Classical Model Reference Adaptive Control Research Articles

Robust engine slipping start control of hybrid electric vehicles with uncertainty in clutch slipping torque and change in driver demand torque

The engine slipping start (ESS) benefits parallel hybrid electric vehicles from stable ignition and emission reduction. However, inappropriate coordination between the traction motor torque and clutch slipping torque during the ESS will lead to poor smoothness of the vehicle and failed start of the engine. Uncertainty in clutch slipping torque and change in driver demand torque bring tough challenges with sluggish convergence and intensive vehicle jerk in practice. To deal with this problem, a novel two-layer model reference adaptive controller (MRAC) which contains two parallel reference models is proposed to improve robustness and convergence rate simultaneously. On one hand, uncertainties of clutch slipping torque are divided into a low-frequency part and a high-frequency part, and adaptive laws based on the output feedback are designed contrapuntally to enhance robustness. On the other hand, two parallel reference models are designed to accelerate the tracking error convergence rate without changing the reference profiles, which is generated according to the driver demand torque in real time. To test the robustness and convergence rate, the proposed two-layer MRAC is compared with the classical MRAC and proportional–integral controller under the driving scenario with uncertain clutch slipping torque and abrupt change in driver demand torque. The sensitivity with different adaptive gains and low-frequency and high-frequency uncertainties in clutch slipping torque are examined. Finally, hardware-in-the-loop experiments are performed to verify the effectiveness of the proposed two-layer MRAC.

Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

SummaryThis paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem.

An adaptive control framework for a class of nonlinear time-delay systems

This paper aims to formulate an adaptive control framework capable of producing desirable tracking performance for uncertain nonlinear systems with an unknown delay in the control input and a nonlinear control coefficient matrix. Since the control framework inherits common components of the classical model-reference adaptive controller (MRAC), it is easy to implement with a low barrier to entry. In addition, the work shows that the deviation of the state of the proposed control scheme from an ideal dynamics system is bounded given that the delays are within a certain margin. Simulation results are presented to illustrate the theoretical contribution and demonstrate the efficacy of the proposed controller in comparison with an existing competing controller. The limitation of this control framework is also discussed with a suggestion for overcoming the limitation toward the end of the paper.

Robust Adaptive Control of Knee Exoskeleton-Assistant System Based on Nonlinear Disturbance Observer

This study presents a control design of an angular position for the exoskeleton knee assistance system based on a model reference adaptive control (MRAC) strategy. Three schemes of the MRAC design have been proposed: the classical MRAC, MRAC with an adaptive disturbance observer, and MRAC with a nonlinear observer. The stability analysis for each scheme has been conducted and developed based on the Lyapunov theorem to prove the uniform ultimate bound of tracking and estimation errors. In addition, the adaptive laws have been developed for the proposed schemes according to the stability analysis. The effectiveness of the proposed state and output feedback controllers has been verified via computer simulation. The results based on numerical simulation have shown that the MRAC with a nonlinear observer could give better robustness characteristics and better performance in terms of tracking and estimation errors as compared to the other controllers.

A Unified Framework for Adaptive Leaderless Consensus of Uncertain Multiagent Systems Under Directed Graphs

Due to the nonsymmetric property of the associated Laplacian matrix and the existence of uncertainties in the agent dynamics, the leaderless consensus problem of uncertain multiagent systems under general directed graphs is challenging. Motivated by the classical model reference adaptive control, in this article, we propose a simple yet efficient scheme, called the model reference adaptive consensus, by arranging each agent a reference output to track, where the output is generated by a linear reference model with the relative state measurements as input. We consider two typical agent dynamics, namely, the general linear dynamics with matching uncertainties and the second-order dynamics with extended matching uncertainties. Different linear reference models are designed for the above uncertain agent dynamics. For the first one, dynamical consensus is achieved under a fixed directed graph containing a directed spanning tree. For the latter one, position consensus is achieved under switching uniformly jointly connected graphs. In the proposed algorithms, only the relative states are interacted among the agents and there is no requirement on the communication of virtual signals.

