DynamicOptimization.mo

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 encapsulated package DynamicOptimization

" file:        DynamicOptimization.mo
  package:     DynamicOptimization
  description: DynamicOptimization contains the function that create dynamic optimization.

"
public import DAE;
public import BackendDAE;
public import BackendDAEOptimize;

protected import BackendDump;
protected import ExpressionDump;

protected import BackendEquation;
protected import BackendDAEUtil;


protected import BackendVariable;
protected import ComponentReference;
protected import Config;

protected import Differentiate;

protected import Expression;
protected import ExpressionSolve;
protected import ExpressionSimplify;
protected import Flags;
protected import List;


public function createDynamicOptimization
 input output BackendDAE.BackendDAE dae;
protected
 BackendDAE.Variables vars;
 BackendDAE.EqSystem syst;
 BackendDAE.EquationArray eqns;
 BackendDAE.Shared shared;
algorithm
  shared := dae.shared;
  {syst} := dae.eqs;
  BackendDAE.EQSYSTEM(orderedVars=vars, orderedEqs=eqns) := syst;
  (vars, eqns, shared) := addOptimizationVarsEqns(vars, eqns, shared);
  syst.orderedVars := vars;
  syst.orderedEqs := eqns;
  dae.eqs := {syst};
  dae.shared := shared;
end createDynamicOptimization;

protected function addOptimizationVarsEqns
"author: Vitalij Ruge
 add objective function and constraints to DAE. Neeed for derivatives"
  input output BackendDAE.Variables vars;
  input output BackendDAE.EquationArray eqns;
  input output BackendDAE.Shared shared;
protected
  Option<DAE.Exp> mayer, lagrange, startTimeE, finalTimeE;
  list<BackendDAE.Var> varlst;
  BackendDAE.Var tG;
  list<BackendDAE.Equation> eqnsLst;

  list< .DAE.ClassAttributes> classAttrs;
  list< .DAE.Constraint> constraints;
  BackendDAE.Variables globalKnownVars;
  Boolean inOptimicaFlag = Config.acceptOptimicaGrammar();
  Boolean inDynOptimization = Flags.getConfigBool(Flags.GENERATE_DYN_OPTIMIZATION_PROBLEM);
  constant Boolean debug = false;
algorithm
   classAttrs := shared.classAttrs;
   constraints := shared.constraints;
   globalKnownVars := shared.globalKnownVars;
   eqnsLst := {};

   if not(inOptimicaFlag or inDynOptimization)
   then
      print("Something going wrong for postOptModul=createDynamicOptimization. Check your flags. You need -g=DynOpt or -g=Optimica!\n");
      fail();
   end if;
   Flags.setConfigEnum(Flags.GRAMMAR, Flags.OPTIMICA);

    //Flags.setConfigString(Flags.INDEX_REDUCTION_METHOD, "dummyDerivatives");

   (mayer,lagrange,startTimeE,finalTimeE) := getOptimicaArgs(classAttrs);
    varlst :=  BackendVariable.varList(globalKnownVars);
    _ := addTimeGrid(varlst, globalKnownVars);
    varlst := listAppend(varlst, BackendVariable.varList(vars));

    (vars, eqnsLst, mayer) := joinObjectFun(makeObject(BackendDAE.optimizationMayerTermName, findMayerTerm, varlst, mayer), vars, eqnsLst);
    (vars, eqnsLst, lagrange) := joinObjectFun(makeObject(BackendDAE.optimizationLagrangeTermName, findLagrangeTerm, varlst, lagrange), vars, eqnsLst);

    (vars, eqnsLst) := joinConstraints(constraints, "$con$", BackendDAE.OPT_CONSTR(), globalKnownVars, varlst, vars, eqnsLst, BackendVariable.hasConTermAnno);
    (vars, eqnsLst) := joinConstraints({}, "$finalCon$", BackendDAE.OPT_FCONSTR(), globalKnownVars, varlst, vars, eqnsLst, BackendVariable.hasFinalConTermAnno);

    // don't work....
    Flags.setConfigBool(Flags.GENERATE_SYMBOLIC_LINEARIZATION, true);

    shared.classAttrs := {DAE.OPTIMIZATION_ATTRS(mayer, lagrange, startTimeE, finalTimeE)};
    if debug then
      print("\neqs");
      BackendDump.printEquationList(eqnsLst);
    end if;
    eqns := BackendEquation.addList(eqnsLst, eqns);

end addOptimizationVarsEqns;

protected function getOptimicaArgs
  input list< .DAE.ClassAttributes> inClassAttr;
  output Option<DAE.Exp> mayer,lagrange,startTimeE,finalTimeE;
algorithm
  (mayer,lagrange,startTimeE,finalTimeE) :=
  match(inClassAttr)
    local Option<DAE.Exp> mayer_, lagrange_, startTimeE_, finalTimeE_;

    case({DAE.OPTIMIZATION_ATTRS(objetiveE=mayer_, objectiveIntegrandE=lagrange_,startTimeE=startTimeE_,finalTimeE=finalTimeE_)})
    then(mayer_,lagrange_,startTimeE_,finalTimeE_);

