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When solving the control and design problems in aerospace and naval
engi neering, energetics, economics, biology, etc., we need to know
the state of investigated dynamic processes. The presence of
inherent uncertainties in the description of these processes and of
noises in measurement devices leads to the necessity to construct
the estimators for corresponding dynamic systems. The estimators
recover the required information about system state from mea
surement data. An attempt to solve the estimation problems in an
optimal way results in the formulation of different variational
problems. The type and complexity of these variational problems
depend on the process model, the model of uncertainties, and the
estimation performance criterion. A solution of variational problem
determines an optimal estimator. Howerever, there exist at least
two reasons why we use nonoptimal esti mators. The first reason is
that the numerical algorithms for solving the corresponding
variational problems can be very difficult for numerical imple
mentation. For example, the dimension of these algorithms can be
very high."
The optimal estimation problems for linear dynamic systems, and in
particular for systems with aftereffect, reduce to different
variational problems. The type and complexity of these variational
problems depend on the process model, the model of uncertainties,
and the estimation performance criterion. A solution of a
variational problem determines an optimal estimator. In addition,
frequently the optimal algorithm for one noise model must operate
under another, more complex assumption about noise. Hence,
simplified algorithms must be used. It is important to evaluate the
level of nonoptimality for the simplified algorithms. Since the
original variational problems can be very difficult, the estimate
of nonoptimality must be obtained without solving the original
variational problem. In this book, guaranteed levels of
nonoptimality for simplified estimation and control algorithms are
constructed. To obtain these levels the duality theory for convex
extremal problems is used. Audience: This book will be of interest
to applied mathematicians, researchers and engineers who deal with
estimation and control systems. The material, which requires a good
knowledge of calculus, is also suitable for a two-semester graduate
or postgraduate course.
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