Related papers: Geometric analysis of differential-algebraic equat…
The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
In this paper we derive necessary optimality conditions for optimal control problems with nonlinear and nonsmooth implicit control systems. Implicit control systems have wide applications including differential algebraic equations (DAEs).…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
The paper continues the authors' study of the linearizability problem for nonlinear control systems. In the recent work [K. Sklyar, Systems Control Lett. 134 (2019), 104572], conditions on mappability of a nonlinear control system to a…
Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…
We investigate an ultraweak variational formulation for (parameterized) linear differential-algebraic equations (DAEs) w.r.t. the time variable which yields an optimally stable system. This is used within a Petrov-Galerkin method to derive…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…
In this paper, we tackle the long-standing challenges of ensemble control analysis and design using a convex-geometric approach in a Hilbert space setting. Specifically, we formulate the control of linear ensemble systems as a convex…
This paper is devoted to a study of linear, differential and topological classifications for linear controlled systems governed by ordinary differential equations. The necessary and sufficient conditions for the linear and topological…
In this thesis, we provide new insights into the theory of cascade feedback linearization of control systems. In particular, we present a new explicit class of cascade feedback linearizable control systems, as well as a new obstruction to…
This paper investigates a new class of homogeneous stochastic control problems with cone control constraints, extending the classical homogeneous stochastic linear-quadratic (LQ) framework to encompass nonlinear system dynamics and…
We investigate the interplay between monomial first integrals, polynomial invariants of certain group action, and the Poincar\'{e}-Dulac normal forms for autonomous systems of ODEs with diagonal matrix of the linear part. Using tools from…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
Optimal decentralized controller design is notoriously difficult, but recent research has identified large subclasses of such problems that may be convexified and thus are amenable to solution via efficient numerical methods. One recently…
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 the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely…
We consider a class of differential-algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the…