1,249 research outputs found
Some numerical challenges in control theory
We discuss a number of novel issues in the interdisciplinary area of numerical linear algebra and control theory. Although we do not claim to be exhaustive we give a number of problems which we believe will play an important role in the near future. These are: sparse matrices, structured matrices, novel matrix decompositions and numerical shortcuts. Each of those is presented in relation to a particular (class of) control problems. These are respectively: large scale control systems, polynomial system models, control of periodic systems, and normalized coprime factorizations in robust control
Spacecraft magnetic attitude control using approximating sequence Riccati equations
This paper presents the results of a spacecraft attitude control system based on magnetic actuators designed for low Earth orbits. The control system is designed by using a nonlinear control technique based on the approximating sequence of Riccati equations. The behavior of the satellite is discussed under perturbations and model uncertainties. Simulation results are presented when the control system is able to guide the spacecraft to the desired attitude in a variety of different conditions
Experimentally validated continuous-time repetitive control of non-minimum phase plants with a prescribed degree of stability
This paper considers the application of continuous-time repetitive control to non-minimum phase plants in a continuous-time model predictive control setting. In particular, it is shown how some critical performance problems associated with repetitive control of such plants can be avoided by use of predictive control with a prescribed degree of stability. The results developed are first illustrated by simulation studies and then through experimental tests on a non-minimum phase electro-mechanical system
The Magnus expansion and some of its applications
Approximate resolution of linear systems of differential equations with
varying coefficients is a recurrent problem shared by a number of scientific
and engineering areas, ranging from Quantum Mechanics to Control Theory. When
formulated in operator or matrix form, the Magnus expansion furnishes an
elegant setting to built up approximate exponential representations of the
solution of the system. It provides a power series expansion for the
corresponding exponent and is sometimes referred to as Time-Dependent
Exponential Perturbation Theory. Every Magnus approximant corresponds in
Perturbation Theory to a partial re-summation of infinite terms with the
important additional property of preserving at any order certain symmetries of
the exact solution. The goal of this review is threefold. First, to collect a
number of developments scattered through half a century of scientific
literature on Magnus expansion. They concern the methods for the generation of
terms in the expansion, estimates of the radius of convergence of the series,
generalizations and related non-perturbative expansions. Second, to provide a
bridge with its implementation as generator of especial purpose numerical
integration methods, a field of intense activity during the last decade. Third,
to illustrate with examples the kind of results one can expect from Magnus
expansion in comparison with those from both perturbative schemes and standard
numerical integrators. We buttress this issue with a revision of the wide range
of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its
applications to several physical problem
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
Iterative and doubling algorithms for Riccati-type matrix equations: a comparative introduction
We review a family of algorithms for Lyapunov- and Riccati-type equations
which are all related to each other by the idea of \emph{doubling}: they
construct the iterate of another naturally-arising fixed-point
iteration via a sort of repeated squaring.
The equations we consider are Stein equations , Lyapunov
equations , discrete-time algebraic Riccati equations
, continuous-time algebraic Riccati equations
, palindromic quadratic matrix equations , and
nonlinear matrix equations . We draw comparisons among these
algorithms, highlight the connections between them and to other algorithms such
as subspace iteration, and discuss open issues in their theory.Comment: Review article for GAMM Mitteilunge
- …