Showing papers by "Kumpati S. Narendra published in 1971"

A two-level system of stochastic automata for periodic random environments

Abstract: A class of nonstationary environments with unknown but periodically changing probabilistic characteristics is considered. It is proposed to optimize the performance in an environment from this class by using a two-level system of variable-structure stochastic automata. The first level estimates the unknown period while the second level operates suitably in the environment for one cycle assuming that this estimate is the true period of the environment. The average output of the environment in this cycle is used as the input to the first level to determine the next estimate of the period. The optimal performance of this two-level system of automata in periodic random environments is demonstrated through computer simulations.

Reachable Sets for Linear Dynamical Systems

Abstract: The properties of reachable sets for linear dynamical systems for specified control sets are discussed. Iterative procedures for determining numerical approximations of the reachable set are suggested and methods of obtaining an admissible control function which transfers an initial state to as near a prescribed target as possible is described. The problem of reachability with multiple control constraints is discussed and certain aspects of reachability for time-invariant systems with adjustable parameters is considered.

On Variable-Structure Stochastic Automata

Abstract: A stochastic automaton with a variable structure (SAVS) may be described by the sextuple {X, Φ, α, p, U, G} where X={x0, x1,⋯,xk} is the input set, Φ = {Φ1, Φ2,⋯,Φs} is the internal state set, α = {α1, α1,⋯,αr} with r ≤ s is the output or action set, p is the state probability vector (i.e., at stage or time instant n, p(n) = (p1(n), p2(n),⋯,ps(n)) governing the choice of the state, U is an updating scheme which generates p(n + 1) from p(n) and G:Φ → α is the output function. In general, G may be a stochastic function. In this paper it is assumed that G is deterministic and one-to-one (i.e., r = s), k = 1 and s < ∞.

Adaptive Control Using Lyapunov's Direct Method.

Abstract: : The main aim of the report is to make transparent most of the interesting ideas involved in the design of adaptive systems using the direct method of Lyapunov, by considering primarily systems described by first-order differential equations. A study is made of three adaptive designs for such systems. (Author)