Adaptive Output Regulation Problem Research Articles

Adaptive Output Regulation of a Class of 1-D Hyperbolic PDEs With Unknown Boundary Scaled Parameters

This paper considers the problem of adaptive output regulation of a class of 1-D anti-collocated hyperbolic PDEs. The model is subject to unknown scaled parameters in both the boundary condition and boundary measurement. An adaptive boundary observer, providing online estimates of the system state and parameters, is designed. Particularly, to realize that the pure boundary state at left side tracks a reference signal, a challenging problem with the estimate of the true value of unknown scaled parameter appearing in measurement (at the left side) is tackled in this paper. It is shown that the proposed observer is exponentially convergent and furthermore the exponential output regulation and stabilization are achieved.

Data-driven Output Regulation via Gaussian Processes and Luenberger Internal Models

This paper deals with the problem of adaptive output regulation for multivariable nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. The approach builds on the recently proposed adaptive internal model design techniques based on the theory of nonlinear Luenberger observers, and the adaptation side is approached as a probabilistic regression problem. Unlike the previous approaches in the field, here only coarse assumptions about the friend structure are required, making the proposed approach suitable for applications where the exosystem is highly uncertain. The paper presents performance bounds on the attained regulation error and numerical simulations showing how the proposed method outperforms previous approaches.

Global adaptive output regulation for nonlinear systems with full-state constraints

ABSTRACT The paper investigates the global adaptive output regulation problem (ORP) for nonlinear systems with full-state constraints (FSCs). First, in order to avoid the disadvantages of barrier Lyapunov functions (BLFs) method and logarithmic constraint functions, radical constraint functions method is proposed to solve the FSCs problem of nonlinear systems. Second, a new internal model is designed based on the regulator equations. Third, the ORP of nonlinear systems is transformed into a stabilization problem. Then, according to the changing supply functions method and the Lyapunov analysis method, a non-backstepping control algorithm is proposed to ensure that all signals of the closed-loop system are globally asymptotically bounded, the tracking error is asymptotically stable, and all states of the system can be constrained. Finally, two simulation examples show the effectiveness of the control algorithm.

Approximate Nonlinear Regulation via Identification-Based Adaptive Internal Models

This paper concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a "right" internal model exists in the identifier's model set. The proposed approach, moreover, does not require "high-gain" stabilization actions.

Adaptive Nonlinear Regulator Design via Immersion and Invariance

This paper studies the adaptive output regulation problem for a class of nonlinear systems. Under a mild immersion condition, a novel adaptive internal model is proposed by using immersion and invariance (I&I) adaptive control and incorporating a high-gain observer. This, together with a high-gain feedback, is shown to be able to solve the desired regulation problem in a semiglobal sense.

Adaptive Output Regulation of Heterogeneous Multiagent Systems Under Markovian Switching Topologies.

This paper investigates the adaptive output regulation problem for heterogeneous linear multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time-homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel distributed adaptive cooperative controller is presented, where the dynamic compensators are utilized to estimate the exogenous signal for all the agents in mean square sense. The distributed control law is based upon the local information of agents, without using the global information of the communication topologies. Finally, illustrative examples are put forward to demonstrate the effectiveness of the given control scheme.

A method for adaptive hybrid output regulation of linear systems

Abstract: In this paper we deal with the problem of adaptive output regulation for a class of uncertain hybrid linear systems whose state jumps periodically according to a known clock. The goal is to present a design methodology for internal model-based hybrid regulators in presence of hybrid exosystems that are unknown both in the flow dynamics and jump map, which are assumed to range in a finite set. The arguments used in this paper strongly rely on the ones recently presented in Cox et al. [2016] and, in particular, on the notion of visibility of the “hybrid steady-state generator”. The design methodology is then applied to the practical case of torque control of a DC-motor in presence of an uncontrolled rectifier.

Adaptive output regulation problem for a class of nonlinear systems

Adaptive output regulation problem for a class of nonlinear systems

Constraint adaptive output regulation of output feedback systems with application to electrostatic torsional micromirror

SummaryThis paper studies a constraint adaptive output regulation design for a class of nonlinear systems with an unknown exosystem by output feedback control. First, by introducing an internal model with some known design parameter, our concerned problem may be formulated as a specific regulation problem with output constraint. Then, the barrier Lyapunov function technique is further integrated to approach the problem. It is shown that such a constraint adaptive output regulation problem is solvable without constraint violation. In particular, the constructed regulator cannot only keep the boundedness of the closed‐loop system signals but also guarantees the parameter convergence for the unknown parameter vector in the exosystem. As an application, it is illustrated that our result is applicable in tracking the control of an electrostatic torsional micromirror with physical geometry constraint. Copyright © 2013 John Wiley & Sons, Ltd.

Cooperative adaptive output regulation for a class of nonlinear uncertain multi-agent systems with unknown leader

In this paper, we study the cooperative global adaptive output regulation problem for a class of nonlinear uncertain multi-agent systems subject to an uncertain leader system. In comparison with the case where the leader system is known exactly, we need to combine adaptive control and robust control techniques to deal with the unknown parameters in the leader system. By employing a distributed internal model for the multi-agent system, we first convert the problem into a global adaptive robust stabilization problem of a distributed augmented system. Then we further solve the global adaptive stabilization problem of the augmented system by a distributed adaptive control law. Finally, we show that the unknown parameters in the leader system can be exactly estimated provided that the distributed internal model is of minimal order.

Adaptive Control of Bilateral Teleoperation with Time Delay

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.

Parameter convergence and minimal internal model with an adaptive output regulation problem

The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense.

Adaptive Output Regulation for Nonlinear Systems with Unknown Periodic Disturbances

Many mechanical systems are subjected to periodic disturbances which may adversely influence control performance. When the plants are nonlinear systems with unknown parameters, this disturbance compensation problem has been considered as adaptive output regulation problem. This paper discusses the problem about adaptive output regulation for nonlinear systems with arbitrary relative degree, which can be transformed into the output feedback form. The nonlinear plant is affected by unknown constant parameters and periodic disturbances with unknown frequencies, magnitudes and phases. The periodic disturbances are considered as signals generated from a linear time invariant exosystem. It is not assumed that the disturbances meet the matching condition for the control input. The design method of the adaptive controller and its parameter update law is based on adaptive backstepping manner for the coordinates-changed extended system, which is generated from the nonlinear plant and the exosystem. Then, it can be achieved that the output asymptotically converges to the output reference and that all signals in the closed-loop system are bounded.

Decentralized Adaptive Output Regulation for Large-Scale Nonlinear Systems

This paper addresses the decentralized adaptive output regulation problem and solve it for a class of large-scale nonlinear systems with commands to be tracked (or disturbances to be rejected) produced by a linear neutrally stable exosystem. An adaptive control scheme is proposed that leads to a closed-loop system with the property that for any initial states of the system and exosystem, all close-loop signals are bounded and asymptotic tracking and/or disturbance rejection is achieved.