Related papers: Flows of vector fields and the Kalman Theorem
Kalman's fundamental notion of a controllable state space system \cite{k} has been generalised to higher order systems by Willems \cite{w}, and further to distributed systems defined by partial differential equations \cite{ps}. It turns…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined…
This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations.…
The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper…
Recently, Kvalheim and Sontag provided a generalized global Hartman-Grobman theorem for equilibria under asymptotically stable continuous vector fields. By leveraging topological properties of Lyapunov functions, their theorem works without…
We consider affine control systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions of local controllability around this equilibrium, involving the iterated Lie…
We give necessary and sufficient conditions for the existence of smooth Lyapunov 1-forms for the flow of a smooth vector field in terms of the behavior of certain locally finite invariant measures. The main statement generalizes a result of…
Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade's theorem is determined. The results are illustrated by an…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
The contraction properties of the Extended Kalman Filter, viewed as a deterministic observer for nonlinear systems, are analyzed. This yields new conditions under which exponential convergence of the state error can be guaranteed. As…
In this paper, we study small-time local controllability of real analytic control-affine systems under small perturbations of their vector fields. Consider a real analytic control system $\mathcal{X}$ which is small-time locally…
We develop an epsilon-controlled algebraic L-theory, extending our earlier work on epsilon-controlled algebraic K-theory. The controlled L-theory is very close to being a generalized homology theory; we study analogues of the homology exact…
A new Small-Gain Theorem is presented for general nonlinear control systems. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…