High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out...

Provably-Stable Stochastic MPC for a Class of Nonlinear Contractive Systems

We present a model predictive control framework for a class of nonlinear systems affected by additive stochastic disturbances with (possibly) unbounded support. We consider hard input constraints and chance state constraints and we employ the unscented transform method to propagate the disturbances over the nonlinear dynamics in a...

Distributionally Robust Strategy Synthesis for Switched Stochastic Systems

We present a novel framework for formal control of uncertain discrete-time switched stochastic systems against probabilistic reach-avoid specifications. In particular, we consider stochastic systems with additive noise, whose distribution lies in an ambiguity set of distributions that are ε−close to a nominal one according to the Wasserstein...

Stochastic Stability of Discrete-time Phase-coupled Oscillators over Uncertain and Random Networks

This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. The stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators coupled with 2π-periodic odd functions over underlying undirected graphs subject to both multiplicative...

Safety Certification for Stochastic Systems via Neural Barrier Functions

Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem. One promising solution to address this problem is the use of barrier functions. Barrier functions are functions whose composition with the system forms a Martingale and enable the computation of the probability that the system stays...

Promises of Deep Kernel Learning for Control Synthesis

Deep Kernel Learning (DKL) combines the representational power of neural networks with the uncertainty quantification of Gaussian Processes. Hence, it is potentially a promising tool to learn and control complex dynamical systems. In this letter, we develop a scalable abstraction-based framework that enables the use of DKL for control...

Formal Abstraction of General Stochastic Systems via Noise Partitioning

Verifying the performance of safety-critical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with nonstandard (e.g., non-affine, non-symmetric, non-unimodal) noise distributions for verification purposes. The method uses a finite...

Macroscopic Noisy Bounded Confidence Models with Distributed Radical Opinions

In this article, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic) approximation of bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of radicals (stubborn individuals). The distribution of radical opinions serves as an infinite-dimensional...

Robust control design for linear systems via multiplicative noise

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control design. Specifically, we examine a multiplicative noise framework which models the inherent uncertainty and...

Distributed computational framework for large-scale stochastic convex optimization

This paper presents a distributed computational framework for stochastic convex optimization problems using the so-called scenario approach. Such a problem arises, for example, in a large-scale network of interconnected linear systems with local and common uncertainties. Due to the large number of required scenarios to approximate the...

Strategy synthesis for partially-known switched stochastic systems

We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via...

Learning Optimal Controllers for Linear Systems with Multiplicative Noise via Policy Gradient

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because...

Reachable sets of hidden CPS sensor attacks: Analysis and synthesis tools

For given system dynamics, control structure, and fault/attack detection procedure, we provide mathematical tools–in terms of Linear Matrix Inequalities (LMIs)–for characterizing and minimizing the set of states that sensor attacks can induce in the system while keeping the alarm rate of the fault detector sufficiently close to its false...

Formal Abstractions for Automated Verification and Synthesis of Stochastic Systems

Stochastic hybrid systems involve the coupling of discrete, continuous, and probabilistic phenomena, in which the composition of continuous and discrete variables captures the behavior of physical systems interacting with digital, computational devices. Because of their versatility and generality, methods for modeling, analysis, and verification...

Stability of Optimal Solutions: Multi- and Single-Objective Approaches

Accurate spacecraft attitude estimation with the ESA starmapper

The ESA starmapper is an optical-electronic instrument with an array of photo-sensitive slits, to "be strapped down to spinning spacecraft. Recorded times of passage of known stars over these slits, together with mathematical models for spacecraft dynamics and starmapper instrument, provide the basis for recursive estimation of the spacecraft...