Related papers: Limit points of the monotonic schemes
The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schr\"odinger…
We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields, without losing monotonic convergence of the algorithm. The method guarantees a close…
We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the field fluence. A standard algorithm designs a control field of fixed duration which both brings the system close…
A great number of quantum control papers have used one of the variants of the monotonically convergent variational control algorithm of Krotov (as described in Maday and Turinici (2003), Tannor et al. (1992), Zhu and Rabitz (1998), etc).…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient…
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
Mathematical problems of optimal control in quantum systems attract high interest in connection with fundamental questions and existing and prospective applications. An important problem is the development of methods for constructing…
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by introducing a new notion of consistency. We apply our general…
In [1] Zhu and Rabitz presented a rapidly convergent iterative algorithm for optimal control of the expectation value of a positive definite observable in a pure-state quantum system. In this paper we generalize this algorithm to a quantum…
Monotone systems, also known as order-preserving or cooperative systems, are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control…
Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions…
This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws…
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor's Monotonicity Conjecture. In contrast, the existing proofs rely in one…
We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…
This work contributes to the field of optimal control of bilinear systems. It concerns a continuous time, finite dimensional, bilinear state equation with a quadratic performance index to be minimized. The state equation is non-autonomous…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
The monotonically controlled integral defined by Bendov\'a and Mal\'y, which is equivalent to the Denjoy-Perron integral, admits a natural parameter $\alpha>0$ thereby leading to the whole scale of integrals called $\alpha$-monotonically…
The chaos control problem of continuous time Rabinovich chaotic system is addressed. An instantaneous control input has been designed using predictive control principle to guarantee the convergence of the chaotic trajectory towards an…