Related papers: Discrete-Time Approximations of Fliess Operators
The paper develops a method for model reduction of bilinear control systems. It leans upon the observation that the input-output map of a bilinear system has a particularly simple Fliess series expansion. Subsequently, a model reduction…
We show that an interesting class of functionals of stochastic differential equations can be approximated by a Chen-Fliess series of iterated stochastic integrals and give a L^{2} error estimate, thus generalizing the standard stochastic…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
A learning control system is presented suitable for control affine nonlinear plants based on discrete-time Chen-Fliess series and capable of incorporating knowledge of a given physical model. The underlying noncommutative algebraic and…
A class of parameter dependent Chen--Fliess series is introduced where the series coefficients are taken from a noncommutative ring of multivariable differential operators. Such series are shown in the linear case to represent formal…
We show how continuous-depth neural ODE models can be framed as single-layer, infinite-width nets using the Chen--Fliess series expansion for nonlinear ODEs. In this net, the output ``weights'' are taken from the signature of the control…
We present a novel technique to drive a nonlinear system to reach a target state under input constraints. The proposed controller consists only of piecewise constant inputs, generated from a simple linear driftless approximation to the…
The goal of this paper is to provide exact and terminating algorithms for the formal analysis of deterministic continuous-time control systems with affine input and polynomial state dynamics (in short, polynomial systems). We consider the…
This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
This paper provides a dendriform-tree setting for Fliess operators with matrix-valued inputs. This class of analytic nonlinear input-output systems is convenient, for example, in quantum control. In particular, a description of such Fliess…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
Model continuity plays an important role in applications like system identification, adaptive control, and machine learning. This paper provides sufficient conditions under which input-output systems represented by locally convergent…
There are many notions of symmetry for state space models. They play a role in understanding when systems are time reversible, provide a system theoretic interpretation of thermodynamics, and have applications in certain stabilization and…
The goal of the paper is two-fold. The first of which is to derive an explicit formula to compute the generating series of a closed-loop system when a plant, given in a Chen-Fliess series description is in multiplicative output feedback…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…