Abstract
A more general and complete predictive guidance problem is considered using optimal control theory. The optimal control law for interception and rendezvous is developed for a system with controllability indexn. The implementation scheme and the effect on miss distance due to errors in guidance are discussed. Finally, an example for a system with controllability index 4 is presented for an interceptor with damping ratio and natural frequency. The solution is presented in closed form.
Similar content being viewed by others
References
Ceranowicz, A. Z., Wyman, B. F., andHermami, H.,Control of Constrained Systems of Controllability Index Two, IEEE Transactions on Automatic Control, Vol. AC-25, No. 6, 1980.
Bryson, A. E., andHo, Y. C.,Applied Optimal Control, Blaisdell, Waltham, Massachusetts, 1969.
Garber, V.,Optimum Intercept Law for Accelerating Targets, AIAA Journal, Vol. 6, No. 11, 1968.
Dickson, R. E., andGarber, V.,Optimum Rendezvous Intercept and Injection, AIAA Journal, Vol. 7, No. 7, 1970.
Salmon, D. M.,Multipoint Guidance—An Efficient Implementation of Predictive Guidance, AIAA Journal, Vol. 11, No. 12, 1973.
Xia, G. H.,An Optimum Intercept Law of 3-Order Systems, Proceedings of the Conference of the Chinese Automatic Control Society, Peking, China, 1978.
Hecht, C., andTroesch, A.,Predictive Guidance for Interceptors with Time Lag in Acceleration, IEEE Transactions on Automatic Control, Vol. AC-25, No. 2, 1980.
Seal, C. E., andStubberud, A. R.,The Singularity Structure of Optimal Final-Value Control Systems, International Transactions on Control, Vol. 12, No. 6, 1970.
Kim, M., andGrider, K. V.,Terminal Guidance for Impact Attitude Angle Constraint Flight Trajectories, IEEE Transactions, Vol. AES-9, No. 6, 1973.
Merriam, C. W., III,Optimization Theory and the Design of Feedback Control Systems, McGraw-Hill, New York, New York, 1964.
Stubberud, A. R.,Theory of Pitch Steering for Ascent Guidance, Proceedings of the Institute of Navigation, pp. 136–163, Los Angeles, California, 1967.
Author information
Authors and Affiliations
Additional information
Communicated by C. T. Leondes
on leave from Peking Institute of Control Engineering, Chinese Academy of Space Technology, Peking, China.
Rights and permissions
About this article
Cite this article
Xia, G.H., Stubberud, A.R. Predictive guidance for systems with controllability indexn . J Optim Theory Appl 41, 327–339 (1983). https://doi.org/10.1007/BF00935228
Issue Date:
DOI: https://doi.org/10.1007/BF00935228