Adaptive Output Regulation for Nonlinear Systems with Unknown Periodic Disturbances

This paper deals with consensus output regulation of a class of network-connected nonlinear systems with unknown parameters. The subsystem may have different dynamics with uncertainties, and under the disturbances generated from an exosystem, and only some subsystems have access to the desired output, which is also formulated as an output of the exosystem, following the standard formulation of output regulation of nonlinear systems. For the clarity of the presentation, we only show the control design of the systems with 2nd-order dynamics. The proposed design makes use of some latest results on Laplacian matrices, and a new design of the internal model, which is based on known functions with unknown constant parameters. Adaptive backstepping design techniques are integrated with the consensus control design to tackle the nonlinearity and unknown constant parameters in the system, and unknown functions relating to the state of the exosystem. The proposed control inputs and adaptive laws are fully decentralized, and ensure the asymptotic convergence to zero of the regulation errors.

Adaptive wavelet output regulation for nonlinear systems

SummaryThe rejection of unknown periodic disturbances in the plant output through adaptive feedback has been an active area of research. In most successful efforts, it is assumed that the plant model is a known LTI stable system. In this paper, we relax the assumption of stable known plant and consider the case where the plant model can be unstable with unknown parameters. We do assume, however, that the plant model is minimum phase and use the model reference adaptive control structure to meet the objectives of reference tracking and unknown periodic disturbance rejection without amplifying the effect of broadband noises. The cost of achieving these objectives is the use of overparameterization that adds to the number of computations. The main contribution of this paper is that it shows that the problem of rejecting unknown periodic disturbances can be solved for unstable plants with unknown parameters as long as they are minimum phase. Numerical examples illustrate the effectiveness of the proposed control methodology.

This paper presents an output feedback design approach based on the adaptive control scheme developed for nonlinearly parameterized systems, to achieve global output regulation for a class of nonlinear systems in output feedback form. We solve the output regulation problem without the knowledge of the sign and the value of the high frequency gain a priori. It is not necessary to have both the limiting assumptions that the exogenous signal w and the unknown parameter μ belong to a prior known compact set and the high frequency gain has a determinate lower and upper bounds. The effectiveness of the proposed algorithm is shown with the help of an example.

The chapter presents controllers that provide adaptive reference tracking and adaptive disturbance rejection for LTI MIMO plants with known parameters and input delay. In other words, the chapter presents design methods applied to the plants with known parameters and input delay in order to solve control Problems 1.2, 1.3, and 1.4 formulated in Sect. 1.3.3. For methodological purposes, we first consider separately the problems of adaptive reference tracking (Sect. 6.1) and adaptive disturbance compensation (Sect. 6.2). Then combine the proposed approaches for solution to the general problem of adaptive output regulation (Sect. 6.3).

Output Feedback Adaptive Robust Learning Control of a Class of Nonlinear Systems with Periodic Disturbances

An Approach Problem with an Unknown Parameter and Inaccurately Measured Motion of the System

In this paper, an event-triggered adaptive control scheme is proposed by backstepping for a class of strict feedback systems with the saturation actuator. The unknown parameters and modelling errors are also considered. By constructing the auxiliary signal system and introducing auxiliary signals into the controller design, the uncertainties caused by unknown saturation effects are compensated for. Based on this auxiliary signal, an event-triggered adaptive control scheme is constructed. The main contributions of this proposed controller can be summarized as follows: (1) A new event-triggered mechanism is proposed by setting a maximum triggering time interval limit. It integrates time triggering in the event triggering mechanism, and avoiding the phenomenon of system performance not being optimized due to control signals not being updated for a long time. It was also proven that this proposed triggering mechanism can prevent the occurrence of Zeno-behavior; (2) The unknown constant parameters in the upper bound function of the unknown nonlinear terms are considered. By estimating these parameters the compensation accuracy for such unknown uncertainties is improved. Finally, simulation results validate the effectiveness of this proposed controller.

