Related papers: The turnpike property in semilinear control
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We consider the problem of driving a finite-state classical system from some initial distribution $p$ to some final distribution $p'$ with vanishing entropy production (EP), under the constraint that the driving protocols can only use some…
We prove the existence of quasi-left continuous semimartingales with continuous local semimartingale characteristics which satisfy a Lyapunov-type or a linear growth condition, where latter takes the whole history of the paths into…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator. For bilinear quantum control problems, no general results are available to fully…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
The problem of state-feedback stabilizability of discrete-time nonlinear systems has been considered in this note. Two assertions have been proved. First, if the system is $N$-step controllable to the origin, then there is a state feedback…
We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by…
A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and general coefficient with Lipschitz continuity, the convergence of the first…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…
We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find…
The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the strict convexity of the reachable set…