Model Reference Adaptive Control Law Research Articles

A Novel Distributed Adaptive Controller for Multi-Agent Systems with Double-Integrator Dynamics: A Hedging-Based Approach

In this paper, we focus on designing a model reference adaptive control-based distributed control law to drive a set of agents with double-integrator dynamics in a leader–follower fashion in the presence of system anomalies such as agent-based uncertainties, unknown control effectiveness, and actuator dynamics. In particular, we introduce a novel hedging-based reference model with second-order dynamics to allow an adaptation in the presence of actuator dynamics. We show the stability of the overall closed-loop multi-agent system by utilizing the Lyapunov Stability Theory, where we analyze the stability condition by using the Linear Matrix Inequalities method to show the boundedness of the reference model and actuator states. Finally, we illustrate the efficacy of the proposed distributed adaptive controller on an undirected and connected line graph in five cases.

Leader‐following consensus of a class of heterogeneous uncertain multi‐agent systems with a distributed model reference adaptive control law

SummaryThis paper considers the leader‐following consensus problem of a multi‐agent system whose agents have heterogeneous uncertain dynamics in homogeneous state dimensions. Each agent utilizes a distributed model reference adaptive control (MRAC) law to deal with uncertainties. The nominal part of the MRAC is a distributed static state feedback control law. The reference model is the leader‐following consensus problem of reference agents with homogeneous linear time‐invariant dynamics. This problem becomes an N‐player graphical differential game under a given cost function. The reference agents utilize distributed static state feedback controllers that constitute a Nash equilibrium solution to the graphical differential game. This paper provides the conditions for the distributed MRAC to guarantee that each agent asymptotically tracks the corresponding reference agent; consequently, the multi‐agent system solves the leader‐following consensus problem as the reference model does. These conditions yield a straightforward design method for the MRAC. A numerical example demonstrates an application of the proposed approach to a multi‐robot system with nonlinear dynamics.

Control- Oriented Linear Fractional Transformation Modelling and H∞ Control of a Two-DOF Mass- Spring- Dashpot Dynamic System

ABSTRACT This paper presents a systematic control-oriented uncertainty modelling approach in the Linear Fractional Transformation (LFT) framework of a Multi-Input-Multi-Output (MIMO) mechanical system for designing an H∞ controller. A compact modelling structure has been formulated by considering the parametric uncertainties and disturbances to implement robust control law to achieve certain performance specifications. A popular mechanical system, namely, Two-Degree-of-Freedom (2DOF) Mass-Spring-Dashpot (MSD) dynamics system, which is highly oscillatory and implements in many classical control techniques have been considered as a candidate system to formulate proposed control-oriented LFT modelling framework and design H∞ controller to verify the effectiveness of the derived modelling structure in a real-time environment. This modelling methodology has been illustrated in the simulation environment and indicating satisfactory robust stability and performance margin of the designed H∞ controller. The proposed control strategy is compared with the standard Model Reference Adaptive Control (MRAC) law to express the effectiveness of the controller.

Novel model reference adaptive control laws for improved transient dynamics and guaranteed saturation constraints

In classical model reference adaptive control (MRAC), the adaptive rates must be tuned to meet multiple competing objectives. Large adaptive rates guarantee rapid convergence of the trajectory tracking error to zero. However, large adaptive rates may also induce saturation of the actuators and excessive overshoots of the closed-loop system’s trajectory tracking error. Conversely, low adaptive rates may produce unsatisfactory trajectory tracking performances. To overcome these limitations, in the classical MRAC framework, the adaptive rates must be tuned through an iterative process. Alternative approaches require to modify the plant’s reference model or the reference command input. This paper presents the first MRAC laws for nonlinear dynamical systems affected by matched and parametric uncertainties that constrain both the closed-loop system’s trajectory tracking error and the control input at all times within user-defined bounds, and enforce a user-defined rate of convergence on the trajectory tracking error. By applying the proposed MRAC laws, the adaptive rates can be set arbitrarily large and both the plant’s reference model and the reference command input can be chosen arbitrarily. The user-defined rate of convergence of the closed-loop plant’s trajectory is enforced by introducing a user-defined auxiliary reference model, which converges to the trajectory tracking error obtained by applying the classical MRAC laws before its transient dynamics has decayed, and steering the trajectory tracking error to the auxiliary reference model at a rate of convergence that is higher than the rate of convergence of the plant’s reference model. The ability of the proposed MRAC laws to prescribe the performance of the closed-loop system’s trajectory tracking error and control input is guaranteed by barrier Lyapunov functions. Numerical simulations illustrate both the applicability of our theoretical results and their effectiveness compared to other techniques such as prescribed performance control, which allows to constrain both the rate of convergence and the maximum overshoot on the trajectory tracking error of uncertain systems.

