Related papers: Computing the Kalman form
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
In this paper we provide direct data-driven expressions for the Linear Quadratic Regulator (LQR), the Kalman filter, and the Linear Quadratic Gaussian (LQG) controller using a finite dataset of noisy input, state, and output trajectories.…
We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be…
Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
The maximum likelihood estimates of an ARMA model can be obtained by the Kalman filter based on the state-space representation of the model. This paper presents an algorithm for computing gradient of the log-likelihood by an extending the…
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…
We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
This paper concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least…