Adaptive control designs for control-based continuation of periodic orbits in a class of uncertain linear systems

This paper proposes two novel adaptive control designs for the feedback signals used in the control-based continuation paradigm to track families of periodic orbits of periodically excited dynamical systems, including black box simulation models and physical experiments. The proposed control designs rely on modifications to the classical model reference adaptive control framework and the more recent $${\mathscr {L}}_1$$ adaptive control architecture, in which an additional low-pass filter is used to ensure guaranteed transient performance and robustness to time delays in the control input even in the limit of arbitrarily large adaptive gains. In contrast to the proportional control formulations that have been used in the literature on control-based continuation, the proposed control designs achieve stable performance with a minimum of parameter tuning. In the context of a class of linear systems with matched uncertainties, the paper demonstrates the successful integration of adaptive control feedback in control-based continuation. Specifically, the control designs are shown to ensure that the control input stabilizes the sought periodic orbits of the uncontrolled system and vanishes along these orbits, provided that an a priori unknown reference input is chosen appropriately. Numerical results obtained using the coco software package demonstrate how the combination of a nonlinear solver (Newton’s method) with the pseudo-arclength parameter continuation scheme can be used to trace the correct choice for the reference input under variations in an excitation parameter.

Robust model reference adaptive control for five-link robotic exoskeleton

In this paper, H∞-based model reference adaptive control (MRAC) for controlling five-link lower limb robotic exoskeleton is developed during the single support phase with uncertainties and unknown external disturbances. Unlike classical MRAC, the presented scheme using H∞ control and MRAC with adaptive error gain is proposed under uncertain parameter vector and external disturbance. For robustness, H∞ method is applied to minimise the impact of perturbation. Moreover, robust asymptotic stability of the overall system is investigated by Barbalat Lemma selecting a suitable Lyapunov functional candidate. Finally, the efficacy of developed scheme is validated by a relevant example.

Reinforcement learning based closed‐loop reference model adaptive flight control system design

SummaryIn this study, we present a reinforcement learning (RL)‐based flight control system design method to improve the transient response performance of a closed‐loop reference model (CRM) adaptive control system. The methodology, known as RL‐CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor‐critic RL agent is designed using the performance‐driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time‐varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high‐fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte‐Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM‐adaptive control system designs, the proposed RL‐CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.

Adaptive Control for a Class of Multi-Input Multi-Output Plants With Arbitrary Relative Degree

In this paper, a new adaptive output-feedback controller for a class of multi-input multi-output linear plant models with relative degree three or higher is developed. The adaptive controller includes a baseline design based on observers and parameter adaptation based on a modified closed-loop reference model. The overall design guarantees stability and tracking performance in the presence of large parametric uncertainties that are common in aircraft models with actuator dynamics. The requisite controller has a computational complexity that is an order of magnitude lower than that of a classical model reference adaptive controller. The proposed adaptive controller is evaluated using a model of a very flexible aircraft with second-order actuator dynamics and parametric uncertainties, and demonstrates stable command tracking behavior in scenarios that cause the failure of an linear quadratic regulator controller and an adaptive controller with a first-order actuator model.

Generalized Model Reference Adaptive Control by Means of Global HOSM Differentiators

In this paper, we combine a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains with classical model reference adaptive control (MRAC) schemes to solve the relevant and yet open problem of trajectory tracking via output feedback of uncertain plants with arbitrary relative degree in a simple-closed form for the control design. The gains of the differentiator are adapted through state-norm observers for the unmeasured state, whereas the control parametrization explores the input–output filters commonly used in the MRAC design. Global asymptotic stability and robust exact tracking are rigorously demonstrated. Simulations highlight the claimed properties as well as the remarkable simplicity of the proposed adaptive control system using robust exact differentiators when compared to more involved alternatives found in standard approaches. The theoretical results are also illustrated with an application to bilateral teleoperation.

Gaussian Processes for Learning and Control: A Tutorial with Examples

Many challenging real-world control problems require adaptation and learning in the presence of uncertainty. Examples of these challenging domains include aircraft adaptive control under uncertain disturbances [1], [2], multiple-vehicle tracking with space-dependent uncertain dynamics [3], [4], robotic-arm control [5], blimp control [6], [7], mobile robot tracking and localization [8], [9], cart-pole systems and unicycle control [10], gait optimization in legged robots [11] and snake robots [12], and any other system whose dynamics are uncertain and for which limited data are available for model learning. Classical model reference adaptive control (MRAC) [13]-[15] and reinforcement learning (RL) methods [16]-[23] have been developed to address these challenges and rely on parametric adaptive elements or control policies whose number of parameters or features are fixed and determined a priori. One example of such an adaptive model are radial basis function networks (RBFNs), with RBF centers pre-allocated based on expected operating domains [24], [25].

