A Theory of Satisficing Control

Abstract

The existence of an optimal control policy and the techniques for finding it are grounded fundamentally in a superlative perspective. These techniques can be of limited value when the global behavior of the system is difficult to characterize, as it may be when the system is nonlinear, when the input is constrained, or when only partial information is available regarding system dynamics or the environment. Satisficing control theory is an alternative approach that is compatible with such systems. This theory is extended by the introduction of the notion of strongly satisficing to provide a rigorous, systematic procedure for the design of satisficing controllers which are consistent with optimal control theory. Because they are often difficult to solve optimally, one application of satisficing control theory is to nonlinear control problems. Of particular interest are the nonlinear quadratic regulator and nonlinear minimum time problems. A controller synthesis procedure and resulting solutions are presented for single agent nonlinear control problems. The application of the satisficing principle to single agent control problems establishes the validity of the principle in a control setting, and motivates its use in multiple agent problems. Multiple agent control problems have proven difficult to solve using classical control methods. Agents may disagree about what constitutes optimality and, even if they agree, an optimal solution may be unknown or computationally impractical. These difficulties are to a significant degree resolved by applying satisficing control theory. A controller synthesis procedure is developed for a general three-team problem with pursuit-evasion and nonlinear regulator characteristics. Simulations demonstrate that the resulting controllers not only perform well in both cooperative and non-cooperative environments, but also that performance degrades gracefully in the presence of partial information.