#*************************************************************
# Test Problem 2 from Chapter 11, section 4.3  
# Singular Control Problem
#*************************************************************

OPTION {{
  FTOL = 1e-6;
  OTOL = 1e-6;
  NLP = "SNOPT";
  RANDOMX;
}}

DECLARATION {{
  INDEX {i};
  SET I = |0:9|;  # Number of control parameters
  SET J = |1:4|;   # Number of states

  XVAR {z4f,   # Final Time Value of state 4
        w(I)   # Control Parameters  
       };

  ZVAR {z(J),u};

  ISPE {z(J)};
  STP z(1) = 0;
  STP z(2) = -1;
  STP z(3) = -sqrt[5];
  STP z(4) = 0;

  TIME {0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1};

# Variable Bounds
  LBDS w(I) = < i E I | -4>;
  UBDS w(I) = < i E I | 10>;
  
  LBDS z4f = 0;
  UBDS z4f = 1;
}}

MODEL {{
  MIN:  z4f;

  dae1: z'(1) =e= z(2);
  dae2: z'(2) =e= -z(3)*u + 16*t - 8;
  dae3: z'(3) =e= u;
  dae4: z'(4) =e= z(1)^2 + z(2)^2 + 0.0005*(z(2) + 16*t - 8 - 0.1*z(3)*u^2)^2;

  control: u =e= interv[i E I| w(i)];

  endtime[10]: z4f - z(4) =e= 0; 

}}