Thomas I. Seidman

How Violent Are Fast Controls

For a linear autonomous system, if a state is reachable from zero in some time duration, then it is reachable within any positive time duration. However, the norm of the control that steers the zero state to the given reachable state increases as the available control time shrinks. This paper gives the asymptotics of minimalLp-norm controls as the time duration goes to zero; there are also some further remarks for other related norms.

Invariance of the reachable set under nonlinear perturbations

For the abstract controlled Volterra equation \[( * )\qquad x(t) = \bar x(t) + \int_0^t {{\boldsymbol{\psi}} (t,s)[\phi (s,x(s)) + {\bf B}(s)v(s)]ds} \] on

Two results on exact boundary control of parabolic equations

[0,T]

An 'optimal filtering' method for the sideways heat equation

, we consider the reachable set

An Abstract Bang-Bang Principle and Time-Optimal Boundary Control of the Heat Equation

\mathcal{K}_\phi : = \{ {x(T):( * ){\text{ for some }}v \in \mathfrak{B}} \}

Optimal filtering for the backward heat equation

. Viewing

Steady state solutions of diffusion-reaction systems with electrostatic convection

\phi ( \cdot , \cdot )

Nonconvergence results for the application of least-squares estimation to Ill-posed problems

as a nonlinear perturbation of an otherwise linear control problem, conditions are obtained under which

On boundary controllability of a vibrating plate

\mathcal{K}_\phi = \mathcal{K}_0

Will the self-tuning approach work for general cost criteria?☆

for a suitable class