Nonlinear Volterra Integrodifferential Systems Research Articles

A modified teaching–learning-based optimization for optimal control of Volterra integral systems

This study aimed to utilize a novel modified approach based on teaching–learning-based optimization (MTLBO), to achieve an approximate solution of optimal control problem governed by nonlinear Volterra integro-differential systems. The scheme was based upon Chebyshev wavelet and its derivative operational matrix, which eventually led to a nonlinear programming problem (NLP). The resulted NLP was solved by the MTLBO. The novel algorithm used a heuristic mechanism to intensify learning on the best students in learner phase. The new strategy was applied to improve learners’ knowledge and to structure the MTLBO. The applicability and efficiency of the MTLBO were shown for three numerical examples. The proposed algorithm was compared with the traditional TLBO algorithm and the Legendre wavelets and collocation method in the literature. The experimental results showed that the proposed MTLBO not only obtained the high-quality solutions with respect to the absolute errors but also provided results with the high speed of convergence.

Ψ-Stability of Nonlinear Volterra Integro-Differential Systems with Time Delay

We give some sufficient conditions forΨ-uniform stability of the trivial solutions of a nonlinear differential system and of nonlinear Volterra integro-differential systems with time delay.

Comparison Theorems for Controllability of Nonlinear Volterra Integrodifferential Systems

Sufficient conditions are derived for controllability of nonlinear Volterra integrodifferential systems. Here the controllability problem is transformed into a fixed point problem for some operator with the help of the notion of the comparison principle and the results are obtained by using the Schauder fixed point theorem.

On 0-stability for nonlinear Volterra integrodifferential systems

0-stability and Lipschitz 0-stability notions of ordinary differential equations (ODEs) are introduced. In this paper, we extend these notions to systems of integro-differential equations (IDEs) and give some criteria of these notions. Our technique depends on Liapunov's direct method.

Controllability of nonlinear Volterra integrodifferential systems with prescribed controls

Sufficient conditions for the global controllability of nonlinear Volterra integrodifferential systems with prescribed controls are derived. The method is a transformation of the given control system into a boundary value problem and then the result is obtained by the application of the Schaefer fixed point theorem.

Lipschitz stability for nonlinear volterra integrodifferential systems

Unlike uniform stability, the linearized system inherits the property of uniform Lipschitz stability from its original nonlinear system. In this paper we investigate sufficient conditions for uniform Lipschitz stability of nonlinear integro-differential systems through their associated variational systems.

Nonlinear Volterra integrodifferential systems with L 1-kernels

Nonlinear Volterra integrodifferential systems with L 1-kernels