A Steady State Optimal Design of Artificial Induced Aeration in Polluted Streams by the Use of Pontryagin's Minimum Principle

Optimal control theory based on Pontryagin's minimum principle has been applied to the problem of specifying the steady state distribution of artificial aeration in polluted rivers. The optimization was developed for a general integral type cost functional with weighted energy constraints. The system equations used were of the classical Streeter‐Phelps genre with an induced aeration term added as the control function. The formulation of the problem yielded the famous Riccati‐Kalman structure and an analytical solution. Several optimal and suboptimal aeration designs at different temperature levels were obtained using a digital computer and an automatic plotting routine. An analog computer was used in the critical stages of the numerical solutions. Results from the analog computer pointed the way to the ultimate use of Laplace transform techniques in conjunction with a digital computer for maximum accuracy.