    else (NONE(), NONE(),NONE(),NONE());
    end match;
end getOptimicaArgs;


protected function addTimeGrid
  input list<BackendDAE.Var> varlst;
  input BackendDAE.Variables iv;
  output BackendDAE.Variables ov = iv;
protected
  list<BackendDAE.Var> tG = findTimeGrid(varlst);
  list<Integer> ind;
algorithm
  if not listEmpty(tG) then
    ind := BackendVariable.getVarIndexFromVars(tG, ov);
    for i in ind loop
      ov := BackendVariable.setVarKindForVar(i, BackendDAE.OPT_TGRID(), ov);
      //BackendDump.printVar(BackendVariable.getVarAt(ov,i));
    end for;
  end if;

end addTimeGrid;

protected function joinConstraints "author: Vitalij Ruge"
  input list< .DAE.Constraint> inConstraint;
  input String name;
  input BackendDAE.VarKind conKind;
  input BackendDAE.Variables globalKnownVars;
  input list<BackendDAE.Var> varlst;
  input BackendDAE.Variables vars;
  input list<BackendDAE.Equation> e;
  input MapFunc findCon;
  output BackendDAE.Variables ovars;
  output list<BackendDAE.Equation> oe;

  partial function MapFunc
    input BackendDAE.Var inVar;
    output Boolean outBoolean;
  end MapFunc;

protected
  list< .DAE.Constraint> constraints;
algorithm
  constraints := addConstraints(varlst, inConstraint, findCon);
  (ovars, oe) := addOptimizationVarsEqns2(constraints, 1, vars, e, globalKnownVars, name, conKind);
end joinConstraints;

protected function joinObjectFun "author: Vitalij Ruge"
  input tuple<BackendDAE.Var, list<BackendDAE.Equation>, Option<DAE.Exp>> obj;
  input BackendDAE.Variables vars;
  input list<BackendDAE.Equation> e;
  output BackendDAE.Variables ovars;
  output list<BackendDAE.Equation> oe;
  output Option<DAE.Exp> objExp;
algorithm
  (ovars, oe, objExp) := match(obj)
                local BackendDAE.Var v; list<BackendDAE.Equation> e_; Option<DAE.Exp> e1;
                case((_,{},_)) then(vars, e, NONE());
                case((v, e_, e1)) then(BackendVariable.addNewVar(v, vars), listAppend(e_, e), e1);
                end match;
end joinObjectFun;

protected function makeObject  "author: Vitalij Ruge"
  input String name;
  input MapFunc findObj;
  input list<BackendDAE.Var> varlst;
  input Option<DAE.Exp> optimicaExp "expression from optimica";
  output  tuple< BackendDAE.Var, list<BackendDAE.Equation>,  Option<DAE.Exp>> outTpl;

  partial function MapFunc
    input list<BackendDAE.Var> varlst;
    output Option<DAE.Exp>  objExp;
  end MapFunc;

protected
  DAE.ComponentRef cr;
  Option<DAE.Exp> annoObj;
  BackendDAE.Var v;
  list<BackendDAE.Equation> e;
algorithm
  (cr, v) := makeVar(name);
  annoObj := findObj(varlst);
  annoObj := mergeObjectVars(annoObj, optimicaExp);
  e := BackendEquation.generateSolvedEqnsfromOption(cr, annoObj, DAE.emptyElementSource, BackendDAE.UNKNOWN_EQUATION_KIND());
  outTpl := (v, e, annoObj);
end makeObject;

protected function makeVar "author: Vitalij Ruge"
  input String name;
  output DAE.ComponentRef cr;
  output BackendDAE.Var v;

algorithm
  cr := ComponentReference.makeCrefIdent(name, DAE.T_REAL_DEFAULT, {});
  v :=  BackendDAE.VAR(cr, BackendDAE.VARIABLE(), DAE.OUTPUT(), DAE.NON_PARALLEL(), DAE.T_REAL_DEFAULT, NONE(), NONE(), {}, DAE.emptyElementSource, NONE(), SOME(BackendDAE.AVOID()), DAE.BCONST(false), NONE(), DAE.NON_CONNECTOR(), DAE.NOT_INNER_OUTER(), false);
end makeVar;

protected function addOptimizationVarsEqns1
 input list<DAE.Exp> constraintLst;
 input Integer inI;
 input BackendDAE.Variables inVars;
 input list<BackendDAE.Equation> inEqns;
 input BackendDAE.Variables globalKnownVars;
 input String prefConCrefName;
 input BackendDAE.VarKind conKind;

 output BackendDAE.Variables outVars = inVars;
 output list<BackendDAE.Equation>  outEqns = inEqns;

protected
 Integer i = inI;
 BackendDAE.Var dummyVar;
 list<BackendDAE.Equation> conEqn;
 String conCrefName;
algorithm

 for elem in constraintLst loop
   try
     conCrefName := prefConCrefName + ComponentReference.crefModelicaStr(Expression.expCref(elem));
   else
     conCrefName := prefConCrefName + intString(i);
     i := i + 1;
   end try;
   (conEqn, dummyVar) := BackendEquation.generateResidualFromRelation(conCrefName, elem, DAE.emptyElementSource, outVars, globalKnownVars, conKind);
   outVars := BackendVariable.addNewVar(dummyVar, outVars);
   outEqns := listAppend(conEqn, outEqns);
 end for;
end addOptimizationVarsEqns1;

protected function addOptimizationVarsEqns2
 input list< .DAE.Constraint> inConstraint;
 input Integer inI;
 input BackendDAE.Variables inVars;
 input list<BackendDAE.Equation> inEqns;
 input BackendDAE.Variables globalKnownVars;
 input String prefConCrefName;
 input BackendDAE.VarKind conKind;

 output BackendDAE.Variables outVars;
 output list<BackendDAE.Equation>  outEqns;
algorithm
  (outVars, outEqns) := match(inConstraint, inI, inVars, inEqns, globalKnownVars,prefConCrefName,conKind)
  local
   list<BackendDAE.Equation> e;
   BackendDAE.Variables v;
   list< .DAE.Exp> constraintLst;
    case({DAE.CONSTRAINT_EXPS(constraintLst = constraintLst)}, _, _, _, _, _, _) equation
      (v, e) = addOptimizationVarsEqns1(constraintLst, inI, inVars, inEqns, globalKnownVars,prefConCrefName,conKind);
      then (v, e);
  else (inVars, inEqns);
  end match;
end addOptimizationVarsEqns2;


protected function findMayerTerm
"author: Vitalij Ruge
find mayer-term from annotation"
input list<BackendDAE.Var> varlst;
output Option<DAE.Exp> mayer = findObjTerm(varlst,BackendVariable.hasMayerTermAnno);
end findMayerTerm;

protected function findLagrangeTerm
"author: Vitalij Ruge
find lagrange-term from annotation"
input list<BackendDAE.Var> varlst;
output Option<DAE.Exp> lagrange = findObjTerm(varlst,BackendVariable.hasLagrangeTermAnno);
end findLagrangeTerm;

protected function findTimeGrid
"author: Vitalij Ruge
find lagrange-term from annotation"
input list<BackendDAE.Var> varlst;
output list<BackendDAE.Var> timeGrids = List.select(varlst, BackendVariable.hasTimeGridAnno);
end findTimeGrid;


protected function findObjTerm
"author: Vitalij Ruge
helper findLagrangeTerm, findMayerTerm"
input list<BackendDAE.Var> InVarlst;
input MapFunc findObjTermFun;
output Option<DAE.Exp> objeExp = NONE();

partial function MapFunc
  input BackendDAE.Var inVar;
  output Boolean outBoolean;
end MapFunc;

protected
DAE.Exp e, nom; DAE.ComponentRef cr;
list<BackendDAE.Var> varlst = List.select(InVarlst, findObjTermFun);

algorithm
  for v in varlst loop
      nom := BackendVariable.getVarNominalValue(v);
      cr := BackendVariable.varCref(v);
      e := DAE.CREF(cr, DAE.T_REAL_DEFAULT);
      e := Expression.expDiv(e, nom);
      objeExp := mergeObjectVars(objeExp, SOME(e));
  end for;

end findObjTerm;

protected function mergeObjectVars
"author: Vitalij Ruge"
input Option<DAE.Exp> inmayer1;
input Option<DAE.Exp> inmayer2;
output Option<DAE.Exp> mayer;

algorithm
  mayer := match(inmayer1, inmayer2)
  local DAE.Exp e1, e2, e3;

    case(SOME(e1), SOME(e2)) equation
      e3 = Expression.expAdd(e1,e2);
    then SOME(e3);
    case(NONE(), SOME(_)) then inmayer2;
    case(_, NONE()) then inmayer1;
    else NONE();

  end match;
end mergeObjectVars;

protected function addConstraints
"author: Vitalij Ruge"
input list<BackendDAE.Var> InVarlst;
input list< .DAE.Constraint> inConstraint;
input MapFunc findCon;
output list< .DAE.Constraint> outConstraint;

  partial function MapFunc
    input BackendDAE.Var inVar;
    output Boolean outBoolean;
  end MapFunc;


protected
list<BackendDAE.Var> varlst;
list< .DAE.Exp> constraintLst;
algorithm
  constraintLst := match(inConstraint)
                   local list< .DAE.Exp> constraintLst_;
                   case({DAE.CONSTRAINT_EXPS(constraintLst = constraintLst_)}) then constraintLst_;
                   else {};
                   end match;

  varlst := List.select(InVarlst, findCon); //BackendVariable.hasConTermAnno //BackendVariable.hasFinalConTermAnno
  constraintLst := addConstraints2(constraintLst, varlst);
  outConstraint := {DAE.CONSTRAINT_EXPS(constraintLst)};

end addConstraints;

protected function addConstraints2
"author: Vitalij Ruge"
input list< .DAE.Exp> inConstraintLst;
input list<BackendDAE.Var> inVarlst;
output list< .DAE.Exp> outConstraintLst = inConstraintLst;

protected
 DAE.ComponentRef cr;
 .DAE.Exp e;
algorithm

  for v in inVarlst loop
    cr := BackendVariable.varCref(v);
    e := DAE.CREF(cr, DAE.T_REAL_DEFAULT);
    outConstraintLst := e :: outConstraintLst;
  end for;

end addConstraints2;

// =============================================================================
// section for preOptModule >>inputDerivativesForDynOpt<<
//
// check for derivatives of inputs and replace (only for dyn. optimization)
// =============================================================================

public function inputDerivativesForDynOpt "
  checks if der(input) is used and replace for dyn. optimization"
  input BackendDAE.BackendDAE inDAE;
  output BackendDAE.BackendDAE outDAE;
algorithm
  if Config.acceptOptimicaGrammar() or Flags.getConfigBool(Flags.GENERATE_DYN_OPTIMIZATION_PROBLEM) then
    (outDAE, _) := BackendDAEUtil.mapEqSystemAndFold(inDAE, inputDerivativesForDynOptWork, false);
  else
    outDAE := inDAE;
  end if;
end inputDerivativesForDynOpt;

protected function inputDerivativesForDynOptWork "author: "
  input BackendDAE.EqSystem isyst;
  input BackendDAE.Shared inShared;
  input Boolean inChanged;
  output BackendDAE.EqSystem osyst;
  output BackendDAE.Shared outShared = inShared;
  output Boolean outChanged;

algorithm

  (osyst, outChanged) := matchcontinue isyst
    local
      BackendDAE.EquationArray orderedEqs "ordered Equations";
      list<DAE.ComponentRef> idercr={}, icr={};
      DAE.ComponentRef cr;
      String s;
      list<BackendDAE.Var> varLst={};
      BackendDAE.Variables vars;

    case BackendDAE.EQSYSTEM(orderedEqs=orderedEqs) algorithm
      vars := BackendVariable.daeGlobalKnownVars(outShared);

      ((_, idercr, icr, varLst)) := BackendDAEUtil.traverseBackendDAEExpsEqnsWithUpdate(orderedEqs, traverserinputDerivativesForDynOpt, (vars, idercr, icr, varLst));
      if listEmpty(idercr) then
        fail();
      end if;
      // der(u) -> u has der
      varLst := BackendVariable.setVarsKind(varLst, BackendDAE.OPT_INPUT_WITH_DER());
      for v in varLst loop
        outShared := BackendVariable.addGlobalKnownVarDAE(v, outShared);
      end for;
      //  der(u) -> new input var
      varLst := List.map(idercr, BackendVariable.makeVar);
      varLst := List.map1(varLst, BackendVariable.setVarDirection, DAE.INPUT());
      for v in varLst loop
        v := BackendVariable.setVarKind(v,BackendDAE.OPT_INPUT_DER());
        outShared := BackendVariable.addGlobalKnownVarDAE(v, outShared);
      end for;
      _ := BackendVariable.daeGlobalKnownVars(outShared);
       //BackendDump.printVariables(vars);
    then (isyst, true);

    else (isyst, inChanged);
  end matchcontinue;
end inputDerivativesForDynOptWork;

protected function traverserinputDerivativesForDynOpt "author:"
  input DAE.Exp inExp;
  input tuple<BackendDAE.Variables, list<DAE.ComponentRef>,list<DAE.ComponentRef> ,list<BackendDAE.Var>> itpl;
  output DAE.Exp e;
  output tuple<BackendDAE.Variables,list<DAE.ComponentRef>,list<DAE.ComponentRef>,list<BackendDAE.Var>> tpl;
algorithm
  (e,tpl) := Expression.traverseExpTopDown(inExp,traverserExpinputDerivativesForDynOpt,itpl);
end traverserinputDerivativesForDynOpt;

protected function traverserExpinputDerivativesForDynOpt
  input DAE.Exp inExp;
  input tuple<BackendDAE.Variables,list<DAE.ComponentRef>,list<DAE.ComponentRef>,list<BackendDAE.Var>> tpl;
  output DAE.Exp outExp;
  output Boolean cont;
  output tuple<BackendDAE.Variables,list<DAE.ComponentRef>,list<DAE.ComponentRef>,list<BackendDAE.Var>> outTpl;
algorithm
  (outExp,cont,outTpl) := matchcontinue (inExp,tpl)
    local
      BackendDAE.Variables vars;
      DAE.Type tp;
      DAE.Exp e;
      DAE.ComponentRef cr, cr1;
      BackendDAE.Var var;
      list<DAE.ComponentRef> lst, lst1;
      list<BackendDAE.Var> varLst;

    case (DAE.CALL(path=Absyn.IDENT(name = "der"),expLst={DAE.CREF(componentRef=cr)}),(vars,lst,lst1,varLst))
      equation
        (var,_) = BackendVariable.getVarSingle(cr, vars);
        true = BackendVariable.isVarOnTopLevelAndInput(var);
        cr1 = ComponentReference.prependStringCref("$TMP$DER$P", cr);
        //cr1 = ComponentReference.crefPrefixDer(cr);
        e = Expression.crefExp(cr1);
      then (e,true,(vars, List.unionElt(cr1,lst), List.unionElt(cr,lst1),  List.unionElt(var,varLst)));

    else (inExp,true,tpl);
  end matchcontinue;
end traverserExpinputDerivativesForDynOpt;


// =============================================================================
// section for postOptModule >>extendDynamicOptimization<<
//
// transform loops from DAE in constraints for optimizer
// - bigger NLP
// - don't solve loop in each step
// - cheaper jacobians
// =============================================================================

public function removeLoops
  input BackendDAE.BackendDAE inDAE;
  output BackendDAE.BackendDAE outDAE;
algorithm
  if not Flags.getConfigString(Flags.LOOP2CON) == "none"  then
    //BackendDump.bltdump("***", inDAE);
    (outDAE, _) := BackendDAEUtil.mapEqSystemAndFold(inDAE, findLoops, false);
    //BackendDump.bltdump("###", outDAE);
  else
    outDAE := inDAE;
  end if;
end removeLoops;

protected function findLoops
  input BackendDAE.EqSystem isyst;
  input BackendDAE.Shared inShared;
  input Boolean inChanged;
  output BackendDAE.EqSystem osyst;
  output BackendDAE.Shared outShared;
  output Boolean outChanged;
protected
  BackendDAE.StrongComponents comps;
algorithm
  BackendDAE.EQSYSTEM(matching=BackendDAE.MATCHING(comps=comps)) := isyst;
  (osyst, outShared, outChanged) := findLoops1(isyst, inShared, comps, inChanged);
end findLoops;

protected function findLoops1
  input BackendDAE.EqSystem isyst;
  input BackendDAE.Shared ishared;
  input BackendDAE.StrongComponents inComps;
  input Boolean inchanged;
  output BackendDAE.EqSystem osyst = isyst;
  output BackendDAE.Shared oshared = ishared;
  output Boolean changed = inchanged "not used";
protected
  BackendDAE.EquationArray eqns;
  Boolean l2p_all = Flags.getConfigString(Flags.LOOP2CON) == "all";
  Boolean l2p_nl;
  Boolean l2p_l;
algorithm

  if l2p_all then
    //l2p_nl := true;
    l2p_l := true;
  else
    l2p_nl := Flags.getConfigString(Flags.LOOP2CON) == "noLin";
    l2p_l := not l2p_nl;
  end if;

  for comp in inComps loop
    (osyst,oshared) := removeLoopsWork(osyst,oshared,comp, l2p_all, l2p_l);
  end for;

end findLoops1;


protected function removeLoopsWork
"
  author: Vitalij Ruge
"
  input BackendDAE.EqSystem isyst;
  input BackendDAE.Shared ishared;
  input BackendDAE.StrongComponent icomp;
  input Boolean l2p_all;
  input Boolean l2p_l;
  output BackendDAE.EqSystem osyst;
  output BackendDAE.Shared oshared;
algorithm
  (osyst,oshared):=
  matchcontinue (isyst,ishared,icomp)
    local
      BackendDAE.Variables vars;
      BackendDAE.EquationArray eqns;
      list<Integer> eindex, vindx;
      Integer eindex_, vindx_;
      BackendDAE.Shared shared;
      DAE.Exp e1, e2, varexp;
      BackendDAE.Var v;
      DAE.ComponentRef cr;
      DAE.FunctionTree funcs;
      BackendDAE.JacobianType jacType;
      BackendDAE.EqSystem syst;
      Boolean linear;

    case ( syst as BackendDAE.EQSYSTEM(orderedVars=vars, orderedEqs=eqns), shared,
           (BackendDAE.EQUATIONSYSTEM(eqns=eindex, vars=vindx, jacType=jacType)) )
    guard l2p_all or (if l2p_l then isConstOrlinear(jacType) else not isConstOrlinear(jacType))
    algorithm
      (eqns, vars, shared) := res2Con(eqns, vars, eindex, vindx, shared);
      syst.orderedEqs := eqns; syst.orderedVars := vars;
    then (BackendDAEUtil.clearEqSyst(syst), shared);

    case ( syst as BackendDAE.EQSYSTEM(orderedVars=vars, orderedEqs=eqns), shared,
           (BackendDAE.TORNSYSTEM(BackendDAE.TEARINGSET(residualequations=eindex, tearingvars=vindx), linear=linear)) )
    guard l2p_all or (if l2p_l then linear else not linear)
    algorithm
      (eqns, vars, shared) := res2Con(eqns, vars, eindex, vindx, shared);
      syst.orderedEqs := eqns; syst.orderedVars := vars;
    then (BackendDAEUtil.clearEqSyst(syst), shared);