We consider the problem of online parameter estimation for a class of structurally perturbed infinite dimensional systems. By viewing the system as an augmented system with the unknown constant parameters being the additional states, a time varying infinite dimensional system results whose evolution operator depends on the available output signal. An optimal filter for the resulting time varying system is proposed which optimally reconstructs both the state and unknown parameters. Well-posedness results for the optimal observer are summarized along with an example that illustrate the applicability of this approach to a parabolic partial differential equation.

An extended direct scheme for robust adaptive nonlinear control

This paper studies a robust output regulation problem with nonlinear exosystems without the assumption that the solution to the regulator equations along the trajectory of the exosystems should be polynomial. Based on the extended concepts of steady-state generator and internal model, a set of sufficient conditions for the solvability of the problem are given. Thus, the result developed in this paper can allow the robust output regulation problem with nonlinear exosystems to accommodate much more general nonlinear given plants including those which contain nonpolynomial nonlinearity.

A normalized frequency adaptive comb filter composed of a number of normalized frequency estimators in parallel is proposed to track unknown frequency and unknown amplitude of each component of an almost periodic signal. The filter consists of two coupled nonlinear differential equations respectively for updating frequencies and estimating state variables. A nonlinear autonomous equation for frequency estimation is deduced after average method is applied to the almost periodic dynamic system resulting from system decoupling by slow integral manifold. Three kinds of local stability of the autonomous system:the exponential stability of isolated equilibrium point,the semistability on center manifold,and the robustness under unknown periodic disturbance are proved. The convergence and the boundedness of amplitude estimation and signal tracking as well as the effect of parameters on the transient and steady-state performance of frequency and amplitude are investigated. Each sinusoidal component and its amplitude are accurately tracked on the condition of given intervals instead of the values of frequencies. The response speed is independent of the component amplitude. Simulation results reveal the validity of the proposed algorithm.

Recently, variable structure design (VSD) has been intensively researched in the literature of model reference adaptive control (MRAC) for its well-behaved transient response and appealing tracking performance. In the recent work by Hsu [6], parameter switching mechanism has been introduced in the design of model reference controller to obtain better transient behavior. By taking a different viewpoint, we apply VSD to the control channel, and develop a new robust model reference adaptive controller for a class of uncertain plants with arbitrary relative degree. It is shown that in the presence of additive, multiplicative unmodeled dynamics, and bounded disturbance, the output tracking error can still be guaranteed to converge to zero with an exponential rate. Since the parameter update law is introduced in the synthesis of this new adaptive control law, the magnitude of the switching control forces can be reduced to a more realistic level for implementation. To highlight the improved performance, simulation results are conducted with an uncertain plant with relative degree two.

Disturbance rejection and output regulation are big topics in control system design. In this chapter, rejection of deterministic disturbances in a class of nonlinear output feedback systems is discussed. The chapter starts from sinusoidal disturbances with unknown frequencies, then disturbances generated from nonlinear exosystems and then general periodical disturbances, etc. Adaptive control techniques are used to deal with the unknown disturbance frequencies and unknown parameters in the system. The presented design concepts can be applied to other classes of nonlinear systems.

This paper presents model-based predictive controllers that achieve a high level of transparency while maintaining stability in bilateral teleoperation under known constant or variable time delay. This goal is accomplished by utilizing available information on system model and time delay within an adaptive predictive control framework. The performance objectives are delay-free position tracking between the master and slave and the establishment of virtual mass-damper tool impedance between the user and environment. The controllers adapt to parameter changes in the user, environment as well as the master and slave dynamics. Delay reduction is accomplished based on a state observer and estimates of the system parameters. Using the delay-reduced dynamics, an adaptive output regulation problem is formulated and solved to obtain the control laws. A Lyapunov analysis of the performance and stability of the resulting system is presented. The proposed controllers are evaluated experimentally under constant and variable delay conditions.