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Optimal control deals with the problem of finding a control law for
a given system such that a certain optimality criterion is
achieved. An optimal control is a set of differential equations
describing the paths of the control variables that minimize the
cost functional. This book, Continuous Time Dynamical Systems:
State Estimation and Optimal Control with Orthogonal Functions,
considers different classes of systems with quadratic performance
criteria. It then attempts to find the optimal control law for each
class of systems using orthogonal functions that can optimize the
given performance criteria. Illustrated throughout with detailed
examples, the book covers topics including: Block-pulse functions
and shifted Legendre polynomials State estimation of linear
time-invariant systems Linear optimal control systems incorporating
observers Optimal control of systems described by
integro-differential equations Linear-quadratic-Gaussian control
Optimal control of singular systems Optimal control of time-delay
systems with and without reverse time terms Optimal control of
second-order nonlinear systems Hierarchical control of linear
time-invariant and time-varying systems
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