Uncertain Constant Parameters Research Articles

A generalized projection estimation algorithm

Given a linear regression model in discrete-time containing a vector of p constant uncertain parameters, this paper addresses the problem of designing an exponentially convergent parameter estimation algorithm, even when the regressor vector is not persistently exciting (not even in a finite time interval). On the basis of the definition of lack of persistency of excitation of order q for the regressor vector, 0≤q≤p (which coincides with the classical definition of persistency of excitation when q=0), a generalized projection estimation algorithm is proposed which guarantees global exponential convergence of the parameter estimation error and allows for the on-line computation of the order q of the lack of persistency of excitation. When the lack of persistency of excitation is of order zero, global exponential convergence to zero of the parameter estimation error is obtained, recovering a well-known result and the projection estimation algorithm as a special case.

An adaptive observer for uncertain linear time-varying systems with unknown additive perturbations

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system, which is satisfied in the present context of regulation.

Hybrid Adaptive Output Feedback Tracking for Stable Systems With Unknown Input Constraints

The problem of global output tracking is addressed for stable minimum phase systems, with constant uncertain parameters and constant disturbances belonging to a known compact set, in the presence of input constraints such as amplitude saturation. The relative degree, the system order, and the sign of the high frequency gain are assumed to be known. A hybrid adaptive output feedback control is designed to achieve global asymptotic output tracking, provided that there exists an input within the input constraints capable of tracking exactly the output reference signal. By virtue of the hybrid control approach, the closed-loop system is linear within each time interval between parameter updating. Moreover, no information on input saturation is required by the controller. In addition to the standard assumptions in adaptive control design when inputs are unconstrained, further requirements on the reference signals, on system stability and on parameter bounds, are needed when inputs are constrained.

Noncertainty Equivalent Adaptive Backstepping Control for Advanced Fighter Subject to Unsteady Effects and Input Constraints

This paper presents a noncertainty equivalent adaptive backstepping control scheme for advanced fighter attitude tracking, in which unsteady effects, parameter uncertainties, and input constraints are all considered which increase the design difficulty to a large extent. Based on unsteady attitude dynamics and the noncertainty equivalent principle, a new observer is first developed to reconstruct the immeasurable and time-varying unsteady states. Afterwards, the unsteady aerodynamics is compensated in the backstepping controller where the command filter is introduced to impose physical constraints on actuators. In order to further enhance the robustness, the noncertainty equivalent adaptive approach is again used to estimate the uncertain constant parameters. Moreover, stability of the closed-loop system that includes the state observer, parameter estimator, and backstepping controller is proven by the Lyapunov theorem in a unified architecture. Finally, simulation results show that performance of the deterministic control system can be captured when attractive manifolds are achieved. The effectiveness and robustness of the proposed control scheme are verified by the Herbst maneuver.

New exponential convergence properties for Bernard–Praly observer and adaptive sensorless control of PMSMs

It is innovatively established, through a nonlinear Persistency of Excitation (PE) analysis, that the latest Bernard–Praly gradient adaptive observer – for nonsalient-pole surface Permanent Magnet Synchronous Motors (PMSMs) with uncertain flux of the permanent magnet (PM) – owns exponential convergence properties under well-known observability conditions. Such exponential properties can be crucially used to provide a new solution to the long-standing problem of guaranteeing position/speed tracking in sensorless PMSMs, in the presence of uncertain constant parameters such as load torque, PM flux and possibly stator resistance.

Stability analysis and output-feedback synthesis of hybrid systems affected by piecewise constant parameters via dynamic resetting scalings

We develop novel criteria for robust stability of a class of hybrid systems that are affected by piecewise constant uncertain parameters with dwell-time constraints. These criteria result from clock-dependent Lyapunov arguments that are based on several new robust stability conditions for continuous-time linear time-invariant systems which are affected by parametric passive uncertainties and do not admit any discrete dynamics. In contrast to other approaches, our stability analysis results rely on separation techniques from robust control involving dynamic resetting scalings. Moreover, these techniques are expected to pave the way for covering much more general uncertainties within the framework of integral quadratic constraints. Building upon the new insights on robust stability, we are able to propose an output-feedback gain-scheduling design methodology similarly to our recently obtained synthesis result involving dynamic resetting D-scalings. Most of the obtained conditions are expressed as infinite-dimensional (differential) linear matrix inequalities which can be numerically solved by using relaxation methods based on, e.g., linear splines or matrix sum-of-squares. We apply our results to obtain novel stability criteria and to design distributed controllers for networked systems over undirected switching topologies. Finally, the approach is illustrated with several numerical examples.

