Numerical solution of a drug displacement problem with bounded state variables

This work proposes a deterministic robust controller to improve tracking performance for a linear motor, taking into account the electrical dynamics imposed by a commercial current controller. The design is split in two parts by means of the backstepping technique, in which the first part corresponds to a typical deterministic robust controller, neglecting the electrical dynamics. In the second part, a second-order electrical dynamics is considered using a particular state transformation. There, the proposed control law is composed of a term to compensate the known part of the model and a robust control term to impose a bound on the effect of uncertainties on tracking error. Stability and boundedness results for the complete controller are given. To this effect, a general result on boundedness and stability of nonlinear systems with conditionally bounded state variables is derived first. Finally, experimental results for the complete controller show an improvement on tracking error of up to 31.7% when compared with the results from the typical controller that neglects the electrical dynamics.

Download Full-text

A Marginal Adjustment Rank Histogram Filter for Non-Gaussian Ensemble Data Assimilation

Monthly Weather Review ◽

10.1175/mwr-d-19-0307.1 ◽

2020 ◽

Author(s):

Jeffrey L. Anderson

Keyword(s):

Ensemble Kalman Filter ◽

Ensemble Methods ◽

State Variables ◽

Histogram Method ◽

Prior Distributions ◽

Bounded State ◽

Rank Histogram ◽

Non Gaussian ◽

Atmospheric Tracer ◽

Filter Algorithms

An extension to standard ensemble Kalman filter algorithms that can improve performance for non-Gaussian prior distributions, non-Gaussian likelihoods, and bounded state variables is described. The algorithm exploits the capability of the rank histogram filter (RHF) to represent arbitrary prior distributions for observed variables. The rank histogram algorithm can be applied directly to state variables to produce posterior marginal ensembles without the need for regression that is part of standard ensemble filters. These marginals are used to adjust the marginals obtained from a standard ensemble filter that uses regression to update state variables. The final posterior ensemble is obtained by doing an ordered replacement of the posterior marginal ensemble values from a standard ensemble filter with the values obtained from the rank histogram method applied directly to state variables; the algorithm is referred to as the Marginal Adjustment Rank Histogram Filter (MARHF). Applications to idealized bivariate problems and low-order dynamical systems show that the MARHF can produce better results than standard ensemble methods for priors that are non-Gaussian. Like the original RHF, the MARHF can also make use of arbitrary non-Gaussian observation likelihoods. The MARHF also has advantages for problems with bounded state variables, for instance the concentration of an atmospheric tracer. Bounds can be automatically respected in the posterior ensembles. With an efficient implementation of the MARHF, the additional cost has better scaling than the standard RHF.

Download Full-text

Asymptotic stability criteria for delay-differential equations

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500024835 ◽

1988 ◽

Vol 110 (1-2) ◽

pp. 31-44

Author(s):

L.C. Becker ◽

T.A. Burton

Keyword(s):

Differential Equations ◽

Direct Method ◽

Infinite Delay ◽

Functional Differential Equations ◽

State Variables ◽

Stability Criteria ◽

Bounded State ◽

Functional Differential ◽

Delay Differential ◽

Liapunov's Direct Method

SynopsisThis paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.

Download Full-text