Applications of dynamic programming to the control of water resource systems

Abstract

The complexity and expense of water system projects have made optimum operation and design by computer-based techniques of increasing interest in recent years. Dynamic programming offers a powerful approach to a wide variety of these problems. Most water system problems can be classed as one of the following three types: 1. (1) Optimum operation during a short period, such as 24 hours, when all quantities are known; 2. (2) Monthly or yearly policy optimization when some system parameters, such as stream inflows, are not known exactly; 3. (3) Long-range planning or resource allocation when demands may or may not be known exactly. Realistic water resource problems have many decision and state variable constraints. There are also nonlinearities or stochastic variations in both the state equations and the return function. This paper describes how dynamic programming can handle these difficulties. Several specialized dynamic programming techniques applicable to water system problems are also introduced. These include successive approximations, forward dynamic programming, dynamic programming for stochastic control, and iteration in policy space. Four examples are solved and discussed—short-term optimization of a two-reservoir system is solved with forward dynamic programming; short-term optimization of a four-reservoir system is treated by successive approximations; optimum operation over a year, when stream-flows are stochastic variables, is found by iteration in policy spaces; and optimum long-term planning of system additions given projected demand is treated by forward dynamic programming.