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In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
If a collection of identical particles is poured into a container, different shapes will fill to different densities. But what is the shape that fills a container as close as possible to a pre-specified, desired density? We demonstrate a…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
We collect some examples of optimal transports in order to explore the (in)stability of the identity map as an optimal transport. First, we consider density and domain perturbations near regular portions of domains. Second, we investigate…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum…
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface.…
To design control strategies that predictably manipulate a system's behavior, it is first necessary to understand how the system's structure relates to its response. Many complex systems can be represented as multilayer networks whose…
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
In this paper, We study the problem of learning a controllable representation for high-dimensional observations of dynamical systems. Specifically, we consider a situation where there are multiple sets of observations of dynamical systems…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
This paper studies the inverse optimal control problem for continuous-time linear quadratic regulators over finite-time horizon, aiming to reconstruct the control, state, and terminal cost matrices in the objective function from observed…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
Network control refers to a very large and diverse set of problems including controllability of linear time-invariant dynamical systems, where the objective is to select an appropriate input to steer the network to a desired state. There…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…