Barrier Lyapunov Functions and Constrained Model Reference Adaptive Control

In classical model reference adaptive control, the closed-loop system’s ability to track a given reference signal can be tuned by choosing the adaptive rates and parameterizing the solution of an algebraic Lyapunov equation that appears in the adaptive law. The projection operator can be employed to impose user-defined constraints on the adaptive gains. However, using the projection operator and quadratic Lyapunov functions to certify uniform ultimate boundedness of the trajectory tracking error, the bounds on the trajectory tracking error can only be estimated, but not explicitly imposed a priori . In this letter, we provide an adaptive control law for the same class of nonlinear dynamical systems as classical model reference adaptive control. A barrier Lyapunov function guarantees that user-defined constraints on both the trajectory tracking error and the adaptive gains are verified.

Combined MRAC for Unknown MIMO LTI Systems With Parameter Convergence

This work proposes a novel combined model reference adaptive controller (MRAC) for unknown multi input multi output (MIMO) LTI systems with guaranteed parameter convergence. An online plant-parameter identification method is developed in conjunction with a direct control-parameter update law to ensure exponential convergence (after a tunable finite time) of tracking error as well as plant and control-parameter estimation errors to zero. Unlike the restrictive persistence of excitation (PE) condition required in classical MRAC approaches, this method guarantees parameter convergence by imposing a significantly milder initial excitation condition on the relevant signals. The introduction of a low-pass filter obviates the need for state derivative knowledge, whereas, the novel inclusion of an integral-like update in the plant-parameter estimation law overcomes the requirement of the restrictive PE condition. As far as the authors are aware, this is the first work on MRAC for MIMO linear time invariant (LTI) systems, which guarantees exponential convergence of the error dynamics without requiring the PE condition as well as the structural knowledge of the system matrices.

Adaptive Control? But is so Simple!

In a recent paper, a few pioneers of adaptive control review the classical model reference adaptive control (MRAC) concept, where the designer is basically supposed to conceive a model of the same order as the (possibly very large) plant, and then build an adaptive controller such that the plant is stable and ultimately follows the behavior of the model. Basically, adaptive control methods based on model following assume full-state feedback or full-order observers or identifiers. These assumptions, along with supplementary prior knowledge, allowed the first rigorous proofs of stability with adaptive controllers, which at the time was a very important first result. However, in order to obtain this important mathematical result, the developers of classical MRAC took the useful scalar Optimal Control feedback signal and made it into an adaptive gain-vector of basically of the same order as the plant, which again had to multiply the plant state-vector in order to finally end with another scalar adaptive control feedback signal. It is quite known today, however, what happens when this requirement is not satisfied, and when "unmodeled dynamics" distorts the controller based on these ideal assumptions. Even though much effort has been invested to maintain stability in spite of so-called "unmodeled dynamics," in some applications, such as large flexible structures and other real-world applications, even if one can assume that the order of the plant is known, one just cannot implement a controller of the same order as the plant (or even a "nominal" or a "dominant" part of the plant), before even mentioning the complexity of such an adaptive controller. Without entering the argument around their special reserve in relation to claimed efficiency of the particular L1-Adaptive Control methodology, this paper first shows that, after the first successful proof of stability and even under the same basic full-state availability assumption, the adaptive control itself can be reduced to just one adaptive gain (which multiplies one error signal) in single-input-single-output (SISO) systems and, as a straightforward extension, an m*m gain matrix in an m-input-m-output (MIMO) plant. Not only is stability not affected, but actually the simplified scheme also gets rid of most seemingly "inherent" problems of the adaptive control represented by classical MRAC. Moreover, proofs of stability have all been based on the so-called Barbalat's lemma which seems to require very strict uniform continuity of signals. The apparent implications are that any discontinuity, such as square-wave input commands or just some occasionally discontinuous disturbance, may put stability of adaptive control in danger, without even mentioning such things as impulse response. Instead, based on old yet amazingly unknown extensions of LaSalle's Invariance Principle to nonautonomous nonlinear systems, recent developments in stability analysis of nonlinear systems have mitigated or even eliminated most apparently necessary prior conditions, thus adding confidence in the robustness of adaptive scheme in real world situations.

Comments on ‘comparison of architectures and robustness of model reference adaptive controllers and L1‐adaptive controllers’

SummaryIn a recent paper it is claimed that adding a filter at the plant input to a classical direct model reference adaptive control constitutes a ‘new architecture’ for adaptive control. The purpose of this note is to show that this claim is specious. Towards this end, we bring to the readers attention the some recent results where a rigorous mathematical analysis shows that the resulting control signal always converges to the output of a linear time‐invariant proportional plus integral (PI) controller, whose gains are independent of the plant parameters. Moreover, it is shown that if the PI controller does not stabilize the plant, the proposed controller will not stabilize it either, making unnecessary the addition of the adaptation. Copyright © 2015 John Wiley & Sons, Ltd.

