1.2k citations · 1.8k across the 38 of their papers we have counts for
45 papers
Lyapunov stability of polynomial vector fields is undecidable
Milan Korda
We show that there are integers and odd such that no algorithm can decide, from the rational coefficients of a homogeneous polynomial vector field in dimension of d…
Global optimization of low-rank polynomials
Llorenç Balada Gaggioli, Didier Henrion, Milan Korda
This work considers polynomial optimization problems where the objective admits a low-rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimiza…
Solving unbounded optimal control problems with the moment-SOS hierarchy *
Karolına Sehnalová, Didier Henrion, Milan Korda +1
The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution foc…
Optimal Control of 1D Semilinear Heat Equations with Moment-SOS Relaxations
Charlie Lebarbé, Emilien Flayac, Michel Fournié +2
We use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of mo…
Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations
Nicolas Augier, Didier Henrion, Milan Korda +1
We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the mo…
Peak Estimation of Time Delay Systems using Occupation Measures
Jared Miller, Milan Korda, Victor Magron +1
This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding…
Convergence rates for sums-of-squares hierarchies with correlative sparsity
Milan Korda, Victor Magron, Rodolfo Rios-Zertuche
This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semi…
Occupation measure relaxations in variational problems: the role of convexity
Didier Henrion, Milan Korda, Martin Kružík +1
This work addresses the occupation measure relaxation of calculus of variations problems, which is an infinite-dimensional linear programming relaxation amenable to numerical appro…
Polynomial argmin for recovery and approximation of multivariate discontinuous functions
Didier Henrion, Milan Korda, Jean-Bernard Lasserre
We propose to approximate a (possibly discontinuous) multivariate function f (x) on a compact set by the partial minimizer arg miny p(x, y) of an appropriate polynomial p whose con…
Controlled Synchronization of Coupled Pendulums by Koopman Model Predictive Control
Loi Do, Milan Korda, Zdeněk Hurák
We propose and experimentally demonstrate a feedback control method that allows synchronizing the motion of a chain of several coupled nonlinear oscillators actuated through one en…
Dictionary-free Koopman model predictive control with nonlinear input transformation
Vít Cibulka, Milan Korda, Tomáš Haniš
This paper introduces a method for data-driven control based on the Koopman operator model predictive control. Unlike exiting approaches, the method does not require a dictionary a…
Time-dependent moments from partial differential equations and the time-dependent set of atoms
Raúl E. Curto, Philipp J. di Dio, Milan Korda +1
We study the time-dependent moments and associated polynomials arising from the partial differential equation , and consider in deta…
Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks
Milan Korda, Monique Laurent, Victor Magron +1
We explore a new type of sparsity for the generalized moment problem (GMP) that we call ideal-sparsity. This sparsity exploits the presence of equality constraints requiring the me…
Urysohn in action: separating semialgebraic sets by polynomials
Milan Korda, Jean-Bernard Lasserre, Alexey Lazarev +2
A classical result from topology called Uryshon's lemma asserts the existence of a continuous separator of two disjoint closed sets in a sufficiently regular topological space. In…
The gap between a variational problem and its occupation measure relaxation
Milan Korda, Rodolfo Rios-Zertuche
Recent works have proposed linear programming relaxations of variational optimization problems subject to nonlinear PDE constraints based on the occupation measure formalism. The m…
Sparsity structures for Koopman operators
Corbinian Schlosser, Milan Korda
We present a decomposition of the Koopman operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems i…
Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems
Jie Wang, Corbinian Schlosser, Milan Korda +1
In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computat…
Revisiting semidefinite programming approaches to options pricing: complexity and computational perspectives
Didier Henrion, Felix Kirschner, Etienne de Klerk +3
In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only…
Clarifying the effect of mean subtraction on Dynamic Mode Decomposition
Gowtham S Seenivasaharagavan, Milan Korda, Hassan Arbabi +1
Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven ap…
Peak Estimation for Uncertain and Switched Systems
Jared Miller, Didier Henrion, Mario Sznaier +1
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete se…
Model Predictive Control of a Vehicle using Koopman Operator
Vít Cibulka, Milan Korda, Tomáš Haniš +1
This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher ord…
Spatio-Temporal Decomposition of Sum-of-Squares Programs for the Region of Attraction and Reachability
Vít Cibulka, Milan Korda, Tomáš Haniš
This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of…
Stability and performance verification of dynamical systems controlled by neural networks: algorithms and complexity
Milan Korda
This work makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and…
Sparse decompositions of nonlinear dynamical systems and applications to moment-sum-of-squares relaxations
Corbinian Schlosser, Milan Korda
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call sub…