combinedControl

Implementation of the combined controller

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

[objContr,res] = combinedControl(benchmark,Param,Opts)

Description

Offline-phase computations for the controller that combines initial state dependent feed-forward part with a feedback controller.

Input Arguments

benchmark

name of the considered benchmark model (see; "aroc/benchmarks/dynamics/...")

Param

a structure containing the benchmark parameters

.R0

initial set of states (class: interval)

.xf

goal state

.tFinal

final time after which the goal state should be reached

.U

set of admissible control inputs (class:; interval)

.W

set of uncertain disturbances (class: interval)

.V

set of measurement errors (class: interval or; zonotope)

.X

set of state constraints (class: mptPolytope)

Opts

a structure containing the algorithm settings

.N

number of time steps [{10} / positive integer]

.feedForward

type of feed-forward controller used [{'genSpace'} / 'poly']

.reachSteps

number of reachability steps in one time step [{10} / positive integer]

.reachStepsFin

number of reachability steps during one time step (final reachable set computation) [{50} / positive integer]

.scale

scaling factor for the tightend input constraints [{0.9} / scalar between 0 and 1]

.Q

state weighting matrix for the cost function of the optimal control problem [{eye(nx)} / pos.-definite square matrix]

.R

input weighting matrix for the cost function of the optimal control problem [{zeros(nu)} / pos.-definite square matrix]

.Qff

state weighting matrix for feed-forward control [{eye(nx)} / pos.-definite square matrix]

.Rff

input weighting matrix for feed-forward control [{zeros(nu)} / pos.-definite square matrix]

.finStateCon

use constraint that the final reachable set is inside the shifted initial set [{false} / boolean]

.maxIter

maximum number of iterations for optimization with fmincon [{5} / positive integer]

.bound

scaling factor between upper and lower bound of the weigthing matrices [{1000} / positive scalar]

.refTraj.Q

state weighting matrix for the cost function of optimal control problem (dimension:[nx,nx])

.refTraj.R

input weighting matrix for the cost function of optimal control problem (dimension:[nu,nu])

.refTraj.x

user provided reference trajectory (dimension: [nx,Opts.N + 1])

-.refTraj.u inputs for the user provided reference trajectory (dimension: [nu,Opts.N])

.cora.alg

reachability algorithm that is used [{'lin'} / 'poly']

.cora.tensorOrder

taylor order for the abstraction of the nonlinear function [{2}/ 3]

.cora.taylorTerms

taylor order for computing e^At [{20} / positive integer]

.cora.zonotopeOrder

upper bound for the zonotope order [{30} / positive integer]

.cora.errorOrder

upper bound for the zonotope order before comp. the abstraction error [{5} / positive integer]

.cora.intermediateOrder

upper bound for the zonotope order during internal computations [{20} / positive integer]

Output Arguments

objContr

resulting controller storing the data computed during the offline phase (class: objCombinedContr)

res

results object storing the computed reachable set and the center trajectory

References

[1] Schuermann et al. (2020)*, Optimizing Sets of Solutions for Controlling Constrained Nonlinear Systems
[2] Gassmann et al. (2021)*, Verified Polynomial Controller Synthesis for Disturbed, Nonlinear Systems

objContr	resulting controller storing the data computed during the offline phase (class: objCombinedContr)
res	results object storing the computed reachable set and the center trajectory