H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.

针对一类系统的H-无穷大最优控制和估计，该系统由带有有限输入和输出算符的偏微分方程控制。扩散方程是此类中的一个重要示例。给出了最优状态反馈控制器以及最优状态估计器的明确公式。与用于H-无穷大合成的传统方法不同，无需迭代即可获得最佳解。此外，明确计算了状态反馈和状态估计问题的最佳性能。这对于解决H无限最佳执行器和传感器位置问题很有用。此外，这些结果可用于测试和标记用于H-无穷大合成的通用算法。结果也适用于有限维系统。