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The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
We introduce and test a general machine-learning-based technique for the inference of short term causal dependence between state variables of an unknown dynamical system from time series measurements of its state variables. Our technique…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics…
Reinforcement learning is a promising approach to learning robotics controllers. It has recently been shown that algorithms based on finite-difference estimates of the policy gradient are competitive with algorithms based on the policy…
By using the quasi-determinant the construction of Gel'fand et al. leads to the inverse of a matrix with noncommuting entries. In this work we offer a new method that is more suitable for physical purposes and motivated by deformation…
We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…
An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…
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…
This paper deals with reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and…
Model order reduction aims to determine a low-order approximation of high-order models with least possible approximation errors. For application to physical systems, it is crucial that the reduced order model (ROM) is robust to any…
The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback…
If embedded with command filter properly, the implementation of backstepping design could be dramatically simplified. In this paper, we introduce a command filter with time-varying gain and integrate it with backstepping design, resulting…
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory…