Transfer function conditions for output feedback disturbance rejection

A recent paper [1] has derived state space conditions under which the disturbance transfer function in a linear multivariable system can be zeroed by a dynamic compensator forced by a prescribed set of measurements. The present note derives necessary conditions for this problem in terms of the orders of the open-loop control, disturbance, and measurement transfer functions. These necessary conditions are shown to be generically sufficient for solvability. Moreover, they provide additional insight into the geometric solvability conditions, are simple to check, and extend the corresponding results obtained for the state feedback case [2].     

Passivity and disturbance attenuation via output feedback foruncertain nonlinear systems

The authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties. The problem is approached by means of adaptive output feedback control which does not require any state observer. The results obtained extend an earlier result of Steinberg and Corless (1985). Sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback     

Feedback passivity approach to output feedback disturbance attenuation for uncertain nonlinear systems

The problem of output feedback disturbance attenuation for a class of uncertain nonlinear systems is studied based on output feedback passification. Previous work on output feedback disturbance attenuation is extended to the case where (1) the nominal system is not transformable into the normal form and (2) the uncertainty is parameterized nonlinearly. An adaptive output feedback controller is also provided that makes a nonlinear system passive. The paper then considers the output feedback disturbance attenuation problem for a class of uncertain nonlinear systems in the normal form and of relative degree one. The difference is that the result is applicable to nonlinear systems that include the uncertainty in the input matrix and do not satisfy the matching condition.     

Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form

A global output feedback dynamic compensator is proposed for stabilization and tracking of a class of systems that are globally diffeomorphic into systems which are in generalized output-feedback canonical form. This form includes as special cases the standard output-feedback canonical form and various other forms considered previously in the literature. Output-dependent nonlinearities are allowed to enter both additively and multiplicatively. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced-order observer and a backstepping controller can be designed to achieve asymptotic tracking. For the special case of linear systems, the designed dynamic controller reduces to the standard reduced-order observer and linear controller. This is the first global output-feedback tracking results for this class of systems.     

Optimal disturbance rejection for nonlinear control systems

The problem of optimal disturbance rejection for a general class of multiinput/multioutput (MIMO) nonlinear systems, achieved over a set of stabilizing compensator operators, is formulated in a Banach space setting. Conditions on the operators are imposed on the basis of the inputs as well as the outputs. An existence theorem for optimal solutions is established under some realistic and verifiable conditions. For solving the optimization problem, a generalized recursive nonlinear programming algorithm is passed, and a simple example of nonlinear optimal feedback design is given to show that the problem can be reduced to standard min-max optimization and is hence solvable     

On nonlinear state feedback controllers for persistent disturbance rejection

An l₁-optimal linear time-invariant (LTI) compensator may have an order significantly higher than that of the plant. In the state feedback case, there has been recent work exploring the use of nonlinear static feedback controllers which provide near optimal performance. In the case of D₁₂ square and invertible, we show that it is enough to have the nonlinearity on a particular substate, which can be used to significantly simplify the design problem.     

A note on global output regulation of nonlinear systems in the output feedback form

This note shows how the adaptive control method developed recently for nonlinearly parameterized systems can be used to solve the problem of global output regulation, for nonlinear systems in the so-called output-feedback form with unknown parameters and exogenous signals belonging to a compact set whose bound is also unknown.     

Robust disturbance attenuation of nonlinear systems using output feedback and state-dependent scaling

This paper presents an approach to output feedback stabilization with disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties. A new formulation of state-dependent scaling is introduced into the output feedback design, which unifies treatment of nonlinear and linear gains. The effect of disturbance on the controlled output, which is allowed to be any function of output measurements, can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear-gains. The uncertain dynamics is not limited to input-to-state stable systems either. The approach is not only a natural extension of popular approaches in robust linear control, but also advantageous to numerical computation which is applicable to non-triangular systems as well as triangular systems.     