    case ( syst as BackendDAE.EQSYSTEM(orderedVars=vars, orderedEqs=eqns),
           shared as BackendDAE.SHARED(functionTree = funcs),
           BackendDAE.SINGLEEQUATION(eqn=eindex_, var=vindx_) )
    guard l2p_all or not l2p_l
    algorithm
      BackendDAE.EQUATION(exp=e1, scalar=e2) := BackendEquation.get(eqns, eindex_);
      (v as BackendDAE.VAR(varName = cr)) := BackendVariable.getVarAt(vars, vindx_);
      varexp := Expression.crefExp(cr);
      varexp := if BackendVariable.isStateVar(v) then Expression.expDer(varexp) else varexp;
      failure(ExpressionSolve.solve2(e1, e2, varexp, SOME(funcs), NONE()));
      (eqns, vars, shared) := res2Con(eqns, vars, {eindex_}, {vindx_}, shared);
      syst.orderedEqs := eqns; syst.orderedVars := vars;
    then (BackendDAEUtil.clearEqSyst(syst), shared);


    else (isyst,ishared);

  end matchcontinue;

end removeLoopsWork;

protected function isConstOrlinear
  input BackendDAE.JacobianType jacType;
  output Boolean b;
algorithm
  b := match jacType
       case BackendDAE.JAC_CONSTANT() then true;
       case BackendDAE.JAC_LINEAR() then true;
       else false;
       end match;
end isConstOrlinear;

protected function res2Con
"
  author: Vitalij Ruge
"
  input BackendDAE.EquationArray ieqns;
  input BackendDAE.Variables ivars;
  input list<Integer> eindex;
  input list<Integer> vindx;
  input BackendDAE.Shared ishared;
  output BackendDAE.EquationArray oeqns = ieqns;
  output BackendDAE.Variables ovars = ivars;
  output BackendDAE.Shared oshared = ishared;
protected
  list<BackendDAE.Equation> eqn_lst = BackendEquation.getList(eindex,ieqns);
  BackendDAE.Equation eqn;
  list<BackendDAE.Var> var_lst = List.map1r(vindx, BackendVariable.getVarAt, ivars);
  BackendDAE.Var var, var_;
  list<DAE.ComponentRef> cr_lst = List.map(var_lst, BackendVariable.varCref);
  DAE.ComponentRef cr, cr_var;
  list<String> name_lst = List.map(cr_lst,ComponentReference.crefStr);
  DAE.Exp e, res;
  Integer ind_e, ind_v;
  list<Integer> ind_lst_v = List.map(vindx,intAbs);
  list<Integer> ind_lst_e = eindex;
  BackendDAE.Variables globalKnownVars;
algorithm

  BackendDAE.SHARED(globalKnownVars=globalKnownVars) := oshared;

  for var_ in var_lst loop

    // res -> con
    cr_var :: cr_lst := cr_lst;
    eqn :: eqn_lst := eqn_lst;
    ind_e :: ind_lst_e := ind_lst_e;
    ind_v :: ind_lst_v := ind_lst_v;
    cr  := ComponentReference.makeCrefIdent("$EqCon$" +  ComponentReference.crefModelicaStr(cr_var) , DAE.T_REAL_DEFAULT , {});
    e := Expression.crefExp(cr);

    var := BackendVariable.makeVar(cr);
    var := BackendVariable.setVarMinMax(var, SOME(DAE.RCONST(0.0)), SOME(DAE.RCONST(0.0)));
    var := BackendVariable.setVarKind(var, BackendDAE.OPT_CONSTR());
    var := BackendVariable.setVarDirection(var, DAE.OUTPUT());

    ovars := BackendVariable.addNewVar(var, ovars);
    res := BackendDAEOptimize.makeEquationToResidualExp(eqn);
    res := Expression.createResidualExp(res, Expression.makeConstZeroE(res));

    //oeqns := BackendEquation.add(BackendDAE.EQUATION(e, res, DAE.emptyElementSource, BackendDAE.EQ_ATTR_DEFAULT_UNKNOWN), oeqns);
    oeqns := BackendEquation.setAtIndex(oeqns,ind_e, BackendDAE.EQUATION(e, res, DAE.emptyElementSource, BackendDAE.EQ_ATTR_DEFAULT_UNKNOWN));
    // new input(resvar)
    (cr,var) := makeVar("$" +  ComponentReference.crefModelicaStr(cr_var));
    var := BackendVariable.setVarDirection(var, DAE.INPUT());
    // resvar = new input(resvar)
    e := Expression.crefExp(cr_var);
    if BackendVariable.isStateVar(var_) then
      e := Expression.expDer(e);
      var := BackendVariable.setVarKind(var, BackendDAE.OPT_LOOP_INPUT(ComponentReference.crefPrefixDer(cr_var)));
    else
      // don't merge der(x) with x
      var := BackendVariable.mergeAliasVars(var, var_, false, globalKnownVars);
      var := BackendVariable.setVarKind(var, BackendDAE.OPT_LOOP_INPUT(cr_var));
    end if;
    oshared := BackendVariable.addGlobalKnownVarDAE(var, oshared);
    oeqns := BackendEquation.add(BackendDAE.EQUATION(e, Expression.crefExp(cr), DAE.emptyElementSource, BackendDAE.EQ_ATTR_DEFAULT_UNKNOWN), oeqns);
  end for;


end res2Con;