A combined model reference adaptive control law for multirotor UAVs

Model reference adaptive control (MRAC) offers the potential to adapt in real-time to changes in the performance of small unmanned air vehicles. There are significant challenges with their use, however, primarily in the implementation and assurance of long-term system stability. This paper presents flight test results for a combined model reference adaptive control (CMRAC) law applied to the height control loop of a multirotor. Key features include the implementation of CMRAC with a baseline controller allowing for in-flight switching between the two; the use of an augmented state to improve the tracking performance and a CMRAC implementation that provides a shorter transient phase, faster parameter convergence, and closer tracking of the desired reference model response when compared with standard MRAC. With the current exponential growth of interest in unmanned air vehicles, the potential benefits of using CMRAC for control system development are significant, particularly for new vehicles with short development and testing phases and in cases where there are significant configuration changes in flight or prior to rapid deployment.

Model Reference Adaptive Control of Switched Dynamical Systems with Applications to Aerial Robotics

This paper presents an adaptive control law for unknown nonlinear switched plants that must follow the trajectory of user-defined linear switched reference models. The effectiveness of the proposed control architecture is proven in two alternative frameworks, that is, analyzing Caratheodory and Filippov solutions of discontinuous differential equations. Numerical and experimental data verify the applicability of the theoretical results to problems of practical interest. The proposed numerical simulation involves the design of a model reference adaptive control law to regulate the roll dynamics of a reconfigurable delta-wing aircraft. The proposed flight tests involve an aerial robot tasked with autonomously mounting a camera of unknown inertial properties to a vertical surface.

Constrained Robust Model Reference Adaptive Control of a Tilt-Rotor Quadcopter Pulling an Unmodeled Cart

This article presents an innovative control architecture for tilt-rotor quadcopters with H-configuration transporting unknown, sling payloads. This control architecture leverages on a thorough analysis of the aircraft's equation of motion, which reveals gyroscopic effects that were not fully characterized and were disregarded while synthesizing control algorithms in prior publications. Furthermore, the proposed control architecture employs barrier Lyapunov functions and a novel robust model reference adaptive control law to guarantee a priori user-defined constraints on both the trajectory tracking error and the control input, despite poor information on the aircraft's inertial properties and the presence of unknown, unsteady payloads. Flight tests involving a quadcopter pulling an unmodeled cart by means of a thin rope of unknown length, which is slack at the beginning of the mission, verify the effectiveness of the theoretical results.

Reconfigurable Nonlinear Dynamic Inversion for Attitude Control of a Structurally Damaged Aircraft

Structural damage induces extensive parameter changes of an aircraft, which leads to the mismatch problem between the offline model and a flying aircraft. Due to extensive parameter changes, motion of a damaged aircraft is difficultly described with a mathematical model. This article uses disturbances in accelerations and angular accelerations to quantify the effects of extensive parameter changes, and derives a mathematical model for a damaged aircraft. Provided that the flight controller of a damaged aircraft has a fixed structure, the mismatch problem may cause the aircraft unstable. Based on the proposed mathematical model, this article proposed a reconfigurable nonlinear dynamic inversion (RNDI) controller for attitude control of a structurally damaged aircraft, which synthesizes a nonlinear disturbance observer (NDO) with a modified nonlinear dynamic inversion (NDI) controller. The NDO is explored to estimate the disturbances in angular accelerations. Afterwards, the estimations are fed into the modified NDI controller realizes control structure reconfiguration. Conventional NDI control law and model reference adaptive control (MRAC) law are compared, and simulation results demonstrate that the proposed RNDI control law is robust to structural damage and possesses satisfactory control performance.

Computing stability limits for adaptive control laws with high-order actuator dynamics

A challenge in the design of adaptive control laws for uncertain dynamical systems is to achieve system stability and a prescribed level of command following performance in the presence of actuator dynamics. It is well-known that if the actuator dynamics do not have sufficiently high bandwidth, their presence cannot be practically neglected in the design since they limit the achievable stability of adaptive control laws. In this paper, we consider the design of model reference adaptive control laws for uncertain dynamical systems in the presence of high-order actuator dynamics. Specifically, a linear matrix inequalities-based hedging approach is proposed, where this approach modifies the ideal reference model dynamics to allow for correct adaptation that is not affected by the presence of actuator dynamics. The stability of the modified reference model is then computed using linear matrix inequalities, which reveals the fundamental stability interplay between the parameters of the actuator dynamics and the allowable system uncertainties. In addition, we analyze the convergence properties of the modified reference model to the ideal reference model. The presented theoretical results are finally illustrated through a numerical example.