Parameter and State Estimation of a Mathematical Model of Carbohydrate Intake

Carbohydrate intake is one of the main disturbances in blood glucose metabolism and one of the major care-issues in diabetes therapy. For this reason, the dynamics of glucose absorption after a meal intake must be included in glucose metabolism models. Current interest in developing patient-specific models has shown the necessity to estimate key parameters in models of carbohydrate intake, which cannot be measured with available sensor technology. In this contribution, we present a scheme to estimate a parameter and a state related to absorption of glucose in the intestine, which depend on the amount of carbohydrates ingested in a meal. The scheme is based on an adaptive observer with exponential convergence to estimate states and uncertain constant parameters.

Adaptive feedback linearization control for twin rotor multiple-input multiple-output system

This paper deals with the tracking problem of a twin rotor multiple-input multiple-output system (TRMS) described by an Euler-Lagrange forced model with constant uncertain parameters and input disturbances. The control of TRMS system is the benchmark problem for control of helicopter which has been a challenging problem due to flexible dynamics, nonlinearities and cross coupling. The control objective is to make this systems track to the given trajectories accurately in spite of the influences of uncertainties and input disturbances. We propose the adaptive feedback linearization controller by using 03 adaptive parameters that stand for the unknown mass parameters of parts in the TRMS. By choosing appropriately controller parameters, the effects of the input disturbances that are friction, cable, gyro moments and the effects caused by the main propeller speed and the tail propeller speed on the vertical and horizontal movements to the yaw and pitch angles will be attenuated. Two functions, including unknown mass parameter adaption and the disturbances attenuation to guarantee the errors of the pitch and yaw angles, are implemented simultaneously by the adaptive feedback linearization controller. The simulation and experimental results show that the good robustness of the TRMS controlled by the proposed controller can be obtained arbitrarily.

ABOUT THE ROBUSTNESS OF ADAPTIVE FEEDBACK LINEARIZATION CONTROLLER FOR INPUT PERTURBED UNCERTAIN FULLY-ACTUATED SYSTEMS

The paper proposes a theorem to assert the arbitrarily good robustness of the fully actuated mechanical system controlled by the adaptive feedback linearization controller. The fully actuated system to be controlled is considerately perturbed by input disturbances and contains constant uncertain parameters in its Euler-Lagrange forced model. It is shown in this paper that independent of input disturbances the adaptive feedback linearization controller with appropriately chosen parameters will drive the output of controlled systems to the desired trajectory for any arbitrary precision. The adaptive controller is applied to the two-link planar elbow arm robot with unknown mass of the end-effector of second link and input torque noises caused by the viscous friction forces and Coulomb friction terms. Simulation results show that the arbitrary precision of the tracking errors always are guaranteed.

Local stability analysis and domain of attraction estimation for a class of uncertain nonlinear discrete‐time systems

SUMMARYThis paper proposes a linear matrix inequality based method for the estimation of domain of attraction for a class of discrete‐time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete‐time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. Numerical examples illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Robust Stabilization of Non-Minimum Phase Nonlinear Systems Using Extended High-Gain Observers

A robust, stabilizing output feedback controller for systems in the normal form, which could potentially include unstable zero dynamics, is presented. The control scheme adopted herein incorporates continuously-implemented sliding mode control-chosen for its robustness properties as well as its ability to prescribe or constrain the motion of trajectories in the sliding phase-and an extended high gain observer to estimate the derivatives of the output and one of the unknown functions. Stabilization in the case of an unknown control coefficient and uncertain constant parameters is shown.

Output Regulation of Non-Minimum Phase Nonlinear Systems Using Extended High-Gain Observers

AbstractIn this paper, a robust output feedback controller for systems in the normal form—which could potentially include unstable zero dynamics—is presented. The control scheme we present incorporates an extended high-gain observer to estimate an unknown function in the system dynamics, in addition to the derivatives of the output. This design scheme is not dependent on any specific type of control law, but continuously implemented sliding mode control was chosen for this paper due to its robustness and the fact that it tends to provide good transient performance. It is shown that regulation can be achieved in the case of an unknown control coefficient and uncertain constant parameters.

