Abstract: The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results ...

Abstract: The purpose of this paper is to formulate, study, and (in certain cases) resolve the Inverse Problem of Optimal Control Theory, which is the following: Given a control law, find all performance ...

Abstract: A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this “variance equation” completely specifies the optimal ...

Abstract: The second method of Lyapunov is applied to the study of discrete-time (sampled-data) systems. With minor variations, the discussion parallels that of the companion paper on continuous-time ...

Abstract: The “second method” of Lyapunov is the most general approach currently in the theory of stability of dynamic systems. After a rigorous exposition of the fundamental concepts of this theory, ...