Stochastic optimal control guidance law with bounded acceleration

This paper presents a novel stochastic optimal control guidance law for a missile with bounded acceleration. The optimal law is obtained by numerically solving the stochastic optimization problem. Since the certainty equivalence principle is not valid in the current problem, the resulting optimal law depends on the conditional probability density function of the estimated states. The stochastic optimal control guidance law is compared to the classical optimal, linear, guidance law. It is shown that the new guidance law is nonlinear in the estimated zero effort miss distance and that the probability density function of the miss is non-Gaussian. Only for an extremely large acceleration limit does the stochastic optimal control guidance law degenerate to the classical one. Thus, the research approach of taking into account the acceleration limit is validated.

[1]  J. Elgin.  The Fokker-Planck Equation: Methods of Solution and Applications , 1984 .

[2]  Jian-Qiao Sun,et al.  Stochastic Optimal Control of Nonlinear Systems via Short-Time Gaussian Approximation and Cell Mapping , 2002 .

[3]  H. Risken.  Fokker-Planck Equation , 1984 .

[4]  J. F. Forbes,et al.  Control design for discrete-time stochastic nonlinear processes with a nonquadratic performance objective , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  H. Witsenhausen.  Separation of estimation and control for discrete time systems , 1971 .

[6]  H. Kushner.  Numerical Methods for Stochastic Control Problems in Continuous Time , 2000 .

[7]  R. G. Cottrell.  Optimal intercept guidance for short-range tactical missiles , 1971 .

[8]  R. Singer.  Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets , 1970, IEEE Transactions on Aerospace and Electronic Systems.

[9]  Ilan Rusnak,et al.  Optimal Guidance for Acceleration Constrained Missile and Maneuvering Target , 1989, The Sixteenth Conference of Electrical and Electronics Engineers in Israel,.

[10]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[11]  Luis G. Crespo,et al.  Stochastic Optimal Control via Bellman’s Principle , 2004 .

[12]  N E Manos,et al.  Stochastic Models , 1960, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[13]  Floyd B. Hanson,et al.  Techniques in Computational Stochastic Dynamic Programming , 1996 .

[14]  V. Garber.  Optimum intercept laws for accelerating targets. , 1968 .

[15]  Joseph Z. Ben-Asher,et al.  TRAJECTORY SHAPING AND TERMINAL GUIDANCE USING LINEAR QUADRATIC DIFFERENTIAL GAMES , 2002 .

[16]  Tal Shima,et al.  An LQG guidance law with bounded acceleration command , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[17]  Robert J. Fitzgerald.  Shaping Filters for Disturbances with Random Starting Times , 1979 .

[18]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .