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<p>In this paper, a&#xa0;constrained bi-objective optimal control problem governed by convection-diffusion equations that models a&#xa0;heating, ventilation and air conditioning (HVAC) system is solved. First, the problem is discretized using the spatially symmetric interior penalty Galerkin (SIPG) method. For the time integration, we employ the backward Euler method. The optimality conditions associated with the discrete optimal control problem are then obtained. Using Fischer-Burmeister function, these conditions are reformulated in an equivalent system with nonlinear and nonsmooth equations. A&#xa0;nonsmooth Newton’s method is introdueced to solve the resulting system and prove its local convergence. Finally, a&#xa0;numerical example is tested to show the accuracy and the efficiency of the proposed approach.</p>

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A nonsmooth Newton’s method for solving discretized bi-objective constrained optimal control modeling HVAC systems

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Souheyla Zelmat,
  • Boubakeur Benahmed,
  • Djillali Bouagada,
  • Imene Khames

摘要

In this paper, a constrained bi-objective optimal control problem governed by convection-diffusion equations that models a heating, ventilation and air conditioning (HVAC) system is solved. First, the problem is discretized using the spatially symmetric interior penalty Galerkin (SIPG) method. For the time integration, we employ the backward Euler method. The optimality conditions associated with the discrete optimal control problem are then obtained. Using Fischer-Burmeister function, these conditions are reformulated in an equivalent system with nonlinear and nonsmooth equations. A nonsmooth Newton’s method is introdueced to solve the resulting system and prove its local convergence. Finally, a numerical example is tested to show the accuracy and the efficiency of the proposed approach.