Related papers: A New Framework for Bounding Reachability Probabil…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
Stochastic control barrier functions (SCBFs) provide a safety-critical control framework for systems subject to stochastic disturbances by bounding the probability of remaining within a safe set. However, synthesizing a valid SCBF that…
This paper studies the problem of finite-time convergence to a prescribed safe set for nonlinear systems whose initial states violate the safety constraints. Existing Control Lyapunov-Barrier Functions (CLBFs) can enforce recovery to the…
This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…
We present a scalable underapproximation of the terminal hitting time stochastic reach-avoid probability at a given initial condition, for verification of high-dimensional stochastic LTI systems. While several approximation techniques have…
Stochastic rounding (SR) offers an alternative to the deterministic IEEE-754 floating-point rounding modes. In some applications such as PDEs, ODEs and neural networks, SR empirically improves the numerical behavior and convergence to…
This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using level sets of a certain class of polynomials known as Christoffel functions. The level…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…
This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…
The vast majority of the literature on stochastic semidefinite programs (stochastic SDPs) with recourse is concerned with risk-neutral models. In this paper, we introduce mean-risk models for stochastic SDPs and study structural properties…
We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (or…
The paper presents Maximal Covariance Backward Reachable Trees (MAXCOVAR BRT), which is a multi-query algorithm for planning of dynamic systems under stochastic motion uncertainty and constraints on the control input with explicit coverage…