Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions

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.