Optimal Control: Linear Quadratic Methods
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.
The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback.
Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.
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achieve approach approximation arbitrary associated assumption asymptotically stable augmented plant bandwidth Chapter characteristic polynomial classical control closed-loop poles closed-loop system Consider constant coprime covariance deﬁned deﬁnite diagonal discrete-time eigenvalues eigenvalues of F eigenvectors entries estimate feedback example exists feed-forward feedback controller feedback design feedback law Figure filter finite ﬁrst frequency shaping frequency-shaped gain margin IEEE Trans infinite-time linear quadratic linear system loop gain loop recovery LQG design minimizing minimum phase nonlinearity nonnegative definite nonsingular nonzero Nyquist plot open-loop optimal control optimal control law optimal estimator optimal performance index phase margin plant input plant output poles polynomial positive definite proportional plus integral Qf(s regulator problem return difference equality Riccati equation robustness properties scalar Show signal solution stabilizable strictly proper Suppose theory time-invariant time-varying time-varying systems trajectory transfer function matrix variable vector weighting x(to zero