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Optimizing Estimation of a Statistically Undefined System

Published on Jan 1, 2018in Automation and Remote Control 0.59
· DOI :10.1134/S0005117918010022
B. I. Anan’ev1
Estimated H-index: 1
(RAS: Russian Academy of Sciences)
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Abstract
Consideration was given to the optimal choice of the parameters for the best estimation of the phase state of a linear system fallible to the action of the Gaussian perturbation with undefined covariances of increments. The matrices at system perturbation and those in the measurement equation are the parameters to be selected for the choice of the observer player. The undefined increment matrices are selected by the opponent player. Both parameters are limited by compact sets. The problem comes to a differential game for the Riccati equation with a performance criterion in the form of a matrix trace. In a special case, consideration was given to the problem with constant matrices. Used were the methods of minimax optimization, optimal control theory, and the theory of differential games. Examples were considered.
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Published on Jan 1, 2012
Bhar K. Aliyu1
Estimated H-index: 1
,
Charles A. Osheku1
Estimated H-index: 1
+ 1 AuthorsAliyu A. Funmilayo1
Estimated H-index: 1
Matrix Riccati Equations arise frequently in applied mathematics, science, and engineering problems. These nonlinear matrix equations are particularly significant in optimal control, filtering, and estimation problems. Essentially, solving a Riccati equation is a central issue in optimal control theory. The needs for such equations are common in the analysis and synthesis of Linear Quadratic Gaussian (LQC) control problems. In one form or the other, Riccati Equations play significant roles in op...
3 Citations Source Cite
Published on Dec 1, 2006in Journal of Mathematical Sciences
A. M. Taras’ev1
Estimated H-index: 1
,
T. B. Tokmantsev1
Estimated H-index: 1
+ 1 AuthorsV. N. Ushakov1
Estimated H-index: 1
Many problems of conflict-control theory can be reduced to approach-avoidance games with a certain terminal set. One of the main approaches to solution of such problems is the approach suggested by N. N. Krasovskii, which is based on positional constructions. The basis of these constructions consists of the extremal aiming principle at stable bridges. In this connection, the problem of constructing the maximal stable bridge, the set of all positions from which the problem of approaching the term...
8 Citations Source Cite
Published on Jan 1, 1999
Andrei I. Subbotin1
Estimated H-index: 1
(RAS: Russian Academy of Sciences)
This chapter first presents the basic notions of the theory of positional differential games, including the notions of feedback strategy and stable bridge, and of the theory of minimax solutions for Hamilton—Jacobi equations. In this framework constructive and numerical methods are developed for time-optimal as well as fixed-horizon games by the procedure of extremal aiming. Mixed feedback strategies and counterstrategies are also studied. Finally the numerical algorithms are tested on some exam...
8 Citations Source Cite
Published on Jan 1, 1999
Panagiotis E. Souganidis39
Estimated H-index: 39
(UW: University of Wisconsin-Madison)
In this chapter I describe some of the recent advances made in the theory of two-person, zero-sum deterministic and stochastic differential games using the theory of viscosity solutions of first-and second-order fully nonlinear elliptic and parabolic partial differential equations.
22 Citations Source Cite
Published on Jan 1, 1998in Automation and Remote Control 0.59
A. R. Pankov1
Estimated H-index: 1
,
K. V. Semenikhin1
Estimated H-index: 1
7 Citations
Published on Jan 1, 1995
A.N. Krasovskii1
Estimated H-index: 1
One of the basic aspirations of contemporary research in differential games is to produce a theory that would combine theoretical depth with the ability to ensure effective calculation and simulation of the solutions. Accumulating research in differential games, this book gives an account of how to design state and output feedback control strategies for a broad class of differential games (such as, pursuit, evasion, tracking, encounter, energy - minimum cost, etc), or more generally, for games w...
120 Citations Source Cite
Published on Aug 1, 1985in Journal of Differential Equations 1.94
Panagiotis E. Souganidis39
Estimated H-index: 39
(Brown University)
Abstract Equations of Hamilton-Jacobi type arise in many areas of applications, including the calculus of variations, control theory and differential games. Recently M. G. Crandall and P.-L. Lions established the correct notion of generalized solutions for these equations. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations as limits...
206 Citations Source Cite
Published on Jan 1, 1977
R. Sh. Liptser9
Estimated H-index: 9
,
Alʹbert Nikolaevich Shiri︠a︡ev4
Estimated H-index: 4
1. Essentials of Probability Theory and Mathematical Statistics.- 2. Martingales and Related Processes: Discrete Time.- 3. Martingales and Related Processes: Continuous Time.- 4. The Wiener Process, the Stochastic Integral over the Wiener Process, and Stochastic Differential Equations.- 5. Square Integrable Martingales and Structure of the Functionals on a Wiener Process.- 6. Nonnegative Supermartingales and Martingales, and the Girsanov Theorem.- 7. Absolute Continuity of Measures corresponding...
1,916 Citations
Published on Sep 1, 1976in IEEE Transactions on Information Theory 3.21
Joel M. Morris12
Estimated H-index: 12
In this paper, theoretical justification is established for the common practice of applying the Kalman filter estimator to three classes of linear quadratic problems where the model statistics are not completely known, and hence specification of the filter gains is not optimum. The Kalman filter is shown to be a minimax estimator for one class of problems and to satisfy a saddlepoint condition in the other two classes of problems. Equations for the worst case covariance matrices are given which ...
70 Citations Source Cite
Published on Jan 1, 1966in IEEE Transactions on Automatic Control 5.09
Donald E. Johansen1
Estimated H-index: 1
The problem of estimating a signal x(t) from linear measurements z(t)=x(t)+w(t) is considered. The signal w(t) is white noise with known statistics, while x(t) is an unknown nonrandom signal drawn from a set of admissible waveforms having bounded second derivatives for which statistics are undefined. Problems of this type arise naturally in the radar tracking of an evasive vehicle under the control of an intelligent adversary. Such problems are also important in trajectory estimation on a missil...
10 Citations Source Cite