Output feedback disturbance decoupling in nonlinear systems

The problem of disturbance decoupling by means of output feedback is addressed. The notion of conditioned invariance is reconsidered in a linear algebraic framework. Using this geometric notion, a necessary and sufficient condition (respectively, necessary condition) is obtained for solving the disturbance decoupling problem by quasi-static output feedback (respectively, the disturbance decoupling problem by dynamic output feedback (DDDPO)). The necessary conditions for DDDPO which are derived are weaker than the existing ones, a sufficient condition for the disturbance decoupling problem by static output feedback is given as well     

Output feedback control with disturbance rejection of a class of nonlinear MIMO systems

Output feedback control with disturbance rejection is developed for a class of nonlinear multi-input-multi-output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance. In the design of an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. The control methodology is robust to bounded disturbances that are both constant and time-varying, with effective performance. The adaptive laws are derived based on the Lyapunov synthesis method; therefore closed-loop asymptotic stability is also guaranteed. Moreover, chattering can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed controller. The text was submitted by the authors in English.     

Universal adaptive control of nonlinear systems with unknown growth rate by output feedback

This paper investigates the problem of global stabilization by output feedback, for a family of uncertain nonlinear systems without zero dynamics. These nonlinear systems are dominated by a triangular system satisfying linear growth condition. In contrast to the previous work in the literature, the growth rate here is a positive constant but not known a priori, and therefore the problem becomes more involved and difficult. Using the idea of universal control combined with the output feedback design method developed in Qian and Lin (2002, 2003), we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the uncertain systems without knowing the growth rate.     

Quantised and sampled output feedback for nonlinear systems

In this paper we consider the analysis and design of an output feedback controller for a perturbed nonlinear system in which the output is sampled and quantised. Using the attractive ellipsoid method, which is based on Lyapunov analysis techniques, together with the relaxation of a nonlinear optimisation problem, sufficient conditions for the design of a robust control law are obtained. Since the original conditions result in nonlinear matrix inequalities, a numerical algorithm to obtain the solution is presented. The obtained control ensures that the trajectories of the closed-loop system will converge to a minimal (in a sense to be made specific) ellipsoidal region. Finally, numerical examples are presented in order to illustrate the applicability of the proposed design method.     

Adaptive tracking and disturbance rejection for uncertain nonlinear systems

This note addresses the problem of asymptotic tracking of arbitrary smooth bounded reference output signals, with simultaneous rejection of disturbances generated by an unknown linear exosystem. The problem is globally solved by output feedback for the class of nonlinear systems with output dependent nonlinearities and unknown linear parameters, under the assumptions that the system is minimum phase and the relative degree, an upper bound on the system order, the sign of the high-frequency gain are known.     

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

Asymptotic output tracking through singular points for nonlinear systems: Stability,disturbance rejection and robustness

The problem of output tracking in the presence of singularities started by Hirschorn and Davis (1987)² is reexamined. A transformation which allows us to make a study of the closed-loop stability of the nonlinear system is proposed. An error feedback control law relaxes the initial conditions imposed on the system and the function to be followed, obtaining asymptotic output tracking. A study of the singular tracking problem, when there exist disturbances or uncertainties in the dynamics, is also made. Again a stability analysis is carried out. Finally, the results obtained for the SISO case, to the MIMO case are extended.     

Limitations of disturbance rejection in feedback systems withfinite bandwidth

Studies limitations of disturbance rejection in closed-loop control systems. The disturbance is modeled as colored noise, and disturbance rejection is measured by the output variance. Lower bounds on the achievable output variance are derived under several practical constraints, the main one being a bound on the system bandwidth; constraints on the stability robustness (measured by the distance from the Nyquist plot to the critical point) and the ability to track low-frequency reference signals (measured by the sensitivity reduction at low frequencies) are also considered. The bounds are derived by finding the sensitivity function that minimizes the output variance. This optimization is performed subject to the above constraints and, in addition, subject to certain sensitivity integral constraints that arise because of closed-loop stability. The utility of the results is illustrated by analyzing the achievable level of passenger comfort in an aircraft subjected to turbulence     

Global practical tracking via disturbance rejection control for uncertain nonlinear systems with quantized input and output

Dear editor, With the rapid development of digital control systems and other fields,quantized control has attracted increasing at-tention[1].Although considerab...     

Asymptotic rejection of finite frequency modes of general periodic disturbances in output feedback nonlinear systems

This paper deals with asymptotic rejection of individual frequency modes in nonlinear systems under general periodic disturbances. An iterative observer design is proposed for disturbance estimation, and it is shown that the proposed observer design successfully extracts individual frequency modes from general periodic disturbances. The proposed iterative observer design is then applied to asymptotic rejection of nonlinear systems under general periodic disturbances.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.