optimalControlReachsetMPC

solve an optimal control problem

Contents

Syntax

[param,res] = optimalControlReachsetMPC(x0,J,L,Opts)

Description

This function solves the optimal control problem as defined in Eq. (7) in [1] to determine a feasible reference trajectory.

Input Arguments

x0

initial state of the considered reference trajectory part (dimension: [nx,1])

L

value of the objective function (=cost) of the previous solution

J

summed distance of the points from the previous solution to the terminal region

Opts

a structure containing following options

.funHandle

function handle to the dynamic function

.nx

number of system states

.nu

number of system inputs

.uMax

upper bound for the input constraints

.uMin

lower bound for the input constraints

.xf

goal state

.N

number of time steps for the prediction horizon. Prediction horizon: Opts.N * Opts.dT [{10} / positive integer]

.dT

time step. Prediction horizon: Opts.N * Opts.dT

.Q

state weighting matrix for the cost function (center trajectory)

.R

input weighting matrix for the cost function (center trajectory)

.termReg

terminal region around the steady state xf (class: mptPolytope)

.alpha

contraction rate for the contraction constraint [{0.1} / alpha > 0]

.maxIter

maximum number of iterations for the optimal control problem [{10} / positive integer]

Output Arguments

param

a structure containing following options

.xc

reference trajectory (dimension: [nx,N+1])

.uc

reference trajectory control inputs (dimension: [nu,N])

.J

summed distance of the reference trajectory points from the terminal region

.L

value of the objective function (=cost) of the reference trajectory

res

flag that specifies if the computed reference trajectory is feasible (0 or 1)

See Also

optimalControl, reachsetMPC

References


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