Method for solving a boundary problem for a nonlinear control system with incomplete information

An easy-to-implement numerical method is proposed for synthesizing a feedback control function that transfers a wide class of nonlinear stationary systems from an initial state to a given terminal state with allowance for measured data. A constructive criterion is obtained for choosing terminal states for which this transfer is guaranteed. The problem of an interorbital flight is considered and numerically simulated.     

Chaotic synchronization by the intermittent feedback method

This paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient. A sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a Lyapunov function and differential inequalities. Numerical simulations for the chaotic Chua oscillator are presented to illustrate the theoretical results.     

A general result in stochastic optimal control of nonlinear discrete-time systems with quadratic performance criteria

It is known that the optimal controller for a linear dynamic system disturbed by additive, independently distributed in time, not necessarily Gaussian, noise is a linear function of the state variables if the performance criterion is the expected value of a quadratic form. This result is known to hold also when the noise is Gaussian and is multiplied by a linear function of the state and/or control variables.In this paper it is proved that the optimal controller for a discrete-time linear dynamic system with quadratic performance criterion is a linear function of the state variables when the additive random vector is a nonlinear function of the state and/or control variables and not necessarily Gaussian noise which is independently distributed in time, provided only that the mean value of the random vector is zero (there is no loss of generality in assuming this) and the covariance matrix of the random vector is a quadratic function of the state and/or control variables. The above-mentioned known results emerge as special cases and certain nonlinear other special cases are exhibited.     

Robust stabilization of discrete-time nonlinear Lur’e systems with sector and slope restricted nonlinearities

In this paper, we present a novel method for the robust control problem of uncertain nonlinear discrete-time linear systems with sector and slope restrictions. The nonlinear function considered in this paper is expressed as convex combinations of sector and slope bounds. Then the equality constraint is derived by using convex properties of the nonlinear function. A stabilization criterion for the existence of the state feedback controller is derived in terms of linear matrix inequalities (LMIs) by using Finsler’s lemma. The proposed method is demonstrated by a system with saturation nonlinearity.     

Solution of the control problem for a linear descriptor system with rectangular coefficient matrix

We pose a control problem for linear stationary algebro-differential system whose coefficients are rectangular matrices. We obtain a controllability criterion for the partially given output function and the boundary values of the state function. We construct a control function and a state function under minimal smoothness requirements on the output function.     

Identification of non-minimum phase transfer function using higher-order spectrum

The present paper treats the identification of parametric nonminimum phase transfer function. We propose a method of identification based on the inner outer factorization of stable transfer function. It consists of identifying the outer and inner parts of a transfer function separately. The outer part is identified by the use of the second-order spectral estimate from the observed linear process, while the inner part is identified by the use of a higher-order cumulant spectral estimate from the observed process. Respective parameter estimators are determined in the light of asymptotic efficiency. In order to estimate the order of the inner part of a transfer function, a criterion is proposed. It is introduced based on the same principle as in the case of Akaike's AIC.     

Continuous time Markovian decision processes average return criterion

Continuous time Markovian decision models with countable state space are investigated. The existence of an optimal stationary policy is established for the expected average return criterion function. It is shown that the expected average return can be expressed as an expected discounted return of a related Markovian decision process. A policy iteration method is given which converges to an optimal deterministic policy, the policy so obtained is shown optimal over all Markov policies.     

确定聚类数目的一个准则

Aiming to provide an appropriate number K of clusters, in this paper, we propose a new criterion function - H criterion function, whose three properties have also been proved. We validate the performance of the H criterion function on one artificial dataset and three real-world datasets, and the results are almostly consistent with a previous method. The nonparametric criterion we proposed is intuitive, simple and the computational cost is acceptable.     

Bendixson-Dulac criterion and reduction to global uniqueness in the problem of estimating the number of limit cycles

For autonomous systems on the real plane, we develop a regular method for localizing and estimating the number of limit cycles surrounding the unique singular point. The method is to divide the phase plane into annulus-shaped domains with transversal boundaries in each of which a Dulac function is constructed by solving an optimization problem, which permits one to use the Bendixson-Dulac criterion. We state the principle of reduction to global uniqueness and use it in the case of existence of an Andronov-Hopf function of limit cycles to obtain a sharp global estimate of the number of limit cycles for an individual system as well as for a one-parameter family of such systems in an unbounded domain.     

