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Title: mpc_buildmatFAST.m
Version: 2.0
Project: Control of MLD systems
Sub-Project: Constrained Finite Time Optimal Control (CFTOC) of MLD systems
Purpose: Formulate multi-parametric (mixed integer) program
equivalent to the CFTOC problem of MLD system
Author: (C) Mato Baotic, Zurich, March 17, 2003
(C) Michal Kvasnica, Zurich, June 23, 2005
History: date subject
2003.11.19 first public release
2003.07.29 fast implementation (static allocation of memory space)
Tobias Geyer = Version 1.2
2003.03.18 Various bugs fixed
= Version 1.1
2003.03.17 Initial Version
= Version 1.0
Description: Given: horizon
SYSTEM,
WEIGHT,
x1, u1, d1, z1, y1,
eps2, xtt, Options
Returns: S1, S2, S3, F1, F2, F3, c1, c2, c3, IntIndex
The optimization for the control problem is formulated as:
min v' S1 v + 2(S2 + x0' S3) v
s.t. F1 v <= F2 + F3 x0
Here we denote:
horizon - vector of time segments (steps) through which
specific SYSTEM is used in state update equation.
NT - prediction horizon [1, inf), NT=sum(horizon)
SYSTEM - cell structure with MLD system descriptions:
A, B1, B2, B3, B5, C, D1, D2, D3, D5, E1, E2, E3, E4, E5
Note: if input is not cell structure (but just a structure)
then we have a time invariant system
WEIGHT - cell structure with weights on u, d, z, x, y:
Qu, Qd, Qz, Qx, Qy
IntIndex - indices of integer variables in optimizer vector v
v = [ U',D',Z',EU',ED',EZ',EX',EY']'
U = [ u'(0), ... , u'(T-1)]'
D = [ d'(0), ... , d'(T-1)]'
Z = [ z'(0), ... , z'(T-1)]'
EU = [ epsu'(0), ... , epsu'(T-1)]'
ED = [ epsd'(0), ... , epsd'(T-1)]'
EZ = [ epsz'(0), ... , epsz'(T-1)]'
EX = [ epsx'(0), ... , epsx'(T-1)]'
EY = [ epsy'(0), ... , epsy'(T-1)]
The steady state values are: x1, d1, u1, z1, y1. These variables
can also be time-varying trajectories.
If the steady state values have not the length n_*NT (n_ is the
corresponding number of components), then the last value of the
steady state vector is repeated.
The terminal state is given by xtt
c1,c2,c3: parameters for the constant term of the optimization
the complete constant term is obtained as:
Jc = 0.5*x(0)'*c1*x(0) + c2*x(0) + c3
It is assumed, that the prediction horizon and the control
horizon are the same
Contact: Mato Baotic
Automatic Control Laboratory
ETH Zentrum,
Zurich, Switzerland
baotic@control.ee.ethz.ch
Comments and bug reports are highly appreciated