op_mc.cpp

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/** @file op_mc.cpp 
 
Method to verify mutual controllability for two given generators.
A definition of mutual controllability is given in 
S.-H. Lee and K. C. Wong, “Structural decentralised control of concurrent
DES,” European Journal of Control, vol. 35, pp. 1125-1134,2002.
*/
 
/* FAU Discrete Event Systems Library (libfaudes)
 
   Copyright (C) 2006  Bernd Opitz
   Exclusive copyright is granted to Klaus Schmidt
 
   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.
 
   This library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.
 
   You should have received a copy of the GNU Lesser General Public
   License along with this library; if not, write to the Free Software
   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA */
 
#include "op_mc.h"
 
namespace faudes {
 
bool IsMutuallyControllable(const System& rGen1, const System& rGen2) {
  OP_DF("IsMutuallyControllable(" << rGen1.Name() << ", "
      << rGen2.Name() << ")");
  // helpers:
  StateSet forbidden1;
  StateSet forbidden2;
  // Tha algorithm is implemented by the following function
  return IsMutuallyControllable(rGen1, rGen2, forbidden1, forbidden2);
}
 
 
bool IsMutuallyControllable(const System& rGen1, const System& rGen2,
    StateSet& rForbidden1, StateSet& rForbidden2) {
  OP_DF("IsMutuallyControllable(" << rGen1.Name() << ", "
      << rGen2.Name() << ", rForbidden1, rForbidden2)");
  // algorithm:
  // Compute the intersection of the generator alphabets
  const EventSet alph12 = rGen1.Alphabet() * rGen2.Alphabet();
  OP_DF("IsMutuallyControllable: shared events \"" << alph12.ToString() 
      << "\"");
  // check for shared events: if there are no shared events, mutual controllability is fulfilled anyway.
  if (alph12.Empty()) {
    OP_DF("IsMutuallyControllable: shared alphabet empty. "
        << "terminating successful");
    return true;
  }
  // check for shared uncontrollable events
  const EventSet ualph12 = rGen1.UncontrollableEvents() * rGen2.UncontrollableEvents();
  OP_DF("IsMutuallyControllable: shared uncontrollable events \""
      << ualph12.ToString() << "\"");
  // if there are no shared uncontrollable events, mutual controllability is fulfilled anyway.
  if (ualph12.Empty()) {
    OP_DF("IsMutuallyControllable: shared uncontrollable alphabet empty "
        << "terminating successful");
    return true;
  }
  // prepare results
  bool result1;
  bool result2;
  rForbidden1.Clear();
  rForbidden2.Clear();
  // The generator g will serve as the plant in the subsequent controllability evaluation
  System g = rGen1.NewCGen();
  // "plant": (P_21)^-1( P_12( L(G_2) )) is the language generated by g
  aProject(rGen2, alph12, g);
  InvProject(g, rGen1.Alphabet());
  // The set of controllable events for the controllability test is alphabet of rGen1 - the shared uncontrollable events
  // mutual controllability test of rGen2 w.r.t. rGen1.
  result1 = IsControllable(g,  (rGen1.Alphabet() - ualph12), rGen1, rForbidden1);
  // print uncontrollable states if result is negative
  if (result1 == false) {
    OP_DF("IsMutuallyControllable(" << rGen1.Name() << ", " << rGen2.Name() 
        << "): uncontrollable states: " << rForbidden1.ToString());
  }
  // "plant": (P_12)^-1( P_21( L(G_1) )) is the language generated by g
  aProject(rGen1, alph12, g);
  InvProject(g, rGen2.Alphabet());
  // The set of controllable events for the controllability test is alphabet of rGen2 - the shared uncontrollable events
  // mutual controllability test of rGen1 w.r.t. rGen2.
  result2 = IsControllable(g, (rGen2.Alphabet() - ualph12), rGen2, rForbidden2);
  // print uncontrollable states if result is negative
  if (result2 == false) {
    OP_DF("IsMutuallyControllable(" << rGen1.Name() << ", " << rGen2.Name() 
        << "): uncontrollable states: " << rForbidden2.ToString());
  }
  
  if (result1 && result2) {
    OP_DF("IsMutuallyControllable: fulfilled");
  }
  else {
    OP_DF("IsMutuallyControllable: failed");
  }
 
  return (result1 && result2);
}
 
// RTI wrapper
void IsMutuallyControllable(const System& rGen1, const System& rGen2, bool& rRes) {
  rRes=IsMutuallyControllable(rGen1, rGen2);
}
 
} // namespace faudes