将最优控制理论应用于建筑供暖、通风和空调系统的仿真。问题如下:给定一个描述商业建筑及其空调系统热行为的常微分方程组，试图找到使总能源成本最小的最佳空调策略。空调是通过在恒定温度下脉动空气来实现的。选择空气流量作为控制变量。当然，这个气流速度必须满足一些舒适性约束:它应该大于与来自外部的空气量相对应的下限，这是出于明显的卫生原因。它应该能够将建筑物占用区域的温度保持在尽可能接近目标温度的水平。最小化算法使用共轭梯度法。 常微分方程的积分采用五阶显式Runge-Kutta-Fehlberg方法，步长可变。在不计算伴随微分系统的情况下，发展了一种计算梯度的原始方法。文中给出了一些计算结果，最后指出了该算法的性能以及改进方法的不同途径，以便将其应用于更复杂的系统。引文:研讨会论文，佐治亚州亚特兰大，1984年

Optimal control theory is applied to the simulation of heating, ventilating, and air-conditioning systems in buildings. The problem is as follows: given a system of ordinary differential equations that describes the thermal behaviour of a commercial building, and its air conditioning system, try to find the optimal air conditioning policy leading to a minimum of the total energy cost.Air conditioning is obtained by pulsing air at a constant temperature. The airflow rate is chosen as the control variable. This airflow rate must, of course, satisfy some comfort constraints:It should be larger than a lower bound corresponding to the amount of air coming from the outside for evident hygienic reasonsIt should be able to maintain the temperature in the occupied zone of the building as close as possible to a target temperatureThe minimizing algorithm uses the conjugate gradient method. Integration of the ordinary differential equations is performed by a fifth order explicit Runge-Kutta-Fehlberg method, with variable step size.An original method was developed to compute the gradient without computing an adjoint differential system.Some computational results are given, and, finally the capabilities of such an algorithm and the different ways to improve the method in order to apply it to more complex systems are pointed out.