Optimal Trajectories and Neighboring Optimal Solutions:

• Section 3 (Parametric Optimization)
  • Problem 2 (b)
    • sect_3_prob_2_part_b.m (performs the needed minimization of J)
      
    • sect_3_prob_2_part_b_J_min_fn.m (the minimization function)
      
    • sect_3_prob_2_part_b_J_ode_fn.m (used to integrate the dynamic equations)
      
  • Problem 2 (d)
    • sect_3_prob_2_part_d.m (performs the needed minimization of J)
      
    • sect_3_prob_2_part_d_J_min_fn.m (the minimization function)
      
    • sect_3_prob_2_part_d_J_ode_fn.m (used to integrate the dynamic equations)
      
  • Problem 2 (e)
    • sect_3_prob_2_part_e.m (performs the needed minimization of J)
      
    • sect_3_prob_2_part_e_J_min_fn.m (the minimization function)
      
    • sect_3_prob_2_part_e_J_ode_fn.m (used to integrate the dynamic equations)
      
  • Problem 3
    • sect_3_prob_3.m (performs the needed minimization of J)
      
    • sect_3_prob_3_J_min_fn.m (the minimization function)
      
    • sect_3_prob_3_J_ode_fn.m (used to integrate the dynamic equations)
      
  • Problem 4
    • sect_3_prob_4.m (performs the needed minimization of J)
      
    • sect_3_prob_4_J_min_fn.m (the minimization function)
      
    • sect_3_prob_4_J_ode_fn.m (used to integrate the dynamic equations)
      
  • Problem 5
    • sect_3_prob_5.m (performs the needed minimization of J)
      
    • sect_3_prob_5_J_min_fn.m (the minimization function)
      
    • sect_3_prob_5_J_ode_fn.m (used to integrate the dynamic equations)
      
• Section 4 (Conditions of Optimality)
  • Problem 2 (the rate of pollution increase - numerics)
    • sect_4_prob_2.m (performs the needed numeric minimization of J)
      
    • sect_4_prob_2_J_min_fn.m (the minimization function)
      
    • sect_4_prob_2_J_ode_fn.m (used to integrate the dynamic equations)
      
    • sect_4_prob_2_u_from_x_N_lambda.m (converts x and lambda into the control)
      
• Section 5 (Constraints and Singular Control)
  • Problem 3 (single room temperature control: hard end constraints)
    • sect_5_prob_3.nb (some algebra for this problem)
      
    • sect_5_prob_3.m (plots the optimal control)
      
    • sect_5_prob_3_ode_fn.m (used to integrate the dynamic equations)
      
  • Problem 4 (single room temperature control: soft end constraints)
    • sect_5_prob_4.nb (some algebra for this problem)
      
    • sect_5_prob_4.m (plots the optimal control)
      
  • Problem 5 (single room temperature control: a continuous penalty)
    • sect_5_prob_5.m (solves this problem)
      
    • sect_5_prob_5_J_min_fn.m (the shooting function to minimize)
      
    • sect_5_prob_5_ode_fn.m (the ODEs for x_1 and lambda)
      
  • Problem 6 (heating a two-room building)
    • sect_5_prob_6.m (solves this problem)
      
    • sect_5_prob_6_J_min_fn.m (the function to minimize)
      
    • sect_5_prob_6_ode_fn.m (the differential equations for x_1 and lambda)