Constrained dynamical systems, robust model reference adaptive control, and unreliable reference signals

ABSTRACTIn this paper, we address the robust control design problem for nonlinear dynamical systems tracking unreliable reference signals. Specifically, we present robust model reference adaptive control laws that guarantee uniform ultimate boundedness of the trajectory tracking error for nonlinear plants that are affected by matched, unmatched, and parametric uncertainties, and are subject to constraints on the state space and the measured output. These control laws guarantee satisfactory results even in case the reference trajectory or the reference output signal do not verify the given constraints and hence, may draw the plant's trajectory or measured output outside their constraint sets. A numerical example involving the attitude control of a spacecraft illustrates the feasibility of the theoretical results presented.

Model reaching adaptive-robust control law for vibration isolation systems with parametric uncertainty

Adaptive control has been used for active vibration isolation and vehicle suspensions systems. A model reference adaptive control law is used for the plant to track the ideal reference model. In a model reaching adaptive control approach, the ideal of a skyhook target without using a reference model is achieved. In this paper, a novel approach, a model reaching adaptive-robust control law is studied for active vibration isolation systems. A dynamic manifold for ideal system is defined using the ideal of a skyhook target model system parameters. First, a new Lyapunov function is defined. Based on the Lyapunov stability theory, a model reaching adaptive and a robust control laws are derived for the uncertain system to reach the ideal manifold. Parameters and upper bounding functions are estimated as a trigonometric function depending on the relative displacements, velocities and the defined manifold. The developed adaptive and the robust compensators are combined and this combination is proposed as an adaptive-robust control law. After that, the controller is applied to a vehicle suspension system and the ideal of a skyhook target without using a reference model is achieved. The results also show that the proposed robust control law can increase the comfort of the vehicle active suspension systems and the ride comfort is remarkably increased.

Cooperative modalities in robotic tele-rehabilitation using nonlinear bilateral impedance control

A nonlinear model reference adaptive bilateral impedance controller is proposed that can accommodate various cooperative tele-rehabilitation modes for patient–therapist interaction using a multi-DOF tele-robotic system. In this controller, two reference impedance models are implemented for the master and slave robots using new model reference adaptive control laws for the nonlinear bilateral teleoperation system. “Hand-over-hand” and “adjustable-flexibility” are two modes of patient–therapist cooperation that are realized using the proposed strategy. The Lyapunov-based stability proof guarantees the patient’s and the therapist’s safety during the cooperation and interaction with robots, even in the presence of modeling uncertainties of the multi-DOF teleoperation system. The performance of the proposed bilateral impedance controller is experimentally investigated for upper-limb tele-rehabilitation in the two mentioned cooperation modes.

Direct Uncertainty Minimization Framework for System Performance Improvement in Model Reference Adaptive Control

Inthispaper, adirectuncertaintyminimizationframeworkisdevelopedanddemonstrated for model reference adaptive control laws. The proposed framework consists of a novel architecture involvingmodificationtermsintheadaptivecontrollawandtheupdatelaw. Inparticular,theseterms areconstructedthroughagradientminimizationprocedureinordertoachieveimprovedclosed-loop system performance with adaptive control laws. The proposed framework is first developed for adaptive control laws with linear reference models and then generalized to adaptive control laws with nonlinear reference models. Two illustrative numerical examples are included to demonstrate the efficacy of the proposed framework.

Estimation of Desired Motion Intention and compliance control for upper limb assist exoskeleton

In this paper, we have addressed two issues for upper limb assist exoskeleton. 1) Estimation of Desired Motion Intention (DMI); 2) Robust compliance control. To estimate DMI, we have employed Extreme Learning Machine Algorithm. This algorithm is free from traditional Neural Network based problems such as local minima, selection of suitable parameters, slow convergence of adaptation law and over-fitting. These problems cause lot of problem in tuning the intelligent algorithm for the desired results. Furthermore, to track the estimated trajectory, we have developed model reference based adaptive impedance control algorithm. This control algorithm is based on stable poles of desired impedance model, forcing the over all system to act as per desired impedance model. It also considers robot and human model uncertainties. To highlight the effectiveness of the proposed control algorithm, we have compared it with simple impedance and target reference based impedance control algorithms. Experimental evaluation is carried on seven degree of freedom upper limb assist exoskeleton. Results describe the effectiveness of ELM algorithm for DMI estimation and robust tracking of the estimated trajectory by the proposed model reference adaptive impedance control law.

