Related papers: On the Computation and Approximation of Backward R…
The recently introduced full-history recursive multilevel Picard (MLP) approximation methods have turned out to be quite successful in the numerical approximation of solutions of high-dimensional nonlinear PDEs. In particular, there are…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
Multi-object estimation in state-space models (SSMs) wherein the system state is represented as a finite set has attracted significant interest in recent years. In Bayesian inference, the posterior density captures all information on the…
We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…
In this study, we propose the lopsided HSS (LHSS) iteration method for solving a class of complex symmetric indefinite systems of linear equations. This method employs an alternating iterative scheme, where each iteration entails solving…
Multiple-environment MDPs (MEMDPs) capture finite sets of MDPs that share the states but differ in the transition dynamics. These models form a proper subclass of partially observable MDPs (POMDPs). We consider the synthesis of policies…
In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex,…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…
This work presents a data-driven method for approximation of the maximum positively invariant (MPI) set and the maximum controlled invariant (MCI) set for nonlinear dynamical systems. The method only requires the knowledge of a finite…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…
The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…
This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters…
The arising application of neural networks (NN) in robotic systems has driven the development of safety verification methods for neural network dynamical systems (NNDS). Recursive techniques for reachability analysis of dynamical systems in…
We consider a family of parallel methods for constrained optimization based on projected gradient descents along individual coordinate directions. In the case of polyhedral feasible sets, local convergence towards a regular solution occurs…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition…
We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty. In our method, at each time step we solve a finite time robust optimal…