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In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carath\'{e}odory dimension characteristic, motivated by the work of Bowen and Pesin etc. We…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…
We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents…
The paper considers the suboptimal H-infinity control problem for a general discrete-time system (whose transfer function matrix is allowed to be improper or polynomial). The parametrization of output feedback controllers is given in a…
The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…
This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate…
We study inhomogeneous non-strictly hyperbolic systems of two equations, which are a formal generalization of the transformed one-dimensional Euler-Poisson equations. For such systems, a complete classification of the behavior of the…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout…
We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…
We consider partial differential equations on networks with a small parameter $\epsilon$, which are hyperbolic for $\epsilon>0$ and parabolic for $\epsilon=0$. With a combination of an $\epsilon$-expansion and Runge-Kutta schemes for…
In this paper a method of controlling nonholonomic systems within the port-Hamiltonian (pH) framework is presented. It is well known that nonholonomic systems can be represented as pH systems without Lagrange multipliers by considering a…
We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions…
The goal of this thesis is to provide efficient and provably convergent numerical methods for solving partial differential equations (PDEs) coming from impulse control problems motivated by finance. Impulses, which are controlled jumps in a…
Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…