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Sum-of-Squares Relaxations for Information Theory and Variational Inference
Foundations of Computational Mathematics, 2022We 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
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Extended bounded real lemma based sum of squares for static output feedback H∞ heading control
International Journal of Robust and Nonlinear Control, 2022Aim 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
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Hamiltonian‐driven adaptive dynamic programming for mixed H2/H∞ performance using sum‐of‐squares
International Journal of Robust and Nonlinear Control, 2021In 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
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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
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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
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Sum‐of‐squares‐based policy iteration for suboptimal control of polynomial time‐varying systems
Asian journal of control, 2021This 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
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A study over the general formula of regression sum of squares in multiple linear regression
Numerical Methods for Partial Differential Equations, 2020In 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
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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
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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
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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 .
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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 .
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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.
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One of the nicest results in elementary number theory is the following, giving the relation between quadratic residues and sums of squares.
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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
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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