Differential games, partial-state stabilization, and model reference adaptive control

In this paper, we develop a unified framework to find state-feedback control laws that solve two-player zero-sum differential games over the infinite time horizon and guarantee partial-state asymptotic stability of the closed-loop system. Partial-state asymptotic stability is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state. The existence of a saddle point for the system׳s performance measure is guaranteed by the fact that this Lyapunov function satisfies a partial differential equation that corresponds to a steady-state form of the Hamilton–Jacobi–Isaacs equation. In the second part of this paper, we show how our differential game framework can be applied not only to solve pursuit-evasion and robust optimal control problems, but also to assess the effectiveness of a model reference adaptive control law. Specifically, the model reference adaptive control architecture is designed to guarantee satisfactory trajectory tracking for uncertain nonlinear dynamical systems, whose matched nonlinearities are captured by the regressor vector. By modeling matched and unmatched nonlinearities, which are not captured by the regressor vector, as the pursuer׳s and evader׳s control inputs in a differential game, we provide an explicit characterization of the system׳s uncertainties that do not disrupt the trajectory tracking capabilities of the adaptive controller. Two numerical examples illustrate the applicability of our results.

Switching control system based on robust model reference adaptive control

For conventional adaptive control, time-varying parametric uncertainty and unmodeled dynamics are ticklish problems, which will lead to undesirable performance or even instability and nonrobust behavior, respectively. In this study, a class of discrete-time switched systems with unmodeled dynamics is taken into consideration. Moreover, nonlinear systems are here supposed to be approximated with the class of switched systems considered in this paper, and thereby switching control design is investigated for both switched systems and nonlinear systems to assure stability and performance. For robustness against unmodeled dynamics and uncertainty, robust model reference adaptive control (RMRAC) law is developed as the basis of controller design for each individual subsystem in the switched systems or nonlinear systems. Meanwhile, two different switching laws are presented for switched systems and nonlinear systems, respectively. Thereby, the authors incorporate the corresponding switching law into the RMRAC law to construct two schemes of switching control respectively for the two kinds of controlled systems. Both closed-loop analyses and simulation examples are provided to illustrate the validity of the two proposed switching control schemes. Furthermore, as to the proposed scheme for nonlinear systems, its potential for practical application is demonstrated through simulations of longitudinal control for F-16 aircraft.

Robust adaptive model tracking for distributed parameter control of linear infinite-dimensional systems in Hilbert space

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinite-dimensional Hilbert space. The result will not require the use of the standard Barbalat's lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.

Direct Adaptive Control for Infinite-dimensional Symmetric Hyperbolic Systems

Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known and unknown waveform, we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The closed loop system is shown to be exponentially convergent to a neighborhood with radius proportional to bounds on the size of the disturbance. The plant is described by a closed densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states.Symmetric Hyperbolic Systems of partial differential equations describe many physical phenomena such as wave behavior, electromagnetic fields, and quantum fields. To illustrate the utility of the adaptive control law, we apply the results to control of symmetric hyperbolic systems with coercive boundary conditions.

State derivative-free variable structure model reference adaptive control of linear parabolic systems

The problem of constructing a model reference adaptive control law for an uncertain 1-dimensional parabolic system is considered in this article. The controller designed here involves only the plant state but no its derivatives. A priori bounds on the plant’s uncertain parameters are used to propose switching laws which serve as an adaptive mechanism. The exponential decay to zero of the state error with any prescribed rate is guaranteed by choosing a controller parameter correspondingly. Numerical studies are also presented to illustrate the applicability of the control law.

Discrete Model Reference Adaptive Control for Gimbal Servosystem of Control Moment Gyro with Harmonic Drive

The double-gimbal control moment gyro (DGCMG) demands that the gimbal servosystem should have fast response and small overshoot. But due to the low and nonlinear torsional stiffness of harmonic drive, the gimbal servo-system has poor dynamic performance with large overshoot and low bandwidth. In order to improve the dynamic performance of gimbal servo-system, a model reference adaptive control (MRAC) law is introduced in this paper. The model of DGCMG gimbal servo-system with harmonic drive is established, and the adaptive control law based on POPOV super stable theory is designed. The MATLAB simulation results are provided to verify the effectiveness of the proposed control algorithm. The experimental results indicate that the MRAC could increase the bandwidth of gimbal servo-system to 3 Hz and improve the dynamic performance with small overshoot.