Related papers: Controlled Optimization of Quadratic Functions in …
Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
We present a gradient-based optimal-control technique for open quantum systems that utilizes quantum trajectories to simulate the quantum dynamics during optimization. Using trajectories allows for optimizing open systems with less…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…
We study the linear-quadratic optimal control problem for infinite-dimensional dissipative systems with possibly indefinite cost functional. Under the assumption that a storage function exists, we show that this indefinite optimal control…
We consider nonlinear scalar-input differential control systems in the vicinity of an equilibrium. When the linearized system at the equilibrium is controllable, the nonlinear system is smoothly small-time locally controllable, i.e.,…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that…
We consider a linear Korteweg-de Vries equation on a bounded domain with a left Dirichlet boundary control.The controllability to the trajectories of such a system was proved in the last decade by using Carleman estimates.Here, we go a step…
We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
This paper considers the problem of regulating a dynamical system to equilibria that are defined as solutions of an input- and state-constrained optimization problem. To solve this regulation task, we design a state feedback controller…
We consider the problem of controlling in minimum time a two-level quantum system which can be subject to a drift. The control is assumed to be bounded in magnitude, and to affect two or three independent generators of the dynamics. We…
By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to…