# dynamicsClosedLoopExactMeasErr

system dynamics for the closed-loop system controlled with the exact control law

## Contents

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

## Syntax

f = dynamicsClosedLoopExactMeasErr(t,x,u,p,nx,dynamics)

## Description

This function implements the closed loop system dynamics for the case that the system is controlled by the nonlinear exact control law. Thereby, the original system dynamics of the benchmark models are extended by auxiliary states that store the linear part of the exact control law and that keep the control input constant during one time step. Further, the control input computed with the exact control law and insterted in the open-loop system dynamic of the benchmark modlel, which yields the equations for the closed-loop system.

## Input Arguments

x | system states x (dimension: [nx,1])
u | disturbances = input to the closed loop controlled system (dimension: [nx,1])
p | parameter vector. Contains the optimal control inputs for all vertices of the parallelotope (dimension: [nu*(2^nx),1])
nx | number of system states
dynamics | function handle to the function implementing the open-loop dynamics of the system

## Output Arguments

f | value of the dynamic funcion = time derivative of x

## See Also

`convexInterpolationControl`, dynamcisClosedLoopLinear

## References

- [1] Schuermann et al. (2017), Convex interpolation control with formal guarantees for disturbed and constrained nonlinear systems

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