Unknown Time-varying Parameters Research Articles

Nonlinear adaptive learning control for unknown time‐varying parameters and unknown time‐varying delays

AbstractA new adaptive learning control approach is proposed for a class of first‐order nonlinear systems with two unknown time‐varying parameters and an unknown time‐varying delay. By reconstructing the system equation, all unknown time‐varying terms, including the time‐varying delay, are combined into an unknown periodic time‐varying vector, which is estimated by a periodic adaptive mechanism. By constructing a Lyapunov–Krasovskii‐like composite energy function (CEF), we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to two classes of high‐order nonlinear systems with mixed parameters. Three simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Supervisory Control of Uncertain Linear Time-Varying Systems

We consider the problem of adaptively stabilizing linear plants with unknown time-varying parameters in the presence of noise, disturbances, and unmodeled dynamics using the supervisory control framework, which employs multiple candidate controllers and an estimator based switching logic to select the active controller at every instant of time. Time-varying uncertain linear plants can be stabilized by supervisory control, provided that the plant's parameter varies slowly enough in terms of mixed dwell-time switching and average dwell-time switching, the noise and disturbances are bounded and small enough in terms of L-infinity norms, and the unmodeled dynamics are small enough in the input-to-state stability sense. This work extends previously reported works on supervisory control of linear time-invariant systems with constant unknown parameters to the case of linear time-varying uncertain systems. A numerical example is included, and limitations of the approach are discussed.

Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays

An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.

Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters

This paper deals with the problem of adaptive robust synchronization of chaotic systems based on the Lyapunov theory. A controller is designed for a feedback linearizable error system with matched uncertainties. The proposed method shows that the drive and response systems are synchronized and states of the response system track the states of the drive system as time tends to infinity. Since this approach does not require any information about the bound of uncertainties, this information is not needed in advance. In order to prevent the frequent switching phenomenon in the control signal, the method is modified such that the norm of tracking error is bounded. Numerical simulations on two uncertain Rossler systems with matched uncertainties show fast responses of tracking error, while the errors are Uniformly Ultimately Bounded, and the control signal is reasonably smooth.

Persistent Dwell-Time Switched Nonlinear Systems: Variation Paradigm and Gauge Design

Asymptotic gain and adaptive control are studied for persistent dwell-time switched systems. Ultimate variations of auxiliary functions are considered for existence of asymptotic gain and a gauge design is introduced for switching-uniform adaptive control by partial state feedback and output feedback of switched systems subject to unmeasured dynamics and persistent dwell-time switching. The usage of the controlled dynamics as a gauge for the instability mode of the unmeasured dynamics makes it possible to design a control rendering the evolution of the overall system interchangeably driven by the stable modes of the controlled and unmeasured dynamics. Unmeasured-state dependent control gains are dealt with and unknown time-varying parameters are attenuated via asymptotic gain. Verification of asymptotic gain conditions is based on the relation between dissipation rates of unmeasured dynamics and timing characterizations ?p and T p of switching sequences.

Stability Margins of ${\cal L}_{1}$ Adaptive Control Architecture

This technical note presents the L 1 adaptive control architecture for systems in the presence of unknown high-frequency gain with known sign, time-varying unknown parameters and disturbances. The L 1 adaptive controller leads to uniform performance bounds for the system's input and output signals, which can be systematically improved by increasing the adaptation rate. For constant unknown parameters, this result leads to analytically computable time-delay margin of a semiglobal nature.

Robust adaptive control of a class of nonlinearly parameterised time-varying uncertain systems

A robust adaptive control is presented for a class of time-varying nonlinear uncertain systems which have a fractional nonlinearly parameterised structure. The proposed design is based on robust adaptive backstepping and neural network approximation. The unknown time-varying parameters in the fractional nonlinear functions are estimated using a smooth projection algorithm and estimation errors are robustly compensated for by the additive terms in the proposed virtual and actual controls. Neural networks are employed to approximate the completely unknown bounding functions of the disturbance terms, and their weights as well as approximation errors are adaptively tuned. It is proved that the proposed robust adaptive control can ensure the semi-global uniform ultimate boundedness of all the closed-loop system signals. The control performance can be improved by an appropriate choice of the design parameters. Simulation results are provided to verify the effectiveness of the proposed design.

