Title :
Nonlinear approximate game-theoretic estimation
Author :
Jang, Jinsheng ; Speyer, Jason L.
Author_Institution :
Dept. of Mech. & Aerosp. Eng., California Univ., Los Angeles, CA, USA
Abstract :
Over a finite-time interval, for a class of linear time-varying dynamical systems with a small nonlinearity, an approximate nonlinear optimal estimation scheme is derived based on a deterministic game-theoretic criterion. Using the calculus of variation approach, this game-theoretic criterion is first maximized by the process disturbance and initial state vectors. The resulting optimality condition is expanded with respect to a small parameter ε and the expression of the worst case state and the Lagrange multiplier vectors are determined. Subsequently, the approximate game-theoretic estimator is derived by minimizing each term in the series of cost criterion over the corresponding element of state estimate vector expansion. The estimator Riccati differential equations (RDE) necessary for the first and higher order correction terms are the same as in the zeroth-order case. The first-order and higher-order correction terms are computed on-line based on nonlinear functions evaluated along the minimax trajectory of the zeroth-order state estimate which has to be updated, through a backward integration, as each new measurement becomes available. The infinite-order approximate minimax estimator is shown to be a priori disturbance attenuating. The Nth-order approximate minimax estimator achieves disturbance attenuation with an incremental increase in the bound proportional to CN+1
Keywords :
Riccati equations; filtering theory; game theory; linear systems; nonlinear differential equations; perturbation techniques; state estimation; time-varying systems; variational techniques; Riccati differential equations; approximate nonlinear optimal estimation scheme; backward integration; calculus of variation approach; disturbance attenuation; first order correction terms; higher order correction terms; infinite-order approximate minimax estimator; linear time-varying dynamical systems; minimax trajectory; nonlinear approximate game-theoretic estimation; nonlinear functions; optimality condition; process disturbance; state estimate vector expansion; Attenuation; Calculus; Costs; Differential equations; Lagrangian functions; Minimax techniques; Riccati equations; State estimation; Time varying systems; Vectors;
Conference_Titel :
Decision and Control, 1996., Proceedings of the 35th IEEE Conference on
Conference_Location :
Kobe
Print_ISBN :
0-7803-3590-2
DOI :
10.1109/CDC.1996.574379