An integral quadratic constraint approach to the robust performance estimation problem of guidance loops
conference paper
The problem of evaluating the performance of an uncertain guidance loop system is considered, when the uncertainty is described in terms of an integral quadratic constraint. The idea of the approach proposed in this paper is to determine the set of all possible state vector values at the end of the flight that are compatible with the model uncertainty and determine the upper and lower bound for the miss distance by solving two optimization problems on this set. The main theoretical result of the paper shows that this is a quadric that can be determined by the solving a differential Riccati equation and a set of coupled linear differential equations. Unfortunately, numerical experiments showed that the method is practically unusable for realistic models of guidance loops. A single integral quadratic constraint is a poor representation of the usual model uncertainties, meaning that the results are certainly too conservative. In addition, the optimization problem turns out to be badly conditioned in all cases of interest for homing guidance loop analysis. This is illustrated using a contrived numerical example based on a relatively well-behaved linear time-invariant system. Although in its present form, the approach taken in this paper did not achieve the results that were hoped for, the ideas advanced here, and some of the technical results are interesting in themselves and may be useful in future research on this theme.
Topics
Aerospace engineeringNumerical methodsOptimizationRiccati equationsUncertainty analysisDifferential Riccati equationIntegral quadratic constraint approachesIntegral quadratic constraintsLinear differential equationLinear time invariant systemsNumerical experimentsOptimization problemsUpper and lower boundsProblem solving
TNO Identifier
242953
ISBN
9781617380839
Source title
Israel Annual Conference on Aerospace Sciences, 17-18 February 2010
Collation
11 p.
Pages
32-42
Files
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