Robust Domain of Attraction Estimates for a Class of Uncertain Discrete-Time Nonlinear Systems

This paper proposes a linear matrix inequality based method to the estimation of a robust domain of attraction for a class of discrete-time nonlinear systems subject to uncertain constant parameters. Recursive algebraic representations of the system dynamics and of the Lyapunov stability conditions are applied to obtain convex conditions which guarantee the system robust local stability while providing an estimate of the domain of attraction. A large class of discrete-time nonlinear systems and of Lyapunov functions can be embedded in the proposed methodology including the whole class of regular rational functions of the system state variable and uncertain parameters. A numerical example illustrates the application of the proposed method.

A global state feedback output regulating control for uncertain systems in strict feedback form

A family of single-input, single-output, nonlinear systems in strict feedback form with uncertain constant parameters which appear linearly and belong to a known compact set Π is considered. A global robust output regulation problem via state feedback is addressed and solved under the assumptions that the regulator equations are solvable in Π , the output equation does not depend on uncertain parameters, no modelled disturbances affect the system and the output reference signal is generated by a known exosystem whose state is bounded and available for feedback. Robust adaptive techniques are used to guarantee closed loop boundedness and to achieve, without requiring persistency of excitation, global asymptotic output regulation for a class of feedback linearizable systems which may have unbounded uncertain tracking dynamics or may not have a well-defined global relative degree.

Stability Analysis of Implicit Polynomial Systems

This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach.

Adaptive Sliding Control of Six-DOF Flight Simulator Motion Platform

There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two groups: the constant and the time-varying. The controller identifies constant uncertain parameters using nonlinear adaptive controller associated with elimination of the influences of time-varying uncertain parameters and compensation of the external disturbance using sliding control. The results of numerical simulation attest to the capability of this control scheme not only to, with deadly accuracy, identify parameters of motion platform such as load, inertia moments and mass center, but also effectively improve the robustness of the system.

Data-based supervisory control of uncertain systems with application to automatic drug delivery for anesthesia

Control of nonlinear noisy systems affected by large uncertainties is approached via the introduction of a supervisor which, whenever needed, switches on, in feedback to the plant, a controller selected from a finite set of precomputed controllers. A Lyapunov-based falsification criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances without a priori information on the system. Applicability of the method is illustrated through simulations on an automatic drug delivery system for anesthesia.

Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm

AbstractA robust hierarchical observer is designed for linear time invariant systems with unknown bounded inputs under conditions of strong observability, providing exact state estimation. The main condition for designing the state estimator is the, so‐called, strong observability condition. The supertwisting (second‐order sliding mode) algorithm is used in each step of the hierarchy; the continuity of the supertwisting output injection allows to reconstruct a vector formed by some full column rank matrix premultiplied by the state vector, and that vector is obtainedin a finite time and without any sort of filtration. For the case when the unknown inputs are considered as constant uncertain parameters, the continuous version of the least‐square method is developed. Two numerical examples illustrate the efficiency of the suggested technique. Copyright © 2007 John Wiley & Sons, Ltd.

ROBUST H∞ FILTERING FOR A CLASS OF NONLINEAR DISCRETE-TIME SYSTEMS1

This paper proposes a convex approach to the design of robust bilinear H∞ filters for a class of nonlinear discrete-time systems subject to convex-bounded uncertain constant parameters. The nonlinear system is described by a difference-algebraic representation, which can model the whole class of system with rational functions of the system state and uncertain parameters, as well as some trigonometric nonlinearities. The filter design is based on Lyapunov functions with rational dependence on the system state and uncertain parameters and it is given in terms of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed method.

タグチメソッドと遺伝的局所探索法による共振器型ＳＡＷフィルタのロバスト最適設計

A robust optimum design technique for the structural design of resonator-type surface acoustic wave (SAW) filters is presented. For deciding desirable structures of SAW filters based on the computer simulation, the equivalent circuit model of interdigital transducer (IDT), which includes several uncertain constant parameters, is usually used. In order to cope well with the designing imperfections caused by the inevitable dispersion of these parameters, the quality engineering technique, or the Taguchi method, combined with a genetic local search (GLS) is employed. Besides the traditional Taguchi's two-step design maximizing the robustness of products before the realization of their specified functions, the concurrent design of robustness and functions is also described.