Nonlinear System Analysis and Synthesis. Part II. Study of the Lur'e Problem and of Stochastic Optimal Control

摘要

Research was mainly concerned with: (a) The construction of Lyapunov functions by machine methods, especially as regards the so-called problem of Lur'e. (b) The formulation of stochastic optimization problems. Research topics presented in this report are: General Discussion; On the absolute stability of sampled-data control systems; On the absolute stability of a system of finite difference equations; On the absolute stability of a nonlinear sampled-data system; Irreducible realizations and the degree of a matrix of rational functions; Resolution of the Problem of Lur'e; General Discussion; Near Optimal control in the presence of small stochastic perturbations; On the differential equations satisfied by conditional probability densities of Markov processes, with applications; On the stochastic maximum principle; fixed-time of control; A 'time-domain' successive approximation method for some linear optimal stochastic systems. (Author)