Nonlinear Exosystems Research Articles

Output regulation of linear systems with non-linear exosystems

This paper deals with output regulation with non-linear exosystems. The dynamic system itself is assumed to be linear. Non-linear observer design techniques are exploited for the internal model design. A new strategy for internal model design is proposed, based on a dynamic extension of the existing non-linear observer design for the non-linear exosystem. Additional filters are used to estimate the invariant manifold in the state space subject to the non-linear exosystem. The proposed design for the internal model and control ensures that the state variable asymptotically converge to the invariant manifold, which implies that the regulated output state asymptotically converge to zero.

Rejection of Nonharmonic Disturbances in Nonlinear Systems With Semi-Global Stability

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> An asymptotic rejection algorithm is proposed for nonlinear dynamic systems under nonharmonic periodic disturbances generated from nonlinear exosystems. The dynamic systems considered in this brief are in the normal form, a larger class of nonlinear dynamic systems than the output feedback systems. A new internal model design method is used to exploit the nonlinearities in the exosystem, together with high gain design to achieve asymptotic rejection of nonharmonic disturbances with the guaranteed semi-global stability of the overall system. An illustrative example demonstrates that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit. </para>

Adaptive rejection of non-linear disturbances in extended non-linear output feedback systems

This paper deals with asymptotic rejection of disturbances generated from non-linear exosystems for uncertain nonlinear systems in an extended output feedback form, which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements. A new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance. Adaptive control techniques are then used to deal with the uncertainty in the system. The proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown nonlinear disturbance and the boundedness of all the variables.

Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems

This paper deals with global output regulation with nonlinear exosystems for a class of uncertain nonlinear output feedback systems. The circle criterion is exploited for the internal model design to accommodate the nonlinearities in the exosystems, and the explicit conditions are given for the exosystems such that the proposed internal model design can be applied. The uncertainties of the output feedback systems are in the form of unknown constant parameters, and adaptive control techniques are used to ensure the global stability of the proposed control design for output regulation.

Output Regulation of Uncertain Nonlinear Systems With Nonlinear Exosystems

An adaptive control algorithm is proposed for output regulation of uncertain nonlinear systems in output feedback form under disturbances generated from nonlinear exosystems. A new nonlinear internal model is proposed to generate the desired input term for suppression of the disturbances. The proposed internal model design is based on boundedness of the disturbance, high gain design and saturation. It is capable to tackle disturbances in any specified initial conditions. Some uncertainties in the systems are allowed, provided that they do not affect the desired feedforward control term, and they are tackled by using nonlinear dominant functions and an adaptive control coefficient. The proposed control algorithm ensures the global convergence of the state variables to the invariant manifold, which implies that the measurement or the tracking error approaches to zero asymptotically.

Robust output regulation with nonlinear exosystems

For over a decade, the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neutrally stable. Thus, the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions. In this paper, we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems. An example with the well known van der Pol oscillator as the exosystem is given to illustrate our approach.