One service mathematics has rendered the 'Bt mm, ... si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point alIe.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Inhalt
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.