Related papers: Finite Elements with Switch Detection for Direct O…
This paper develops high-accuracy methods for numerically solving optimal control problems subject to nonsmooth differential equations with set-valued step functions. A notable subclass of these systems are Filippov systems. The set-valued…
This paper introduces Finite Elements with Switch Detection (FESD), a numerical discretization method for nonsmooth differential equations. We consider the Filippov convexification of these systems and a transformation into dynamic…
The Finite Elements with Switch Detection (FESD) method is a highly accurate direct transcription method for optimal control of several classes of nonsmooth dynamical systems. This paper extends the FESD method to Projected Dynamical…
The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of optimal control problems subject to discontinuous ODEs. In this article, we extend the FESD method [Nurkanovi\'c et al.,…
This paper extends the Finite Elements with Switch Detection and Jumps (FESD-J) [1] method to problems of rigid body dynamics involving patch contacts. The FESD-J method is a high accuracy discretization scheme suitable for use in direct…
Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a…
This letter introduces the NOnSmooth Numerical Optimal Control (NOSNOC) open-source software package. It is a modular MATLAB tool based on CasADi and IPOPT for numerically solving Optimal Control Problems (OCP) with piecewise smooth systems…
This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear…
Real-time model predictive control of non-smooth switching systems remains challenging due to discontinuities and the presence of discrete modes, which complicate numerical integration and optimization. This paper presents a real-time…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
This paper studies the design of controllers for discontinuous dynamics that ensure the safety of non-smooth sets. The safe set is represented by arbitrarily nested unions and intersections of 0-superlevel sets of differentiable functions.…
Neural Stochastic Differential Equations (Neural SDEs) have emerged as powerful mesh-free generative models for continuous stochastic processes, with critical applications in fields such as finance, physics, and biology. Previous…
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
State-of-the-art approaches to optimal control use smooth approximations of value and policy functions and gradient-based algorithms for improving approximator parameters. Unfortunately, we show that value and policy functions that arise in…
In this work, we consider a nonsmooth minimisation problem in which the objective function can be represented as the maximum of finitely many smooth ``subfunctions''. First, we study a smooth min-max reformulation of the problem. Due to…
Finite element methods have been successfully used to develop physics-based models of soft robots that capture the nonlinear dynamic behavior induced by continuous deformation. These high-fidelity models are therefore ideal for designing…
In this paper, we focus on the decentralized stochastic subgradient-based methods in minimizing nonsmooth nonconvex functions without Clarke regularity, especially in the decentralized training of nonsmooth neural networks. We propose a…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…