Lyapunov exponents and predictability of the tropical coupled ocean-atmosphere system

It has recently been proposed that the broad spectrum of interannual variability in the tropics with a peak around four years results from an interaction between the linear low-frequency oscillatory mode of the coupled system and the nonlinear higher-frequency modes of the system. In this study we determine the Lyapunov exponents of the conceptual model consisting of a nonlinear low-order model coupled to a linear oscillator for various values of the coupling constants.

Quadratic Lyapunov functions for linear systems Journal

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable sy

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.

A direct adaptive neural command controller design for an unstable helicopter

This paper presents an off-line (finite time interval) and on-line learning direct adaptive neural controller for an unstable helicopter. The neural controller is designed to track pitch rate command signal generated using the reference model. A helicopter having a soft inplane four-bladed hingeless main rotor and a four-bladed tail rotor with conventional mechanical controls is used for the simulation studies. For the simulation study, a linearized helicopter model at different straight and level flight conditions is considered. A neural network with a linear filter architecture trained using backpropagation through time is used to approximate the control law. The controller network parameters are adapted using updated rules Lyapunov synthesis. The off-line trained (for finite time interval) network provides the necessary stability and tracking performance. The on-line learning is used to adapt the network under varying flight conditions. The on-line learning ability is demonstrated through parameter uncertainties. The performance of the proposed direct adaptive neural controller (DANC) is compared with feedback error learning neural controller (FENC).

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

A Novel Approach for Designing Generator Excitation controllers Using the IDA-PBC Technique

This paper presents a novel approach for designing of generator excitation controllers using Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) technique for a Single Machine Infinite Bus (SMIB) system that can also be directly used in a multi-machine environment. The generator system equations are modified by referencing the rotor angle with respect to the secondary of the transformer bus instead of the infinite bus. For the modified system equations, IDA-PBC is applied to stabilize the system around an operating condition. The IDA-PBC design results in a Lyapunov function for the modified system. The new control law is practically feasible and can be applied directly to multi-machine system without referring to external system parameters. The effectiveness of the proposed controller is tested on a SMIB and a 10 generator 39 bus test system for a range of operating conditions. The Proposed excitation controller has shown good performance for both small and large disturbances when compared to the performance of a conventional static exciter with power system stabilizer.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Interval Data Classification under Partial Information: A Chance-Constraint Approach

This paper presents a Chance-constraint Programming approach for constructing maximum-margin classifiers which are robust to interval-valued uncertainty in training examples. The methodology ensures that uncertain examples are classified correctly with high probability by employing chance-constraints. The main contribution of the paper is to pose the resultant optimization problem as a Second Order Cone Program by using large deviation inequalities, due to Bernstein. Apart from support and mean of the uncertain examples these Bernstein based relaxations make no further assumptions on the underlying uncertainty. Classifiers built using the proposed approach are less conservative, yield higher margins and hence are expected to generalize better than existing methods. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle interval-valued uncertainty than state-of-the-art.

Anisochrony of O-methylene protons of ethyl ester functions and structural factors in the connected chiral entities

(i) Incistrans pairs of cyclic 1,3-dicarboxylic acid ethyl esters thecis-foms exhibit higher O-methylene proton (HA, HB) anisochrony than thetrans-forms; (ii) anisochrony, easily observed in certain decalin-10-carboxylic ethyl esters, ‘disappears’ on one of the rings attaining the possibility of transforming into a ‘twist’ form; (iii) in certain pairs of chiralsecethyl esters and theirtert-methylated analogues anisochrony is higher in the latter, contrary to expectation, while, in certain others, the reverse is observed. Attempted explanations are based on assessments whether H A and H B are or are not in highly different magnetic environments in confomers regarded as preferred. This subsumes the possibility thatXYZC-CO2H A H B Me chiral ethyl acetates differ fromXYZC-CH A H B Me ethanes because intervention by the carboxyl group insulates the prochiral centre and allows anisotropic effects to gain somewhat in importance among mechanisms that discriminate between H A and H B so long as rotamerpopulation inequalities persist. Background information on why rotamer-population inequalities will always persist and on a heuristic that attempts to generalize the effects ofXYZ inXYZC - CU AUB V is provided. Possible effects when connectivity exists between a pair amongX, Y, Z or when specific interactions occur betweenV andX, Y orZ are considered. An interpretation in terms of ‘increasing conformational mobility’ has been suggested for the observed increase in the rate of temperature-dependence of O-methylene anisochrony down a series of chiral ethyl esters.

Karnaugh map analysis and synthesis of threshold functions

A unate function can easily be identified on a Karnaugh map from the well-known property that it cons ist s only ofess en ti al prime implicante which intersect at a common implicant. The additional property that the plot of a unate function F(x, ... XII) on a Karnaugh map should possess in order that F may also be Ivrealizable (n';:; 6) has been found. It has been sh own that the I- realizability of a unate function F corresponds to the ' compac tness' of the plot of F. No resort to tho inequalities is made, and no pre-processing such as positivizing and ordering of the given function is required.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.