Invariant imbedding in control, estimation, and system identification

摘要

The areas of modern control, estimation, and systems identification theory often result in the need for solution of nonlinear two-point boundary-value problems. These problems are generally difficult to handle both analytically and computationally. Due to the split boundary conditions, a simple integration is not possible, and an iterative technique is time-consuming and often complicated to solve. High-speed computational approaches will often enable solutions if the algorithm to be processed is efficient and effective with regard to computer solution time. The invariant-imbedding procedure is an approach whereby the missing initial (or terminal) conditions are obtained in a direct manner. The original problem is thereby effectively reduced to an initial-value problem. Comprehensive discussions of the principle of invariant imbedding in the context of control-systems engineering first appeared in various works by Bob Kalaba, Richard Bellman, and others. In this paper, we provide an overview of these contributions, together with some extensions in the area of systems control, estimation, and identification.