Related papers: The Canonical Controller for Distributed Systems
A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage…
A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…
The purpose of this article is the investigation of the global control properties of a coupled nonlinear dispersive system posed in the periodic domain $\mathbb{T}$, a system with the structure of a nonlinear Schr\"odinger equation and a…
The problem of open-loop dynamical control of generic open quantum systems is addressed. In particular, I focus on the task of effectively switching off environmental couplings responsible for unwanted decoherence and dissipation effects.…
In this paper, we discuss a distributed control architecture, aimed at networks with linear and time-invariant dynamics, which is amenable to convex formulations for controller design. The proposed approach is well suited for large scale…
The main goal of this manuscript is to prove the existence of insensitizing controls for the fourth-order dispersive nonlinear Schr\"odinger equation with cubic nonlinearity. To obtain the main result we prove a null controllability…
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are…
Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…
We consider a decentralized system with multiple controllers and define substitutability of one controller by another in open-loop strategies. We explore the implications of this property on the optimization of closed-loop strategies. In…
This short book is the result of various master and summer school courses I have taught. The objective is to introduce the readers to mathematical control theory, both in finite and infinite dimension. In the finite-dimensional context, we…
This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
In this paper, a class of convex feasibility problems (CFPs) are studied for multi-agent systems through local interactions. The objective is to search a feasible solution to the convex inequalities with some set constraints in a…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann--Liouville derivatives is…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
In this paper we consider two-dimensional canonical systems with discrete spectrum and study their eigenvalue densities. We develop a formula that determines the Stieltjes transform of the eigenvalue counting function up to universal…
Willems' fundamental lemma asserts that all trajectories of a linear time-invariant system can be obtained from a finite number of measured ones, assuming that controllability and a persistency of excitation condition hold. We show that…
The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…