Related papers: A structure exploiting SDP solver for robust contr…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite…
Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certify their robustness. A number of techniques based on convex…
Grid-interfacing inverters act as the interface between renewable resources and the electric grid, and have the potential to offer fast and programmable controls compared to synchronous generators. With this flexibility there has been…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
Models used for control design are, to some degree, uncertain. Model uncertainty must be accounted for to ensure the robustness of the closed-loop system. $\mu$-analysis and $\mu$-synthesis methods allow for the analysis and design of…
We study finite-state controllers (FSCs) for partially observable Markov decision processes (POMDPs) that are provably correct with respect to given specifications. The key insight is that computing (randomised) FSCs on POMDPs is equivalent…
We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
This paper presents an automatic formal controller synthesis method for nonlinear sampled-data systems with safety and reachability specifications. Fundamentally, the presented method is not restricted to polynomial systems and controllers.…
The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent…
We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential equations and integral equations, commonly used in fluid…
We show how to sketch semidefinite programs (SDPs) using positive maps in order to reduce their dimension. More precisely, we use Johnson\hyp{}Lindenstrauss transforms to produce a smaller SDP whose solution preserves feasibility or…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
Repair mechanisms are important within resilient systems to maintain the system in an operational state after an error occurred. Usually, constraints on the repair mechanisms are imposed, e.g., concerning the time or resources required…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
Semidefinite programming (SDP) provides a fundamental framework for studying properties of sum-of-squares (sos) representations of nonnegative polynomials. In this paper we study the quartic forms GF = (|x|^4 + F(x))/2 associated with…