相关论文: Computing the Kalman form
This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only…
This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one is based on Krylov iterates and Gaussian…
The Kalman decomposition for Linear Quantum Stochastic Systems in the real quadrature operator representation, that was derived indirectly in [1] by the authors, is derived here directly, using the "one-sided symplectic" SVD-like…
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to…
We consider the problem of learning a linear control policy for a linear dynamical system, from demonstrations of an expert regulating the system. The standard approach to this problem is policy fitting, which fits a linear policy by…
The Kalman filter and its extensions are used in a vast number of aerospace and navigation applications for nonlinear state estimation of time series. In the literature, different approaches have been proposed to exploit the structure of…
We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are…
We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.
Linear time-invariant control systems can be considered as finitely generated modules over the commutative principal ideal ring $\mathbb{R}[\frac{d}{dt}]$ of linear differential operators with respect to the time derivative. The Kalman…
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system with quadratic cost function, we study polynomial systems…
An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant…
We describe a provably quasi-polynomial algorithm to compute discrete logarithms in the multiplicative groups of finite fields of small characteristic, that is finite fields whose characteristic is logarithmic in the order. We partially…
There is a growing interest in using Kalman-filter models in brain modelling. In turn, it is of considerable importance to make Kalman-filters amenable for reinforcement learning. In the usual formulation of optimal control it is computed…
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…
We present normal forms for elliptic curves over a field of characteristic $2$ analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient…
In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
Let $k$ be a finite field, and $L$ be a $q$-linearized polynomial defined over $k$ of $q$-degree $r$ ($L=\sum^r_{i=0}a_iZ^{q^i}$, with $a_i\in k$). This paper provides an algorithm to compute a characteristic polynomial of $L$ over a large…
Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…
Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and…
Two central problems in modern control theory are the controller design problem: which deals with designing a control law for the dynamical system, and the state estimation problem (observer design problem): which deals with computing an…