Related papers: Performance and Robustness Analysis of Stochastic …
In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a…
In this note, we provide a unified framework for the mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric known as an optimal transport, that assesses the distance between probability density…
This paper provides a method to design an optimal switching sequence for jump linear systems with given Gaussian initial state uncertainty. In the practical perspective, the initial state contains some uncertainties that come from…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
To deal with stochastic hybrid systems with general state-dependent switching, we propose an approximation method by a sequence of stochastic hybrid systems with piecewise constant type switching. The convergence rate in the Wasserstein…
Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modelling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
We present a methodology for predictable and safe covariance steering control of uncertain nonlinear stochastic processes. The systems under consideration are subject to general uncertainties, which include unbounded random disturbances…
1. Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behavior often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent…
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…
The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded…
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…
The paper studies the robustness properties of discrete-time stochastic optimal control under Wasserstein model approximation for both discounted-cost and average-cost criteria. Specifically, we study the performance loss when applying an…
Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, we…