LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS AND CONTROL AND ESTIMATION PROBLEMS

In this dissertation a fairly general class of linear control systems governed by Functional Differential Equations (FDE) of neutral type both in finite dimensional Euclidean spaces and Hilbert spaces is considered. Such systems are formulated as abstract control systems modeled by differential equations in the Product Space, within the framework of the theory of C(,0) semigroup.;The optimal solution in (i) is given by the feedback law in terms of the solution to a class of Riccati equations. The method of investigation is based on the techniques of linear functional analysis and semigroup theory. The problem (ii) is investigated by studying Abstract Riccati Equation in the product space, where the detectability notion plays a key role. The filter equation in (iii) is derived by a new approach, i.e. by exploiting the martingale representation theorem. The error covariance operator is characterized by a Riccati equation. The results for (i) and (iii) are combined to obtain a separation principle to (iv).;Also we are concerned with controllability problem. A necessary and sufficient condition for approximately controllability is obtained.;It is also worth noticing that these investigations contribute to further the study of control systems described by retarded FDE.;For finite dimensional case, the following problems are investigated by using the abstract formulation: (i) optimal control with delay in quadratic cost, (ii) infinite-time quadratic optimal control, (iii) optimal state estimation with delay in observation, and (iv) stochastic control with quadratic cost.