computeAlpha

compute the control law for generator space control

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

alpha = computeAlpha(R0,A,B,c,xf,iter,Opts)

Description

Computes the control law for one time step by solving an optimal control problem in a set based manner for the control algorithm that is based on optimal control in generator space (see Eq. (12) and (13) in [1]).

Input Arguments

R0

initial set of states (class: zonotope)

A

cell-array storing the system matrices of the linearized discrete time system

B

cell-array storing the input matrices of the linearized discrete time system

c

cell-array storing the constant offsets of the linearized discrete time system

xf

cell-array storing the goal states for all time steps

iter

current time step

Opts

a structure containing the algorithm settings

.U

set of admissible control inputs

.N

number of time steps

.Ninter

number of intermediate time steps

.nx

number of states

.nu

number of inputs

.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']

Output Arguments

alpha

computed control law parameters alpha

References

[1] Schuermann et al. (2017), Guaranteeing constraints of disturbed nonlinear systems using set-based optimal control in generator space