Related papers: The turnpike property in semilinear control
Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit…
This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand…
We study several controllability properties for some semilinear parabolic PDE with a quadratic gradient term. For internal distributed controls, it is shown that the system is approximately and null controllable. The proof relies on the…
In this paper, minimal time and minimal norm control problems are studied. The target sets considered are the origin of state spaces and controls are point-wisely bounded functions. The system stuided in this paper is assumed to have no the…
Using the semigroup approach to abstract boundary control problems we characterize the space of all exactly reachable states. Moreover, we study the situation when the controls of the system are required to be positive. The abstract results…
In this article, we are discussing a more vital concept of controllability, termed total controllability. We have considered a nonlocal semilinear functional evolution equations with non-instantaneous impulses and finite delay in Hilbert…
The duality between controllability and observability enables methods developed for full-state control to be applied to full-state estimation, and vice versa. In applications in which control or estimation of all state variables is…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or…
In this paper a novel approach is presented for control design with guaranteed transient performance for multiple-input multiple-output discrete-time linear polytopic difference inclusions. We establish a theorem that gives necessary and…
It is shown that an oblique projection based feedback control is able to stabilize the state of the Kuramoto-Sivashinsky equation, evolving in rectangular domains, to a given time-dependent trajectory. The number of actuators is finite and…
In this paper we revise the theory of turnpikes in discounted Markov decision processes, prove the turnpike theorem for the undiscounted model and apply the results to the specific random walk.
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…
This work is concerned with two optimisation problems that we tackle from a qualitative perspective. The first one deals with quantitative inequalities for spectral optimisation problems for Schr\"{o}dinger operators in general domains, the…
The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental…
Output reference tracking of unknown nonlinear systems is considered. The control objective is exact tracking in predefined finite time, while in the transient phase the tracking error evolves within a prescribed boundary. To achieve this,…
This paper investigates the asymptotic behavior of the solution to a linear-quadratic stochastic optimal control problems. The so-called probability cell problem is introduced the first time. It serves as the probability interpretation of…
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…
A remarkably simple result is derived for the minimal time $T_{\rm min}$ required to drive a general initial state to a final target state by a Landau-Zener type Hamiltonian or, equivalently, by time-dependent laser driving. The associated…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…