# Numerical Solutions for Linear Two-Point Boundary-Value Problems

• Robert Kalaba
• Karl Spingarn
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG)

## Abstract

Linear systems with quadratic performance criteria typically lead to two-point boundary-value problems. Analytical solutions for these problems can only be obtained for simple systems. Thus in general numerical methods must be used. The numerical methods considered in this chapter are the matrix Riccati equation, the method of complementary functions, and invariant imbedding. While it would be desirable to be able to use only one of the numerical methods exclusively, this is not always possible since there are advantages and disadvantages to each method. The numerical solutions of two-point boundary-value problems are sometimes difficult because of round-off and truncation errors. In such cases the method of invariant imbedding should be used. Examples are given in this chapter and the results are compared on the basis of numerical accuracy.

## Keywords

Optimal Control Problem Riccati Equation Optimal Trajectory Linear Algebraic Equation Hamiltonian Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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© Plenum Press, New York 1982

## Authors and Affiliations

• Robert Kalaba
• 1
• Karl Spingarn
• 2
1. 1.University of Southern CaliforniaLos AngelesUSA
2. 2.Hughes Aircraft CompanyLos AngelesUSA