Results 11 to 20 of about 927,941 (284)
Observability inequalities for degenerate transport equations [PDF]
Journal of Evolution Equations, 2021 In this paper we prove an observability inequality for a degenerate transport equation. First we introduce a local in time Carleman estimate for the degenerate equation, then we apply it to obtain a global in time observability inequality by using also an energy estimate.
Floridia G., Takase H.
semanticscholar +6 more sources
Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications [PDF]
SIAM Journal on Control and Optimization, 2016 This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained.
Donghui Yang, J. Zhong
semanticscholar +3 more sources
Sharp Observability Inequalities for Hyperbolic Systems with Potentials
ESAIM: Control, Optimisation and Calculus of Variations, 2023 This paper is devoted to a sharp internal/boundary observability inequality for a hyperbolic system with a zero order potential. For this purpose, we first establish a new Carleman estimate for hyperbolic operator inH1-norm. Based on this Carleman estimate and a modified auxiliary optimal control problem, we obtain Carleman estimate for hyperbolic ...
Fu, Xiaoyu, Liao, Zhonghua, Lü, Qi
openaire +2 more sources
Robust Distributed Observers for Simultaneous State and Fault Estimation over Sensor Networks [PDF]
SensorsThis paper focuses on simultaneous estimation of states and faults for a linear time-invariant (LTI) system observed by sensor networks. Each sensor node is equipped with an observer, which uses only local measurements and local interaction with ...
Dingguo Liang +3 more
doaj +2 more sources
Fault Location Observability using Phasor Measurements Units via Semidefinite Programming
IEEE Access, 2016 This paper presents a placement algorithm for fault location observability using phasor measurement units (PMUs) in the presence or absence of zero injection buses.
Theodoros A. Alexopoulos +2 more
doaj +2 more sources
Observability Inequalities for Transport Equations through Carleman Estimates [PDF]
Trends in Control Theory and Partial Differential Equations, 2019 We consider the transport equation $\ppp_t u(x,t) + H(t)\cdot \nabla u(x,t) = 0$ in $\OOO\times(0,T),$ where $T>0$ and $\OOO\subset \R^d $ is a bounded domain with smooth boundary $\ppp\OOO$. First, we prove a Carleman estimate for solutions of finite energy with piecewise continuous weight functions. Then, under a further condition which guarantees
Piermarco Cannarsa +2 more
openaire +6 more sources
Discrete & Continuous Dynamical Systems - B, 2021 This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback controller with a
A. Kong +4 more
semanticscholar +1 more source
Quantitative observability for one-dimensional Schrödinger equations with potentials [PDF]
Journal of Functional Analysis, 2023 In this note, we prove the quantitative observability with an explicit control cost for the 1D Schr\"odinger equation over $\mathbb{R}$ with real-valued, bounded continuous potential on thick sets.
Pei Su, Chenmin Sun, Xu Yuan
semanticscholar +1 more source
Observability inequalities and measurable sets [PDF]
Journal of the European Mathematical Society, 2014 This paper presents two observability inequalities for the heat equation over \Omega\times (0,T) . In the first one, the observation is from a subset of positive measure in \Omega\times (0,T)
Apraiz, J. +3 more
openaire +2 more sources
A sharp observability inequality for Kirchhoffplate systems with potentials
Computational and Applied Mathematics, 2006 Xu Zhang, E. Zuazua
semanticscholar +3 more sources