A note on solving nonlinear equations and the natural criterion function

We consider the natural criterion function for controlling a damped Newton iteration used for solving systems of nonlinear equations. An example is given which shows that the method can cycle in an undesirable manner, not possible when using the more conventional least-squares criterion function. Despite this, the natural criterion function is of value in particular applications. This point is illustrated using a system derived from a nonlinear two-point boundary-value problem.     

Systems of control over set-valued trajectories with terminal quality criterion

We consider the optimal control problem with terminal quality criterion in which the state of a system is described by a set-valued mapping, and an admissible control is a summable function. We describe an algorithm that approximates the admissible control function by a piecewise-constant function and prove theorems on the closeness of the corresponding trajectories and the values of quality criteria.     

Parametric vs. divisor methods of apportionment

This paper formulates a new criterion that distinguishes the set of parametric methods within the set of all the divisor methods of apportionment. The criterion—that a method transfer seats as it “should”—asks that as population (or the votes of parties in a PR system) is shifted more and more from one state to another state (from one party to another party) at some point the first state (or party) is apportioned one less seat, the second state (or party) one more seat, and the remaining apportionments are as they were. It goes on to examine several properties of parametric methods.     

Stochastic optimization of forward recursive functions

This note solves a finite-horizon stochastic optimization problem with forward recursive criterion through dynamic programming. The forward recursive criterion is wide; it includes additive (discounted), multiplicative (discounted risk-sensitive), minimum and terminal criteria. The basic idea is to apply invariant imbedding method for the stochastic optimization. The method incorporates recursive accumulation process into dynamics by expanding the original state space.     

Optimal boundedness criteria for extended-real-valued functions

The notion of genuinely bounded below function is introduced and characterized by means of the concept of co-equilibrated function. As an application, we state two boundedness criteria for extended-real-valued functions, both optimal in a clearly defined sense. The first one says that an extended-real-valued function minorized by an affine map and coinciding from some value up with a co-equilibrated function is bounded below. The second criterion states that an extended-real-valued function minorized by an affine map is bounded below provided that one of its sub-level sets is co-equilibrated.     

Finite approximation for finite-horizon continuous-time Markov decision processes

In this paper we study the continuous-time Markov decision processes with a denumerable state space, a Borel action space, and unbounded transition and cost rates. The optimality criterion to be considered is the finite-horizon expected total cost criterion. Under the suitable conditions, we propose a finite approximation for the approximate computations of an optimal policy and the value function, and obtain the corresponding error estimations. Furthermore, our main results are illustrated with a controlled birth and death system.     

Robust guaranteed cost control for uncertain linear differential systems of neutral type

In this paper, the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated. The uncertainty is assumed to be norm-bounded and time-varying nonlinear. The problem is to design a state feedback control laws such that the closed-loop system is robustly stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay. A criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the Lyapunov method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.     

A method for solving a boundary problem for a nonlinear controlled system

An algorithm is proposed for constructing a control function that transfers a wide class of nonlinear systems of ordinary differential equations from an initial state to an arbitrarily small neighborhood of a given terminal state. The algorithm is convenient for numerical implementation. Taking into account the restrictions on the control and phase coordinates, a constructive criterion is obtained for choosing terminal states for which this transfer is possible. The problem of an interorbital flight is considered and modeled numerically.     

An extensive-form analysis for comparing fuzzy information systems by means of the worth and quietness of information

Statistical decision problems deal with the choice among several actions, whose consequences depend upon the state of nature, and this choice is usually made on the basis of the outcome of an experiment selected from a collection of experiments whose probability measures depend upon the state. The selection criteria among the experiments are generally based on some measures of the information contained in each experiment about that true state.In this paper we suggest a new selection criterion among the experiments associated with a statistical decision problem, when the experimental outcomes cannot be exactly perceived by the decision maker, but rather the available information from each experimental outcome can be regarded as an element in a fuzzy information system (as defined by Tanaka, Okuda and Asai).In a previous paper we have proposed a method for comparing fuzzy information systems on the basis of the maximization of the ‘oworth of information of a fuzzy park information system’ (Tanaka et al). When the application of such a method leads to indifference between two fuzzy information systems, this indifference can be avoided by applying the criterion in this paper.This selection criterion is an extensive-form analysis which is based on two measures of the information contained in a fuzzy information system about the true state: the ‘worth of information of a fuzzy information system’ and the ‘expected quietness of information of a fuzzy information system’.The suitability of the criterion stated above is corroborated by studying its main properties and contrasting this procedure with other ones making use of different measures of information.