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Sum-of-Squares Relaxations for Information Theory and Variational Inference

Foundations of Computational Mathematics, 2022
We consider extensions of the Shannon relative entropy, referred to as f-divergences. Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing integrals, and (c)
F. Bach
semanticscholar   +1 more source

Extended bounded real lemma based sum of squares for static output feedback H∞ heading control

International Journal of Robust and Nonlinear Control, 2022
Aim at the fore and aft asymmetry of unmanned surface vehicle (USV) and the loss of linear velocity, a static output feedback (SOF) H∞$$ {H}_{\infty } $$ control method is proposed by the sum of squares (SOS) based on two types of extended bounded real ...
Yanwei Huang, Tao Lin, Wenchao Huang
semanticscholar   +1 more source

Hamiltonian‐driven adaptive dynamic programming for mixed H2/H∞ performance using sum‐of‐squares

International Journal of Robust and Nonlinear Control, 2021
In this article, the mixed H2/H∞ performance optimization is first formulated as a nonzero‐sum game, of which the sufficient condition guaranteeing the existence of the Nash equilibrium is derived using the Hamilton–Jacobi (HJ) theory.
Yongliang Yang   +2 more
semanticscholar   +1 more source

Tube-model predictive control based on sum of squares for hypersonic vehicle with state-dependent input constraints

Transactions of the Institute of Measurement and Control, 2021
In this paper, tube-model predictive control based on the sum of squares technique is developed for hypersonic vehicles with state-dependent input constraints.
Xiaohe Yang   +3 more
semanticscholar   +1 more source

Sum‐of‐squares‐based policy iteration for suboptimal control of polynomial time‐varying systems

Asian journal of control, 2021
This paper investigates the suboptimal control design for polynomial time‐varying systems. It is known that the solution to this problem relies on the solution of the Hamilton–Jacobi–Bellman (HJB) equation, which is a nonlinear partial differential ...
Sajjad Pakkhesal, S. Shamaghdari
semanticscholar   +1 more source

A study over the general formula of regression sum of squares in multiple linear regression

Numerical Methods for Partial Differential Equations, 2020
In this study, in addition to the formula of regression sum of squares (SSR) in linear regression, a general formula of SSR in multiple linear regression is given. The derivations of the formula presented are given step by step.
M. Korkmaz
semanticscholar   +1 more source

Sum of Squares Circuits

AAAI Conference on Artificial Intelligence
Designing expressive generative models that support exact and efficient inference is a core question in probabilistic ML. Probabilistic circuits (PCs) offer a framework where this tractability-vs-expressiveness trade-off can be analyzed theoretically ...
Lorenzo Loconte   +2 more
semanticscholar   +1 more source

Sums of Odd Squares

gmj, 2006
Abstract The number of representations of an integer as a sum of 𝑛 odd squares for 𝑛 ≡ 0 mod 4 is expressed by the number of representations as a sum of 𝑛 squares of integers and the number of representations by the lattice .
openaire   +2 more sources

Sum of Squares Rings

Canadian Journal of Mathematics, 1977
One of the nicest results in elementary number theory is the following, giving the relation between quadratic residues and sums of squares.
openaire   +1 more source

Koopman-based control using sum-of-squares optimization: Improved stability guarantees and data efficiency

European Journal of Control
In this paper, we propose a novel controller design approach for unknown nonlinear systems using the Koopman operator. In particular, we use the recently proposed stability- and feedback-oriented extended dynamic mode decomposition (SafEDMD) architecture
Robin Strässer   +2 more
semanticscholar   +1 more source

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