This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory...

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neuralnetwork learning to a linear quantum Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter. In this paper, we present a bidirectional quantum associative memory model f...

Whereas stable linear systems with inputs have a unique steady-state solution, which is independent on the initial conditions and only depends on the input signals, nonlinear systems in general do not possess this property. Due to the lack of this property it is often hard to evaluate the exact behavior of the system, and thus to evaluate the ‘exact’ performance. In this article we present the ...

An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete necessary conditions for optimality are derived, and an efficient computational approach is proposed to solve the resulting two point boundary value problem. The us...

The Cahn–Hilliard equation plays an important role in the phase separation in a binary mixture. This is a fourth order nonlinear partial differential equation. In this paper, we study the behaviour of the solution by using orthogonal cubic spline collocation method and derive optimal order error estimates. We discuss some computational experiments by using monomial basis functions in the spatia...

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The ...

This paper focuses on the design of robust vision based control of a 2-DOF planar manipulator. The controller is expressed in the image space, where the system can be modeled as a pure integrator with a nonlinear matrix gain. It involves a simple proportional controller with a feedforward velocity input. Robustness is provided by the guarantee of a bounded tracking error, thanks to the online c...

Lyapunov stability of fractional differential equations is addressed in this paper. The key concept is the frequency distributed fractional integrator model, which is the basis for a global state space model of FDEs. Two approaches are presented: the direct one is intuitive but it leads to a large dimension parametric problem while the indirect one, which is based on the continuous frequency di...

A novel adaptive nonlinear controller based on backstepping with integrator is proposed for motion control systems. Backstepping is a practical nonlinear control scheme based on Lyapunov design approach, which can therefore guarantee the convergence of the position tracking error to zero. We utilize the integral action in the backstepping to increase control action in the steady state against t...