Adaptive output feedback actuator nonlinearity compensation for multivariable systems

The problem of direct model reference adaptive control for multi input multi output (MIMO) uncertain plants with unknown high frequency gain matrix (HFGM) is addressed in the paper. Two schemes of adaptive control algorithms using augmented error estimators and relaxed assumption concerning HFGM are proposed. It is assumed that the minimum of modulus of HFGM determinant is known. The first scheme involves the resettable approximation of the inversion of HFGM estimate in control law. The second scheme is based on modification of conventional augmented error estimator by introduction of a switched projection mechanism. The proposed theoretical ideas are wrapped up by simulation examples.

This paper investigates adaptive output feedback control problem for switched uncertain nonlinear systems with input quantization, unmeasured system states and state constraints. Firstly, fuzzy logic systems are introduced to identify system uncertainties, then the fuzzy based observer is constructed to estimate unavailable states. Secondly, combing the backstepping technique and the barrier Lyapunov function method, an adaptive fuzzy output feedback control law is designed, which guarantees that all signals in the closed-loop system are bounded, the system output tracks the reference signal, and system states satisfy their corresponding constraint conditions. Finally, simulation results further show the good performances of the proposed control scheme.

A parameter dependent Riccati equation approach is taken to analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment a nominal, fixed gain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controll er does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller above that of a fixed gain control law is far less than that of other methods. The error signals are shown to be uniformly ultimately bounded and an expression for the ultimate bound is provided. The control design process and theoretical results are illustrated using a model for wing-rock dynamics. Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure.

In this paper an adaptive output feedback control law is proposed for attitude control of a rigid spacecraft under a-priori known angular velocity constraints. The multiple model and switching approach is employed to improve the transient response of the control system in the case of large uncertainty in parameter space of the inertia matrix. Rigorous stability analysis for the proposed control law in the non-switching case is presented. An orbit and attitude simulator for a LEO satellite is developed and used to evaluate the proposed control scheme. The reported results show the effectiveness of the introduced scheme.

This paper develops adaptive output feedback control to reduce stop-and-go oscillations in congested traffic regime. The macroscopic traffic dynamics are governed by Aw-Rascle-Zhang(ARZ) model, consisting of second-order, nonlinear hyperbolic PDEs of traffic density and velocity. We linearize the PDE system around steady states of congested traffic regime. The boundary input through ramp metering is then introduced for the linearized ARZ traffic model. The goal is to stabilize the oscillations in a freeway segment upstream of the ramp, without the knowledge of relaxation time and boundary parameter. Control is applied at the outlet and the measurement is taken from the inlet. In the absence of both parameter knowledge and full-state measurement, we use backstepping method to transform the system into an observer canonical form in which unknown parameters multiply with measured output. We obtain a parametric model based on this form and gradient-based parameter estimators are employed. An explicit state observer involving the delayed values of the input and the output is proposed for state estimation. Using the parameter and state estimates, we develop an adaptive output feedback control law, which achieves convergence to the steady states in the $L^{2}$ sense.

Traffic congestion control for Aw–Rascle–Zhang model

In this chapter, we further the study of adaptive actuator failure compensation control to nonlinear systems with parameter uncertainties. We fisrt develop adaptive control solutions to parametric-strict-feedback systems without zero dynamics in the presence of actuator failures in Section 10.1. The actuator failure compensation problem is characterized in terms of two actuation models, and output matching conditions for the two actuation models are derived. Adaptive compensation control schemes are developed for parametric-strict-feedback systems without zero dynamics based on matching designs for two different actuation models. Closed-loop signal boundedness and asymptotic output tracking are ensured by the developed adaptive control schemes. Simulation results for the control of an aircraft wing-rock model with augmented actuators verifies the desired performance of our adaptive designs.

Nonlinear adaptive control of an underwater towed vehicle

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.

This paper investigates the application of direct adaptive control to suppress the aeroelastic response of a flexible wing model for a range of flight conditions, including pre- and post-flutter airspeeds, while also subject to unmodeled nonlinearities such as nonlinear structural stiffness and actuator free-play. A three-dimensional aeroelastic wing is developed in which the structural dynamics are modeled using a three-dimensional extension of a typical aeroelastic section by mode shape weighting. The aerodynamic forcing is incorporated via an unsteady vortex lattice method. Nonlinear structural stiffness and actuator free-play models are developed and incorporated into the aeroelastic model as well as exogenous disturbances, such as continuous turbulence and discrete gust models. A direct adaptive control strategy is employed that takes the form of an adaptive regulator in which the feedback gain represents the adaptive augmentation of a baseline linear quadratic regulator (LQR) that is designed using the linear aeroelastic model at a pre-flutter flight condition. Simulation studies are presented to evaluate the performance of the adaptive controller in comparison to the baseline LQR controller for a range of flight conditions and with the inclusion of a torsional structural nonlinearity and actuator free-play. The results show that the adaptive controller provides improved attenuation of the linear aeroelastic model as the airspeed increases past the flutter point. In addition, for the case where torsional nonlinearity is included, the adaptive controller is able to stabilize the aeroelastic response at the flutter speed whereas the closed-loop response using the baseline LQR controller is unstable.

An adaptive failure compensation control scheme is developed based on linear quadratic (LQ) control for discrete-time possibly nonminimum phase systems with unknown actuator failures with characterizations that some unknown system inputs are stuck at some unknown fixed or varying values at unknown time instants. The failure compensation control problem is formulated as a new LQ control problem. Based on some results on new controller structures and design conditions developed in [9], a stable adaptive law is proposed for the estimation of uncertain parameters from both the plant and actuator-failures. The adaptive failure compensation controller is implemented with adaptive parameter estimates, for achieving closed-loop stability and output regulation. Simulation results are presented to verify the desired adaptive control performance in the presence of uncertain actuator failures.

The paper considers rejection of unmatched general periodic disturbances with time-varying gains for a class of nonlinear systems. The period of the periodic disturbances is known, the gains of the disturbances depend on the output of the system, and the coefficient vector of the disturbance input channel is not assumed to be a Hurwitz vector. A novel filtered transformation is presented. Based on the filtered transformation, an adaptive output feedback control law is proposed, which guarantees that the output of the closed loop system converges to zero.

Distributed adaptive fuzzy control for multi-agent systems with full state constraints and unmeasured states

This paper derives a stable multivariable model reference adaptive control (MRAC) scheme for systems with abrupt parameter variations (which may cause uncertain sign changes in the system’s high frequency gain matrix), motivated by the application to in-flight aircraft systems with damages. Such sign changes are illustrated by an aircraft model with asymmetric abrupt damages, and their uncertainty is handled by a Nussbaum gain based adaptive control design to control the aircraft for both healthy and post-damage situations, by adapting controller parameters autonomously after the damages occur, for which the knowledge of time instants, structures and values of the damages is not required. A piecewise continuous Lyapunov function is utilized to prove the desired system stability and tracking properties in the presence of damages.