Related papers: Moment Analysis of Stochastic Hybrid Systems Using…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
The use of approximate solution techniques for the Chemical Master Equation is common practice for the analysis of stochastic chemical systems. Despite their widespread use, however, many such techniques rely on unverifiable assumptions and…
In this article we provide an experimental algorithm that in many cases gives us an upper bound of the global infimum of a real polynomial on $\R^{n}$. It is very well known that to find the global infimum of a real polynomial on $\R^{n}$,…
In this paper we propose a compositional framework for the construction of approximations of the interconnection of a class of stochastic hybrid systems. As special cases, this class of systems includes both jump linear stochastic systems…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to…
This paper presents algorithms that upper-bound the peak value of a state function along trajectories of a continuous-time system with rational dynamics. The finite-dimensional but nonconvex peak estimation problem is cast as a convex…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…