// =============================================================================
// section for postOptModule >>simplifyConstraints<<
//
// simplify nonlinear constraints if possible in  box constraints
// =============================================================================

public function simplifyConstraints
"
  author: vitalij
"
  input BackendDAE.BackendDAE inDAE;
  output BackendDAE.BackendDAE outDAE;
protected
  list<BackendDAE.EqSystem> systlst, new_systlst = {};
  BackendDAE.Shared shared;
  BackendDAE.Equation eqn_;
  BackendDAE.Var var_, var_con;
  BackendDAE.StrongComponents comps;
  Integer eindex,vindx;
  DAE.ComponentRef cr;
  list<BackendDAE.Var> var_lst, var_lst_opt, var_lst1;
  DAE.Exp e1, e2, e, c;
  DAE.FunctionTree funcs;
  BackendDAE.Variables vars, globalKnownVars;
  BackendDAE.EquationArray eqns;
  BackendDAE.BaseClockPartitionKind partitionKind;
  BackendDAE.StateSets stateSets;
  DAE.FunctionTree funcs;
  Option<DAE.Exp> oMax_con, oMin_con;
  DAE.Exp max_con, min_con, zero, con2, z, der_e;
  Boolean b1,b2,b, b3, b4;
  DAE.Type tp;
algorithm

  if Flags.getConfigBool(Flags.GENERATE_DYN_OPTIMIZATION_PROBLEM) then

    //BackendDump.bltdump("START:", inDAE);
    BackendDAE.DAE(systlst, shared) := inDAE;
    BackendDAE.SHARED(functionTree = funcs, globalKnownVars = globalKnownVars) := shared;

    for syst in systlst loop
      BackendDAE.EQSYSTEM(orderedVars=vars,orderedEqs=eqns,matching=BackendDAE.MATCHING(comps=comps)) := syst;
      b := false;
      for comp in comps loop
        //BackendDump.dumpComponent(comp);
       if (match comp case BackendDAE.SINGLEEQUATION() then true; else false; end match) then

         BackendDAE.SINGLEEQUATION(eqn=eindex,var=vindx) := comp;
         var_con := BackendVariable.getVarAt(vars, vindx);
         b3 := BackendVariable.isRealOptimizeConstraintsVars(var_con);
         if b3 then
           try
             (eqn_ as BackendDAE.EQUATION(exp=e1, scalar=e2)):= BackendEquation.get(eqns, eindex);
             true := Expression.expEqual(e1, BackendVariable.varExp(var_con));
           else
             b3 := false;
           end try;
         end if;
         if b3 then
           //print("\neqn " + BackendDump.equationString(eqn_));
           var_lst := BackendEquation.equationsLstVars({eqn_}, vars);
           var_lst_opt := list(vv for vv  guard BackendVariable.isStateVar(vv) in var_lst);
           b3 := listLength(var_lst_opt) == 1;
           var_lst := BackendEquation.equationsLstVars({eqn_}, globalKnownVars);
           var_lst_opt := listAppend(var_lst_opt, list(vv for vv guard BackendVariable.isInput(vv) in var_lst));
           //print("\nn = " + intString(listLength(var_lst_opt)));
           if listLength(var_lst_opt) == 1 then
             {var_} := var_lst_opt;
             BackendDAE.VAR(varName=cr) := var_;
             e := Expression.crefExp(cr);
             tp := Expression.typeof(e);
             zero := Expression.makeConstZero(tp);
             try
              der_e := Differentiate.differentiateExpSolve(e2,cr,SOME(funcs));
              (der_e,_) := ExpressionSimplify.simplify(der_e);
              if Expression.isZero(e) then
                continue;
              end if;
              (z,_) := Expression.makeZeroExpression(Expression.arrayDimension(tp));
              ((c,_)) := Expression.replaceExp(e2, e, z);
              (c,_) := ExpressionSimplify.simplify(c);
              //print("\nde = " + ExpressionDump.printExpStr(der_e));
              //print("\nc = " + ExpressionDump.printExpStr(c));
              //print("\ne = " + ExpressionDump.printExpStr(e));
              //print("\ne2 = " + ExpressionDump.printExpStr(e2));

              var_lst := BackendEquation.expressionVars(der_e, globalKnownVars);
              if b3 then
                var_lst := list(vv for vv guard not BackendVariable.isParam(vv) in var_lst);
              end if;
              var_lst := listAppend(BackendEquation.expressionVars(der_e, vars), var_lst);

              var_lst1 := BackendEquation.expressionVars(c, globalKnownVars);
              if b3 then
                var_lst1 := list(vv for vv guard not BackendVariable.isParam(vv) in var_lst1);
              end if;
              var_lst1 := listAppend(BackendEquation.expressionVars(c, vars), var_lst1);

              var_lst := listAppend(var_lst1, var_lst);

              b4 := Expression.expHasCref(der_e,DAE.crefTime) or Expression.expHasCref(c,DAE.crefTime);
              //print("\nn = " + intString(listLength(var_lst)));
              if listEmpty(var_lst) and not b4 then
                (oMin_con, oMax_con) := BackendVariable.getMinMaxAttribute(var_con);
                b1 := isSome(oMin_con);
                b2 := isSome(oMax_con);
                con2 := Expression.makeNoEvent(DAE.RELATION(der_e,  DAE.LESS(tp), zero,-1,NONE()));

