Discrete Linear Control Systems, Softcover reprint of the original 1st ed. 1991 Mathematics and its Applications Series, Vol. 67

Deals with various results of modern control theory. Emphasis is placed on the investigation of linear systems and quadratic criteria in a discrete time domain. Control, with or without noise, with complete or partial information, and other cases are discussed. Major attention is paid to the foundat

1 Basic concepts and statement of problems in control theory.- 1.1 Initial Premises.- 1.2 Basic concepts of control theory.- 1.3 Modelling of control objects and their general characteristics.- 1.4 Precising the statement of the control problem.- 2 Finite time period control.- 2.1 Dynamic programming.- 2.2 Stochastic control systems.- 2.3 Stochastic dynamic programming.- 2.4 Bayesian control strategy.- 2.5 Linear quadratic Gaussian Problem.- 2.A Appendix.- 2.P Proofs of lemmas and theorems.- 3 Infinite time period control.- 3.1 Stabilitzation of dynamic systems using Liapunov’s method.- 3.2 Discrete form for analytical design of regulators.- 3.3 Transfer function method in linear optimization problem.- 3.4 Limiting optimal control of stochastic processes.- 3.5 Minimax control.- 3.A Appendix.- 3.P Proofs of the lemmas and theorems.- 4 Adaptive linear control systems with bounded noise.- 4.1 Fundamentals of adaptive control.- 4.2 Existence of adaptive control strategy in a minimax control problem.- 4.3 Self-tuning systems.- 4.P Proofs of the lemmas and theorems.- 5 The problem of dynamic system identification.- 5.1 Optimal recursive estimation.- 5.2 The Kalman-Bucy filter for tracking the parameter drift in dynamic systems.- 5.3 Recursive estimation.- 5.4 Identification of a linear control object in the presence of correlated noise.- 5.5 Identification of control objects using test signals.- 5.P Proofs of lemmas and theorems.- 6 Adaptive control of stochastic systems.- 6.1 Dual control.- 6.2 Initial synthesis of adaptive control strategy in presence of the correlated noise.- 6.3 Design of the adaptive minimax control.- 6.P Proofs of the lemmas and the theorems.- Comments.- References.- Operators and Notational Conventions.