the stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. this paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (mdnn) and studies the stability of this algorithm. also, stable learning algorithm for parameters of ...

Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. We derive an upper bound on the norm of the error of network states from its average states, which it achieves in finite time. Then, we devise a decentralized compensator to asymptotically pin the network of mismatched systems to a desired trajectory. Next, we design distributed estima...

To compensate for heave motion, which has an adverse impact on the response of a drill-string or a riser, passive and active devices are usually used. Active heave compensators, whose control system is an essential part, allow conducting operations under more extreme weather conditions than passive ones. This paper presents a constructive method to design a nonlinear controller for an active he...

We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Well-known stability concepts of ordinary differential equations are generalised to DAEs and characterised. Lyapunov’s direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs, which are transferable into standard canonical form; in this case t...

A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d . 4 the cascade is always direct. For a small enough degree of compressibility, the cascade is direct again. Otherwise i...

This paper demonstrates the use of Lyapunov direct method in synchronizing two identical Lorenz-Stenflo (LS) systems, two identical Qi systems and two non-identical systems comprising the LS and Qi chaotic systems.The designed controllers enable the state variables of the slave system to globally synchronize with the state variables of the master system in both the identical and non-identical s...

We investigate global stability properties of a HIV/AIDS population model with constant recruitment rate, mass action incidence, and variable population size. Existence and uniqueness results for disease-free and endemic equilibrium points are proved. Global stability of the equilibria is obtained through Lyapunov’s direct method and LaSalle’s invariance principle.

A new method for designing multivariable model reference adaptive control system is presented. In many adaptive control approaches, at least the following two assumptions regarding the plant have to be made. (1) The number of plant poles and zeros is known. (2) The plant is the minimum phase. The proposed method can avoid these restrictions by using the adaptive controller designed for an autor...

Multiple model approach is a powerful tool for modelling nonlinear systems. Two structures of multiple models can be distinguished. The first structure is characterised by decoupled submodels, i.e. with no common state (decoupled multiple model), in opposition to the second one where the submodels share the same state (Takagi-Sugeno multiple model). A wide number of research works investigate t...