                if b1 then
                  SOME(min_con) := oMin_con;
                  min_con := Expression.makeDiv(Expression.expSub(min_con,c),der_e);
                else
                  min_con := DAE.RCONST(-1e64);
                end if;

                if b2 then
                  SOME(max_con) := oMax_con;
                  max_con := Expression.makeDiv(Expression.expSub(max_con,c),der_e);
                else
                  max_con :=  DAE.RCONST(1e64);
                end if;

                oMin_con := SOME(DAE.IFEXP(con2, max_con, min_con));
                oMax_con := SOME(DAE.IFEXP(con2, min_con, max_con));

                oMin_con := ExpressionSimplify.simplify1o(oMin_con);
                oMax_con := ExpressionSimplify.simplify1o(oMax_con);

                var_con := BackendVariable.setVarMinMax(var_con, oMin_con, oMax_con);
                var_ := BackendVariable.mergeMinMaxAttribute(var_con, var_, false);

                //vars := BackendVariable.addVar(var_, vars);

                var_con := BackendVariable.setVarKind(var_con,  BackendDAE.VARIABLE());
                vars := BackendVariable.setVarAt(vars, vindx, var_con);

                try
                  (_,vindx) := BackendVariable.getVarSingle(cr, vars);
                  vars := BackendVariable.setVarAt(vars, vindx, var_);
                  //print("var" +  BackendDump.varString(var_));
                else
                  (_,vindx) := BackendVariable.getVarSingle(cr, globalKnownVars);
                  globalKnownVars := BackendVariable.setVarAt(globalKnownVars, vindx, var_);
                  //print("var" +  BackendDump.varString(var_));
                end try;

                //(vars,_) := BackendVariable.removeVar(vindx, vars);
                //eqns := BackendEquation.delete(eindex, eqns);
                b := true;
              end if;
             else
             end try;

           end if;
         end if;
       end if;
      end for;

      if b then
        // remove empty entries from vars/eqns
        //vars := BackendVariable.listVar1(BackendVariable.varList(vars));
        //eqns := BackendEquation.listEquation(BackendEquation.equationList(eqns));
        new_systlst := BackendDAEUtil.clearEqSyst(syst) :: new_systlst;
      else
       new_systlst := syst :: new_systlst;
      end if;
    end for;

    shared := BackendDAEUtil.setSharedGlobalKnownVars(shared, globalKnownVars);
    outDAE := BackendDAE.DAE(new_systlst, shared);
  else
    outDAE := inDAE;
  end if;


end simplifyConstraints;


// =============================================================================
// section for postOptModule >>reduceDynamicOptimization<<
//
// remove eqs which not need for the calculations of cost and constraints
// =============================================================================


public function reduceDynamicOptimization
"
  author: vitalij
"
  input BackendDAE.BackendDAE inDAE;
  output BackendDAE.BackendDAE outDAE;
protected
  list<BackendDAE.Var> varlst, opt_varlst, conVarsList, fconVarsList, objMayer, objLagrange;
  list<BackendDAE.EqSystem> systlst, newsyst = {};
  BackendDAE.Variables v;
  BackendDAE.Shared shared;
algorithm
  //BackendDump.bltdump("START:reduceDynamicOptimization", inDAE);
  BackendDAE.DAE(systlst, shared) := inDAE;
  // ToDo
  shared := BackendVariable.removeAliasVars(shared);

  for syst in systlst loop

    syst := BackendEquation.removeRemovedEqs(syst);

    BackendDAE.EQSYSTEM(orderedVars = v) := syst;
    varlst := BackendVariable.varList(v);

    conVarsList := List.select(varlst, BackendVariable.isRealOptimizeConstraintsVars);
    fconVarsList := List.select(varlst, BackendVariable.isRealOptimizeFinalConstraintsVars);
    objMayer := checkObjectIsSet(v,BackendDAE.optimizationMayerTermName);
    objLagrange := checkObjectIsSet(v,BackendDAE.optimizationLagrangeTermName);

    opt_varlst := listAppend(conVarsList, listAppend(fconVarsList, listAppend(objMayer, objLagrange)));

    if not listEmpty(opt_varlst) then
      newsyst := BackendDAEUtil.tryReduceEqSystem(syst, shared, opt_varlst) :: newsyst;
    end if;
  end for;

  outDAE := BackendDAE.DAE(newsyst, shared);
  //BackendDump.bltdump("END:reduceDynamicOptimization", outDAE);
end reduceDynamicOptimization;

public function checkObjectIsSet
"check: mayer or lagrange term are set"
  input BackendDAE.Variables inVars;
  input String CrefName;
  output list<BackendDAE.Var> outVars;
protected
  DAE.ComponentRef leftcref;
algorithm
  leftcref := ComponentReference.makeCrefIdent(CrefName, DAE.T_REAL_DEFAULT, {});

  try
    outVars := BackendVariable.getVar(leftcref, inVars);
  else
    outVars := {};
  end try;
end checkObjectIsSet;

annotation(__OpenModelica_Interface="backend");
end DynamicOptimization;