polynomialControl

Implementation of polynomial controller synthesis

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

[objContr,res] = polynomialControl(benchmark,Param,Opts)
[objContr,res] = polynomialControl(benchmark,Param,Opts,Post)

Description

Offline-phase computations for the polynomial controller synthesis algorithm.

Input Arguments

benchmark

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

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]

.Ninter

number of intermediate timesteps between two center trajectory timesteps [{4} / positive integer]

.ctrlOrder

polynomial order for the controller [{2} / positive integer]

.reachSteps

number of reachability steps during one time step (optimization) [{10} / positive integer]

.reachStepsFin

number of reachability steps during one time step (final reachable set computation) [{20} / positive integer]

.Q

state weighting matrix for the cost function of the optimization problem

.splits

number of recursive splits used to refine the bounds for the control parameters [{0} / positive integer]

.refInput

use the input from the reference trajectory as input for the center instead of optimizing [{true} / boolean]

.refUpdate

update the reference trajectory after each time step [{false} / boolean]

.extHorizon.active

use extended optimization horizon for optimal control problems [{false} / true]

.extHorizon.horizon

length of the extended optimization horizon in center trajectory time steps [{'all'} / positive integer]

.extHorizon.decay

decay function for the objective function of the optimization problem with extended optimization horizon [{'fall+End'} / 'uniform' / 'fall' /; 'fallLinear' / 'fallLinear+End' /; 'fallEqDiff' / 'FallEqDiff+End' /; 'rise' / 'quad' / 'riseLinear' /; 'riseEqDiff' / 'end']

.refTraj.Q

state weighting matrix for the cost function of the optimal control problem

.refTraj.R

input weighting matrix for the cost function of the optimal control problem

.refTraj.x

user provided reference trajectory (dimension: [nx,N*Ninter + 1])

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

Post

function handle to the postprocessing function that is used to compute the occupancy set

Output Arguments

objContr

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

res

results object storing the computed reachable set and the center trajectory

References

[1] Gassman et al. (2021), Verified Polynomial Controller Synthesis for Disturbed Nonlinear Systems

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