A particle-filtering approach for on-line fault diagnosis and failure prognosis

This paper introduces an on-line particle-filtering (PF)-based framework for fault diagnosis and failure prognosis in non-linear, non-Gaussian systems. This framework considers the implementation of two autonomous modules. A fault detection and identification (FDI) module uses a hybrid state-space model of the plant and a PF algorithm to estimate the state probability density function (pdf) of the system and calculates the probability of a fault condition in real-time. Once the anomalous condition is detected, the available state pdf estimates are used as initial conditions in prognostic routines. The failure prognostic module, on the other hand, predicts the evolution in time of the fault indicator and computes the pdf of the remaining useful life (RUL) of the faulty subsystem, using a non-linear state-space model (with unknown time-varying parameters) and a PF algorithm that updates the current state estimate. The outcome of the prognosis module provides information about the precision and accuracy of long-term predictions, RUL expectations and 95% confidence intervals for the condition under study. Data from a seeded fault test for a UH-60 planetary gear plate are used to validate the proposed approach.

Nonstationary modelling approaches of neutralization process for model–based control

In this paper, two simplified models of the neutralization process are investigated in terms of the modelling accuracy. Both models have relatively simple and affine form, which is the key requirement for their application as a basis for the model-based control. One of these models is a simple input-output model while the second one has a phenomenological origin. Both of them include the estimation of the unknown time-varying parameter representing modelling inaccuracies. The estimation procedure is based on the scalar form of the Recursive Least-Squares method. The modelling accuracy of both models is tested by simulation in the application to the complex model of the neutralization process and on the basis of the real measurement data from the laboratory neutralization pilot plant.

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME-VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time-varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time-delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.

Adaptive controller for systems with unknown time-varying parameters and disturbances in the presence of non-zero trajectory initialization error

This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbances. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for both the system's input and output signals, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Robustness of the adaptive controller to non-zero trajectory initialization error is addressed. Simulations of a robotic arm with time-varying friction verify the theoretical findings.

Robust adaptive nonlinear control for uncertain control-affine systems and its applications

This paper addresses the robust tracking control problem for a class of uncertain nonlinear systems with time-varying parameters, perturbed by external disturbances. The unknown time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Depending on the characteristics of disturbance signals, two adaptive-based control algorithms are developed. First, an adaptive H ∞ control is designed that achieves: (i) an H ∞ tracking performance when the external disturbances are L 2 signals, and (ii) the convergence of tracking error to zero if the disturbances are bounded and L 2 signals. Then a novel adaptive control algorithm is proposed, only with the assumption of boundedness of disturbances, to drive the tracking error to zero. The designed tracking controllers are then used for controlling a cart-pendulum system, as an underactuated mechanical system, and chaos synchronization of uncertain Genesio–Tesi chaotic system. Numerical simulations are also given to demonstrate the effectiveness of the proposed control schemes.

A Particle Filtering Approach for On-Line Failure Prognosis in a Planetary Carrier Plate

This paper introduces an on-line particle-filtering-based framework for failure prognosis in nonlinear, non-Gaussian systems. This framework uses a nonlinear state-space model of the plant(with unknown time-varying parameters) and a particle filtering(PF) algorithm to estimate the probability density function(pdf) of the state in real-time. The state pdf estimate is then used to predict the evolution in time of the fault indicator, obtaining as a result the pdf of the remaining useful life(RUL) for the faulty subsystem. This approach provides information about the precision and accuracy of long-term predictions, RUL expectations, and 95% confidence intervals for the condition under study. Data from a seeded fault test for a UH-60 planetary carrier plate are used to validate the proposed methodology.

Robust Adaptive Observer Design for Uncertain Systems With Bounded Disturbances

This paper presents a robust adaptive observer design methodology for a class of uncertain nonlinear systems in the presence of time-varying unknown parameters with absolutely integrable derivatives, and nonvanishing disturbances. Using the universal approximation property of radial basis function (RBF) neural networks and the adaptive bounding technique, the developed observer achieves asymptotic convergence of state estimation error to zero, while ensuring boundedness of parameter errors. A comparative simulation study is presented by the end.

