Numerical Solutions for Linear Two-Point Boundary-Value Problems
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.
KeywordsOptimal Control Problem Riccati Equation Optimal Trajectory Linear Algebraic Equation Hamiltonian Function
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- 7.Courant, R., and Hilbert, D., Methods of Mathematical Physics, Interscience Publishers, Inc., New York, p. 183, 1966.Google Scholar
- 9.Kalaba, R. E., A New Approach to Optimal Control and Filtering, University of Southern California Report USCEE-316, Los Angeles, California, November, 1968.Google Scholar
- 10.Kagiwada, H., and Kalaba, R., Optimal Trajectories for Quadratic Variational Processes via Invariant Imbedding, RM-5929-PR, The Rand Corporation, Santa Monica, California, January, 1969.Google Scholar
- 11.Spingarn, K., Some numerical results using Kalaba’s new approach to optimal control and filtering, Proceedings of the Fourth Hawaii International Conference on System Sciences, Honolulu, Hawaii, pp. 186–187, January 1971.Google Scholar
- 11a.Also, Technical Note, Spingarn, K., IEEE Transactions on Automatic Control, pp. 713–715, October, 1972.Google Scholar
- 12.Bryson, A., Jr., and Ho, Y. C., Applied Optimal Control, Blaisdell Publishing Co., Waltham, Massachusetts, 1969.Google Scholar