Discrete Linear Control Systems

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.