Raju K. George

Controllability of nonlinear systems

In this paper we obtain global controllability of a semilinear system involving monotone nonlinearities of both Lipschitzian and non-Lipschitzian types.

Estimation of Controllable Initial Fuzzy States of Linear Time-Invariant Dynamical Systems

In this paper, we consider linear time-invariant dynamical systems with fuzzy initial condition. Dynamics of such systems is given by linear time-invariant fuzzy differential equations. First, we discuss the evolution of solution to such fuzzy differential dynamical systems and also establish the existence and uniqueness of the solution. We then provide an estimate of initial fuzzy state that can be controlled to a predefined target fuzzy state, that is, given any two crisp states x0, x1 in ℝ n , and a fuzzy state X1 around x1, we compute a fuzzy state X0 around x0 so that X0 is fuzzy-controllable to X1. In a special case, when the plant matrix has non-negative entries, the fuzzy state X0 is fuzzy-controllable to X1 with the crisp control that steers x0 to x1. Examples are given to substantiate the results obtained.

Exact Controllability of a Semilinear Thermoelastic System

Abstract In this paper, we obtain the exact controllability of a semi-linear thermo-elastic system described by the partial differential equations: with Dirichlet boundary conditions when the Lipschitz constants of the non-linearities f and g are small.

Controllability of impulsive matrix Lyapunov systems

In this paper, we establish some sufficient conditions for the complete controllability of linear and semilinear impulsive matrix Lyapunov systems. For the semilinear systems, we assume that nonlinearities are Lipschitz type or monotone type. Few illustrative examples are given to compare and substantiate the results of the paper.

Trajectory controllability of fractional dynamical systems

AbstractIn this paper, we discuss the trajectory controllability of linear and nonlinear fractional dynamical systems represented by the fractional differential equations in the sense of Caputo fractional derivative by using the Mittag–Leffler function and Gronwall–Bellman inequality. For the nonlinear system, we assume Lipschitz-type conditions on the nonlinearity. Examples are given to illustrate the theoretical results.

On the Controllability of Linear and Semilinear Impulsive Systems

ABSTRACT In this paper, we establish some sufficient conditions for the complete controllability of linear and semilinear impulsive systems. For the semilinear systems, we assume that nonlinearities are Lipschitzian type. We invoke the tools of nonlinear functional analysis and fixed point theorems to establish the results. The results are also compared with the existing results in the literature in order to show the effectiveness of the results obtained. Few illustrative examples are provided to substantiate the results.

Ordinary differential equations : principles and applications

Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke readers interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

Functional approach to observability and controllability of linear fractional dynamical systems

Abstract In this paper, a set of equivalent conditions for observability and controllability of linear fractional dynamical systems represented by the fractional differential equation in the sense of Caputo fractional derivative of order α ϵ (0,1] are established by using the tools of linear bounded operators. Examples are included to illustrate the theoretical results.

Identification of an unknown coefficient in KdV equation from final time measurement

Abstract In this article, we study an inverse problem of reconstructing a space dependent coefficient in a generalized Korteweg–de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework and existence of a minimizer for the cost functional is established. Then we prove a stability estimate for retrieving the unknown coefficient in KdV equation with the upper bound of given measurements. The local uniqueness of the coefficient is also discussed.

On the controllability of a class of nonlinear stochastic systems

We study the controllability properties of the class of stochastic differential systems characterized by a linear controlled diffusion perturbed by a bounded Lipschitz nonlinearity. We obtain conditions that guarantee the weak and strong controllability of the system. Also, given any open set in the state space we construct a control such that the hitting time of the set has a finite expectation with respect to all initial conditions.