Sufficient Criteria and Sharp Geometric Conditions for Observability in Banach Spaces
From MaRDI portal
Publication:5130928
DOI10.1137/19M1266769MaRDI QIDQ5130928
Martin Tautenhahn, Dennis Gallaun, Christian Seifert
Publication date: 30 October 2020
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.10285
Banach space\(C_0\)-semigroupselliptic operatorsnull-controllabilityobservability estimatecontrol costs
Controllability (93B05) One-parameter semigroups and linear evolution equations (47D06) Observability (93B07) Applications of operator theory in systems, signals, circuits, and control theory (47N70) PDEs in connection with control and optimization (35Q93)
Related Items
Observability for Non-autonomous Systems ⋮ The reflection principle in the control problem of the heat equation ⋮ An abstract Logvinenko-Sereda type theorem for spectral subspaces ⋮ Uncertainty principles with error term in Gelfand-Shilov spaces ⋮ Final state observability estimates and cost-uniform approximate null-controllability for bi-continuous semigroups ⋮ Observability and null-controllability for parabolic equations in \(L_p\)-spaces ⋮ On null‐controllability of the heat equation on infinite strips and control cost estimate ⋮ Final state observability in Banach spaces with applications to subordination and semigroups induced by Lévy processes ⋮ Control problem for quadratic parabolic differential equations with sparse sensor sets of finite volume or anisotropically decaying density ⋮ A unified observability result for non-autonomous observation problems ⋮ Sharp estimates and homogenization of the control cost of the heat equation on large domains ⋮ Characterizations of stabilizable sets for some parabolic equations in \(\mathbb{R}^n\) ⋮ Scale-free unique continuation estimates and Logvinenko-Sereda theorems on the torus
Cites Work
- Unnamed Item
- Unnamed Item
- A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-diffusion equation
- Observability inequalities and measurable sets
- Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport-diffusion equation
- Note on the cost of the approximate controllability for the heat equation with potential
- A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups
- Sharp observability estimates for heat equations
- Observation from measurable sets for parabolic analytic evolutions and applications
- Null-controllability of the Kolmogorov equation in the whole phase space
- Some results on controllability for linear and nonlinear heat equations in unbounded domains
- Two results on exact boundary control of parabolic equations
- A lower bound of the norm of the control operator for the heat equation
- Null-controllability of a system of linear thermoelasticity
- Sharp geometric condition for null-controllability of the heat equation on \(\mathbb R^d\) and consistent estimates on the control cost
- Scale-free unique continuation principle for spectral projectors, eigenvalue-lifting and Wegner estimates for random Schrödinger operators
- Unique continuation estimates for the Laplacian and the heat equation on non-compact manifolds
- Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
- How violent are fast controls for Schrödinger and plate vibrations?
- An observability estimate for parabolic equations from a measurable set in time and its applications
- Carleman commutator approach in logarithmic convexity for parabolic equations
- Observability of the heat equation, geometric constants in control theory, and a conjecture of Luc Miller
- On the null-controllability of the heat equation in unbounded domains
- Observable set, observability, interpolation inequality and spectral inequality for the heat equation in \(\mathbb{R}^n\)
- On the cost of observability in small times for the one-dimensional heat equation
- On exponential observability estimates for the heat semigroup with explicit rates
- New blow-up rates for fast controls of Schrödinger and heat equations
- The functional calculus for sectorial operators
- On null controllability of linear systems in Banach spaces
- Some results related to the Logvinenko-Sereda theorem
- On the null-controllability of diffusion equations
- On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
- The Control Transmutation Method and the Cost of Fast Controls
- A General Theory of Observation and Control
- Contróle Exact De Léquation De La Chaleur
- Null-controllability of hypoelliptic quadratic differential equations
- Observability Inequalities from Measurable Sets for Some Abstract Evolution Equations
- Exact null internal controllability for the heat equation on unbounded convex domains
- On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
- The cost of approximate controllability for heat equations: The linear case
- On null‐controllability of the heat equation on infinite strips and control cost estimate