## Contents

- computeTerminalRegionNonlinSys
- Syntax
- Description
- Input Arguments
- Output Arguments
- See also
- References

## computeTerminalRegionNonlinSys

computes a terminal region of nonlinear

    %systems by solving a sequence of optimization problems.%

## Syntax

T = computeTerminalRegionNonlinSys(benchmark,Param,Opts)

## Description

This function implements the iterative optimization-based algorithms for computing the terminal region of nonlinear sampled-data systems proposed in [1], [2], as well as the disrete-time version of the algorithm in [1].

## Input Arguments

benchmark | name of the considered benchmark model (see; "aroc/benchmarks/...")
Param | .X: set of admissible states (class: interval/zonotope/polytope) .U: set of admissible control inputs (class: interval/zonotope/polytope) .W: set of disturbances (class: zonotope)
Opts | .termRegOrder: (optional) order of the zonotope representing the terminal region (positive integer) .xEq: equlibrium state to be stabilized (double vector) .uEq: equilibrium control input (double vector) .dt: sampling time (positive scalar) .nonlinSysTermRegAlg: (`'lin'` / `'poly'`)
.sysType | type of dynamical system, e.g., sampled-data or discrete-time system (class: termRegSysType)
.integrator: (optional) integration scheme for time- discretizing the dynamical system - only considered if sysType == termRegSysType.DT (class: discretizeDynamics) .initialGuess: (optional) structure storing state and control input weighting matrices for computing an initial guess .Q: state weighting matrix (positive-definite matrix of dimension; [Param.X.dim,Param.X.dim]) .R: control input weighting matrix (positive-definite matrix of dimension; [Param.U.dim,Param.U.dim])

## Output Arguments

T | verified solution (class: termRegNonlinSysOpt)

## See also

-

## References

[1] L. Schäfer et al., "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", 2024, IEEE Transactions on Automatic Control, vol. 69, no. 2, pp. 755-770 [2] 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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