Indirect adaptive linearizing control of a class of bioprocesses – Estimator tuning procedure

In the paper, a class of bioprocesses with fully unknown kinetics is considered. Indirect adaptive control algorithm where the process kinetics is presented as unknown time-varying parameter is derived. A general procedure for optimal tuning of kinetic estimator design parameters is proposed by stability analysis of the control scheme. Theoretical results are verified by simulations of the control scheme of continuous fermentation of gluconic acid production by Aspergillus niger. In the conclusion, some other applications of proposed procedure are discussed.

Robust synchronization and parameter identification on a class of uncertain chaotic systems

This letter studies the robust synchronization and parameter identification problems on a class of uncertain chaotic systems with bounded time-varying unknown parameters. Based on Lyapunov stability theory, a novel robust controller and a parameter identification scheme are proposed. The proposed scheme can successfully synchronize some typical chaotic systems, such as Rössler and Lorenz chaotic systems, with their parameters also convergence to the nominal value despite the noise of the parameters. Simulation results verify the proposed scheme’s effectiveness.

Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization

We address the problem of output tracking for a class of nonlinearly parameterized systems with unstabilizable linearization. To achieve practical output tracking globally in the case when both the bound of reference signals and the bound of unknown time-varying parameters are not known a priori, we present a robust adaptive control method that is based on the idea of universal control combined with the new adaptive feedback design method developed recently for controlling uncertain systems with nonlinear parameterization. Continuous adaptive tracking controllers are explicitly constructed in this paper. The proposed adaptive tracking controllers use only the information of a prescribed reference signal but not its derivatives, nor its bound.

Robust adaptive synchronization of Rossler and Chen chaotic systems via slide technique

This Letter considers the robust adaptive synchronization problem of Rossler and Chen chaotic systems with different time-varying unknown parameters. When system's unknown parameters vary in bound intervals and the bounds of intervals are unknown, a robust adaptive controller is designed. In order to increase the robustness of the closed loop systems, the key idea is that a sliding mode type of controller is employed. Besides, instead of the estimate values of systems' unknown parameters being taken as updating object, a new updating object is introduced in constructing controller. The proposed controller can make the states of Rossler and Chen chaotic systems globally asymptotically robustly synchronized. Simulation results are given to show the effectiveness of the proposed method.

Integrated optimal actuator/sensor placement and robust control of uncertain transport-reaction processes

This paper focuses on transport-reaction processes with unknown time-varying parameters and disturbances described by quasi-linear parabolic PDE systems, and addresses the problem of computing optimal actuator/sensor locations for robust nonlinear controllers. Initially, Galerkin's method is employed to derive finite-dimensional approximations of the PDE system which are used for the synthesis of robust nonlinear state feedback controllers via geometric and Lyapunov techniques and the computation of optimal actuator locations. The controllers enforce boundedness and uncertainty attenuation in the closed-loop system. The optimal actuator location problem is subsequently formulated as the one of minimizing a meaningful cost functional that includes penalty on the response of the closed-loop system and the control action. Owing to the boundedness of the state, the cost is defined over a finite-time interval (the final time is defined as the time needed for the process state to become smaller than the desired uncertainty attenuation limit), while the optimization is performed over a broad set of initial conditions and time-varying disturbance profiles. Subsequently, under the assumption that the number of measurement sensors is equal to the number of slow modes, we employ a standard procedure for obtaining estimates for the states of the approximate finite-dimensional model from the measurements. The optimal location of the measurement sensors is computed by minimizing a cost function of the estimation error in the closed-loop infinite-dimensional system. We show that the use of these estimates in the robust state feedback controller leads to a robust output feedback controller, which guarantees boundedness of the state and uncertainty attenuation in the infinite-dimensional closed-loop system, provided that the separation between the slow and the fast eigenvalues is sufficiently large. We also establish that the solution to the optimal actuator/sensor problem, which is obtained on the basis of the closed-loop finite-dimensional system, is near-optimal in the sense that it approaches the optimal solution for the infinite-dimensional system as the separation between the slow and fast eigenvalues increases. The theoretical results are successfully applied to a typical diffusion-reaction process with nonlinearites and uncertainty to design a robust nonlinear output feedback controller and compute the optimal actuator/sensor locations for robust stabilization of an unstable steady state.