Discrete Linear Control Systems [Paperback]

1 Basic concepts and statement of problems in control theory.- 1.1 Initial Premises.- 1.2 Basic concepts of control theory.- 1.2.1 The control object.- 1.2.2 Control algorithm.- 1.2.3 Control objective.- 1.3 Modelling of control objects and their general characteristics.- 1.3.1 State equations of discrete processes.- 1.3.2 Observability and controllability.- 1.3.3 Linear proces.- 1.4 Precising the statement of the control problem.- 1.4.1 Classification of control objectives.- 1.4.2 Optimisation of control.- 1.4.3 Observations on selection of control strategies.- 2 Finite time period control.- 2.1 Dynamic programming.- 2.1.1 Statement of the optimization problem.- 2.1.2 Description of the Dynamic programming methods.- 2.1.3 Bellmans equation.- 2.1.4 Example: Linear-quadratic deterministic system.- 2.1.5 Generalisation of Bellmans equation for infinite time control problems.- 2.2 Stochastic control systems.- 2.2.1 Statement of the problem.- 2.2.2 Dependence of the optimal solution on the choice of the admissible control strategies.- 2.3 Stochastic dynamic programming.- 2.3.1 Description of the method.- 2.3.2 Bellmans equation for stochastic control systems.- 2.3.3 Example: Linear quadratic problem with randomly varying coefficients and observable states of the control object.- 2.3.4 Example: Linear stationary object with control delay.- 2.4 Bayesian control strategy.- 2.4.1 Bayesian approach to the optimization problem.- 2.4.2 A posteriori distribution and Bayesian formula.- 2.4.3 Regularity in Bayesian control strategy.- 2.4.4 Recursive formulae for computations of a posteriori distributions.- 2.5 Linear quadratic Gaussian Problem.- 2.5.1 Statement of the problem.- 2.5.2 Conditional Gaussism of the states and sufficient statistics.- 2.5.3 Bayesian control strategy.- 2.A Appendix.- 2.A.1 General forms of probability theory.- 2.A.2 Convergence of random variables.- 2.P Proofs of lemmas and theorems.- 2.P.1 Proof of the theorem 2.1.1.- 2.P.2 Proof of the theorem 2.1.lc¶