time Linear Complementarity Systems (SDLCS) In our formulation, we explicitly consider joint chance constraints for complementarity as well as states to capture the evolution of dynamics. The robustness proposed approach outperforms some recent approaches for robust trajectory optimization for SDLCS.
  arXiv  Detail & Related papers  (2022-03-05T00:16:22Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• A Backward SDE Method for Uncertainty Quantification in Deep Learning [9.7140720884508]
  We develop a probabilistic machine learning method, which formulates a class of neural networks by an optimal control problem. An efficient descent algorithm is introduced under the maximum principle framework.
  arXiv  Detail & Related papers  (2020-11-28T15:19:36Z)
• Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems [81.7983463275447]
  Learning-based control algorithms require data collection with abundant supervision for training. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained optimal control with dynamics learning and feedback control.
  arXiv  Detail & Related papers  (2020-05-09T05:57:43Z)
• Learning Control Barrier Functions from Expert Demonstrations [69.23675822701357]
  We propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs) We analyze an optimization-based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz assumptions on the underlying dynamical system. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
  arXiv  Detail & Related papers  (2020-04-07T12:29:06Z)
• Adaptive Stochastic Optimization [1.7945141391585486]
  Adaptive optimization methods have the potential to offer significant computational savings when training large-scale systems. Modern approaches based on the gradient method are non-adaptive in the sense that their implementation employs prescribed parameter values that need to be tuned for each application.
  arXiv  Detail & Related papers  (2020-01-18T16:30:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.