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Max-Plus Algebra >> Max-Plus Algebra > maxpluslinsol

maxpluslinsol

max-plus algebra greatest solution to A⊗x ≤b in ℝnmax

Calling Sequence

[x] = maxpluslinsol(A,b)

Parameters

A
: is a matrix of size m times n with a i,j ∊ ℝ max
b
: is a vector in ℝ m
x
: is an output vector in ℝ n max

Description

Function return to x = x*(A,b) (it is principle solution) which is a greatest solution to the max-plus inequality A⊗x ≤ b .

For details see: B. Heidergott, G.J. Olsder and J.W. van der Woude, "Max Plus at work, Modelling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Application", Princeton University Press. (2006).

Examples

A=[-%inf    3.  -%inf  -%inf;  
     2.   -%inf    6.  -%inf;  
   -%inf    7.     8.     9.;  
   -%inf  -%inf  -%inf    1.;  
     8.   -%inf    7.  -%inf;  
     0.   -%inf  -%inf    6.;];
b=[1;2;5;-6;4;-1];  
x=maxpluslinsol(A,b)
x  =

- 4.  
- 2.  
- 4.  
- 7.  
// check !

maxplusotimes(A,x) <= b
ans  =

  T  
  T  
  T  
  T  
  T  
  T  
// Indeed x is the solution of Ax=b
isequal(maxplusotimes(A,x),b)
ans  =

T

Author

Copyright (C) Subiono, "Max-Plus Algebra Toolbox", ver. 1.01, April, 2009

See Also


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