# paramReach

parameterized reachability analysis

## Contents

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

## Syntax

[R_next,mapsReduce] = paramReach(obj,dynamics,candTermReg,ctrl_template,candP,bloatAbsErr,flagReduceFeasible)

## Description

This function computes the time-point reachable set in [1, Eq. (17)]. This involves computing reachable sets of the abstraction using the polynomialization algorithm, computation of the abstraction error, and the parameterized order reduction to limit the number of variables and constraints in [1, Eq. (19)].

## Input Arguments

obj | instance of class computeTermRegNonlinSysPolyApproach
dynamics | instance of class termRegNonlinSysDynamics
candTermReg | candidate terminal region (class: polyZonotope)
ctrl_template | controller template (class: polyZonotope)
candP | candidate controller prarameters (double array of dimension; [length(obj.id.p),1])
bloatAbsErr | scaling factor for enlarging the set of abstraction errors (see the verification; procedure described in [2, Sec. III 2]) (bloatAbsErr >= 1)
flagReduceFeasible | true if the currenct candidate solution is feasible, triggers adaptive order reduction, see method reduceTemplate

## Output Arguments

Rfin | parameterized reachable set (class: polyZonotope)
mapsReduce | struct storing the ingredients for the parameterized order reduction, see method reduceTemplate

## See Also

@computeTermRegNonlinSysPolyApproach/reduceTemplate

## References

[1] L. Schäfer and M. Althoff, "Computing Robust Control Invariant Sets of Nonlinear Systems Using Polynomial Controller Synthesis," American Control Conference, 2024, pp. 4162-4169.

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