# computeAbstrErrDim

identifies the states of the dynamical system that contribute to its Lagrange remainder

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See Also
- References

## Syntax

remStates = computeAbstrErrDim(opts)

## Description

By evaluating the Lagrange remainder for the (augmented) set of admissible states and computing the gradient, the states that contribute to the Lagrange remainder are identified. The Lagrange remainder is evaluated or, more precisely, over-approximated using the approach in [2, Sec. 5].

## Input Arguments

opts | a structure containing the algorithm settings
.X | set of admissible states (class: interval)
.U | set of admissible control inputs (class: interval)
.W | set of disturbances (class: interval)
.xEq | equilibrium point for the terminal region
.uEq | control input for the equilirium point
.nx | dimension of state space (class: bouble)
.sys.nlSys | object of class nonlinearSys

## Output Arguments

remStates | array of indices of the states contributing to the Lagrange remainder

## See Also

`terminalRegion`, `termRegNonlinSysLinApproach`

## References

[1] L. Schäfer et al. "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", 2023, IEEE Transactions on Automatic Control [2] M. Althoff et al. "Reachability Analysis of Nonlinear Systems with Uncertain Parameters using Conservative Linearization", 2008 47th IEEE Conference on Decision and Control, 2008, pp. 4042-4048

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