Zhengtao Ding

Global stabilization and disturbance suppression of a class of nonlinear systems with uncertain internal model

This paper deals with global stabilization and disturbance suppression of a class of nonlinear systems using output feedback. The disturbances generated from a unknown linear exosystem are completely compensated. The order of the exosystem is assumed known and the eigenvalues are distinct. No other assumptions are needed in the control design. This means that the proposed control design is able to completely compensate the disturbances without knowing their amplitudes, frequencies and phases, as long as the number of different frequency components in the disturbances is known. A new formulation of state estimation is introduced to ensure the global stabilization and complete disturbance suppression. Adaptive control technique is used to design an adaptive internal model based on a recently introduced formulation of unknown exosystems and the parameters in the adaptive internal model converge to the actual values, from which the unknown disturbance frequencies can be calculated. In the proposed control design, a number of control coefficients are made adaptive so that the result is global with respect to unknown frequencies in the disturbances.

Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems

This technical note deals with consensus output regulation of network connected multi-agent systems. Every agent or subsystem is a nonlinear system in the output feedback form with relative degree one, but subsystems may have different dynamics in terms of different nonlinear functions and even different system orders. The subsystem dynamics are influenced by state variables generated from an exosystem. The outputs of the subsystems are required to follow a desired trajectory which is a function of the exosystem state. Only some subsystems have access to the desired trajectory, and the other subsystems will have to rely on the exchange of information through the network. In this technical note, a consensus control design is proposed to ensure that the outputs of all the subsystems converge to the same desired output trajectory by exploiting the internal model design strategy. The proposed control design only uses the relative outputs of the subsystems, and does not require the estimation of subsystem state variables.

Universal disturbance rejection for nonlinear systems in output feedback form

This note deals with global disturbance rejection via output feedback of a class of uncertain nonlinear systems subject to a class of unknown disturbances. Both the uncertainty in the system model and the uncertainty in the exosystem are tackled concurrently. The disturbances generated from an unknown linear exosystem are completely rejected. The order of the exosystem is assumed known, and the eigenvalues are distinct. The system is assumed in the format of the minimum-phase output feedback form, with no knowledge of the values of any system parameters, including the high-frequency gain. No other assumptions are needed in the control design. A new set of filters are introduced for state estimation. The stability of the internal model is exploited to design a new auxiliary error, involving both the unknown parameters of the reformatted exosystem and those of the system, which makes it possible to group all the unknown parameters in a format suitable to adaptive control design. A Nussbaum gain is introduced in adaptive control design to tackle the unknown high-frequency gain and a number of control coefficients are also made adaptive so that the disturbance rejection is global with respect to unknown frequencies in the disturbances.

Brief Global output regulation of uncertain nonlinear systems with exogenous signals

The paper addresses the global output tracking of a class of uncertain output feedback systems affected by disturbances which are generated from a known exosystem. The system uncertainty is parametrized by a unknown parameter vector, which is absorbed in the parametrization of disturbances. A controller based on the estimation of states and disturbances from the output is designed using backstepping to asymptotically track arbitrary trajectories and to guarantee the boundedness of all other variables. The proposed control algorithm provides an alternative with global tracking to structurally stable regulation of nonlinear output feedback systems. It can also be viewed as a generalization to adaptive control algorithms.

Adaptive control of non-linear systems with unknown virtual control coefficients

This paper deals with state feedback adaptive control of parametric-strict-feedback (triangular) non-linear systems with unknown virtual control coefficients. A priori knowledge of the signs of the virtual coefficients is not required, and control signals and adaptive laws are smooth. Asymptotic tracking of smooth reference signals is achieved while all the variables remain bounded. The proposed algorithms make use of backstepping and tuning functions, and enlarge the class of non-linear systems with unknown parameters for which asymptotic output tracking can be achieved. Copyright (C) 2000 John Wiley & Sons, Ltd.

Brief paper: 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.

Decentralised power system load frequency control beyond the limit of diagonal dominance

The design of decentralised robust load frequency control for interconnected multi-area power systems is studied in this paper. It is shown that although the design can be naturally formulated as a large-scale system decentralised control problem, it can be translated into an equivalent problem of decentralised controller design for a multi-input multi-output (MIMO) control system. It is known that simple controllers can be designed to achieve satisfactory performances if diagonal dominance can be achieved in a multivariable system. This is further extended in this paper. Using the design method proposed in this paper, even when the diagonal dominance cannot be achieved, subject to a condition based on the structured singular values (SSVs), each local area load-frequency controller can be designed independently. The robust stability condition for the overall system can be easily stated as to achieve a sufficient interaction margin, and a sufficient gain and phase margin during each independent design.

Adaptive consensus output regulation of a class of nonlinear systems with unknown high-frequency gain

This paper deals with adaptive consensus output regulation of a class of network-connected nonlinear systems with completely unknown parameters, including the high frequency gains of the subsystems. The subsystems may have different dynamics, as long as the relative degrees are the same. A new type of Nussbaum gain is proposed to deal with adaptive consensus control of network-connected systems without any knowledge of the high frequency gains. Adaptive laws and internal models are designed for the subsystems to deal with unknown parameters for tracking trajectories and unknown system parameters. In the control design, only the relative information of subsystem outputs are used, provided that regulation error of one of the subsystems is available. The proposed control inputs and the adaptive laws are decentralized. If the relative degree is one, only the relative subsystem outputs are exchanged. For the case of higher relative degrees, the nonlinear model structure of the subsystems is exploited for backstepping control design, and some variables generated by the subsystem controllers are exchanged among the subsystems in the neighbourhood defined by the connection graph.

Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high-frequency gains

This paper presents an algorithm for adaptive output feedback stabilization of nonlinear single-input/single-output, minimum phase systems of any relative degree which are linear with respect to input and unknown constant parameter vector. The algorithm does not require the knowledge of the sign of the high-frequency gain.

A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains

This note deals with adaptive control of perturbed nonlinear output feedback systems with unknown high-frequency gains. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. A flat-zone modification is proposed to incorporate both the bound estimation and Nussbaum gain design in the nonlinear adaptive control. To ensure the differentiability of stabilizing functions needed for backstepping design, high order terms are introduced in the Lyapunov function candidate with a flat zone around the neighborhood of the origin. The output tracking error converges to an arbitrarily small interval around zero.