L1–“Adaptive” Control Always Converges to a Linear PI Control and Does Not Perform Better than the PI

We show in the paper that the, so–called, “new architecture” of L1–adaptive control is, indeed, different from classical model reference adaptive control. Alas, it is not new, since it exactly coincides with a full–state feedback, linear time–invariant proportional plus integral (PI) controller with a decaying additive disturbance. Moreover, it is shown that if the PI controller does not stabilize the plant the L1–adaptive controller will not stabilize it either.

Fractionalization: A New Tool for Robust Adaptive Control of Noisy Plants

Recently, many research works have focused on fractional order control (FOC) and fractional adaptive control. It has been proven to be a good tool for improving the plant dynamics with respect to response time and disturbance rejection. In this paper we propose a new approach for adaptive robust control by fractionalizing an integer order integrator in the classical model reference adaptive control (MRAC) scheme. The implementation of the fractionalized terms is realized by mean of the well established numerical approximation methods. Illustrative simulation examples show that the disturbance rejection has been improved by 50%. This approach can also be generalized to a wide range of control methods.

Simple Adaptive Control: The Optimal Model Reference – Short tutorial

Classical Model Reference Adaptive Control methods have been developed to allow control of systems with uncertainty. Basically assuming full state availability, the developers of this methodology have showed how these techniques can cope with uncertainties and under what condition can guarantee stability of the Adaptive Control systems. When full state availability cannot be assumed, various techniques had to be contrived that deal with the so-called “unmodeled dynamics” and other similar problems. For very large systems such as large flexible structures, where the order of the controller cannot be even close to the plant order, reduced order adaptive controllers have been developed that have become known as Simple Adaptive Control. While they allow using low-order controllers with large-order plants and also showed their efficiency with many real-world applications, it was usually believed that under similar circumstances, their performance would be limited when compared with the “real” large-order Model Reference Adaptive Control. However, recent comparative analysis of the methodologies seems to show that maybe the Simple Adaptive Control methodology is the right Direct Adaptive Controller and even the proper extension of Optimal Control into the domain of Control with uncertainty.

Model-based Fault-tolerant Control to Guarantee the Performance of a Hybrid Wind-Diesel Power System in a Microgrid Configuration

This paper presents a comparison of two different adaptive control schemes for improving the performance of a hybrid wind-diesel power system in an islanded microgrid configuration against the baseline controller, IEEE type 1 automatic voltage regulator (AVR). The first scheme uses a model reference adaptive controller (MRAC) with a proportional-integral-derivative (PID) controller tuned by a genetic algorithm (GA) to control the speed of the diesel engine (DE) for regulating the frequency of the power system and uses a classical MRAC for controlling the voltage amplitude of the synchronous machine (SM). The second scheme uses a MRAC with a PID controller tuned by a GA to control the speed of the DE, and a MRAC with an artificial neural network (ANN) and a PID controller tuned by a GA for controlling the voltage amplitude of the SM. Different operating conditions of the microgrid and fault scenarios in the diesel engine generator (DEG) were tested: 1) decrease in the performance of the diesel engine actuator (40% and 80%), 2) sudden connection of 0.5 MW load, and 3) a 3-phase fault with duration of 0.5seconds. Dynamic models of the microgrid components are presented in detail and the proposed microgrid and its fault-tolerant control (FTC) are implemented and tested in the Simpower Systems of MATLAB/Simulink® simulation environment. The simulation results showed that the use of ANNs in combination with model-based adaptive controllers improves the FTC system performance in comparison with the baseline controller.

A new approach to model reference adaptive control

In classical model reference adaptive control, the goal is to design a controller to make the closed-loop system act like a prespecified reference model in the face of significant plant uncertainty. Typically, the controller consists of an identifier (or tuner) which is used to adjust the parameters of a linear time-invariant (LTI) compensator, and under suitable assumptions on the plant model uncertainty it is proven that asymptotic matching is achieved. However, the controller is typically highly nonlinear, and the closed loop system can exhibit undesirable behavior, such as large transients or a large control signal, especially if the initial parameter estimates are poor. Furthermore, its ability to tolerate time-varying parameters is typically limited. Here, we propose an alternative approach. Rather than estimating the plant or parameters, instead we estimate what the control signal would be if the plant parameters and plant state were known and the ideal LTI compensator were applied. We end up with a linear periodic controller. Our assumptions are reasonably natural extensions of the classical ones to the time-varying setting; we allow rapid parameter variations, although we add a compactness requirement. We prove that we can obtain arbitrarily good tracking, explore the benefits and limitations of the approach, and provide a simulation study.