Closed-loop Adaptive System Research Articles

BIFURCATIONS AND LIMIT DYNAMICS IN ADAPTIVE CONTROL SYSTEMS

Adaptive controllers are used in systems where one or more parameters are unknown. Such controllers are designed to stabilize the system using an estimate for the unknown parameters that is adapted automatically as part of the stabilization. One drawback in adaptive control design is the possibility that the closed-loop limit system is not stable. The worst situation is the existence of a destabilized limit system attracting a large open subset of initial conditions. These situations lie behind bad behavior of the closed-loop adaptive control system. The main issue in this paper is to identify and characterize the occurrence of such bad behavior in the adaptive stabilization of first- and second-order systems with one unknown parameter. We develop normal forms for all possible cases and find the conditions that lead to bad behavior. In this context, we discuss a number of bifurcation-like phenomena.

Optimal and adaptive compensation of voltage and current harmonics under nonstiff-voltage conditions

The concept of an optimal and flexible control (OFC) strategy for active filtering has been reported in the literature. The paper demonstrates that, under nonstiff-voltage conditions, due to the source impedance, the OFC strategy performs as a closed-loop adaptive system. This closed-loop system may exhibit poor transient response or even unstable behaviour. Based on source-impedance identification, the paper proposes an improved OFC (IOFC) algorithm to overcome the shortcomings of the OFC. Desirable performance of the IOFC algorithm, based on digital-time-domain-simulation studies in a MATLAB/SIMULINK environment, is also presented. Based on the IOFC algorithm, a new and important harmonic compensation strategy to minimise load-voltage harmonics is introduced and verified.

A novel parameter projection mechanism for smooth and stable adaptive control

A novel parameter projection technique for handling uncertain parameters with a priori available upper and lower bounds is the subject of this paper. It is a wellknown fact that the conventional parameter projection method employed in certainty equivalence adaptive control is able to guarantee global asymptotic stability only after compromising control smoothness. In contrast, the technique presented in this paper preserves both stability and smoothness guarantees for the closed-loop adaptive system. The novelty of the proposed adaptive control formulation comes through our deliberate introduction of a nonlinear re-parameterization of uncertainty, thereby amounting to a significant shift from the classical certainty equivalence methodology. The proposed controller is non-overparameterized and has the potential to significantly improve transient performance because of full and proper utilization of all the available prior information on the unknown parameters. The technical descriptions are further elaborated via the Duffing nonlinear oscillator example to highlight the advantages of this new approach.

Adaptive fuzzy robust tracking controller design via small gain approach and its application

An adaptive fuzzy robust tracking control (AFRTC) algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function, which are all the unstructured (or nonrepeatable) state-dependent unknown nonlinear functions arising from modeling errors and external disturbances. The Takagi-Sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the AFRTC algorithm is designed by use of the input-to-state stability approach and small gain theorem. The algorithm is highlighted by three advantages: 1) the uniform ultimate boundedness of the closed-loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed; 2) the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed; and 3) the adaptive mechanism with minimal learning parameterizations can be obtained. The performance and limitations of the proposed method are discussed. The uses of the AFRTC for the tracking control design of a pole-balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples. Simulation results show the effectiveness of the control scheme.

Decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections

The problem of decentralized control is considered for a class of time-varying large scale systems with uncertainties and external disturbances in the interconnections. In this paper, the upper bounds of the uncertainties and external disturbances are assumed to be unknown. The adaptation laws are proposed to estimate such unknown bounds, and by making use of the updated values of these unknown bounds, a class of decentralized linear and non-linear state feedback controllers are constructed. It is shown that by employing the proposed decentralized non-linear state feedback controllers, the solutions of the resulting adaptive closed-loop large scale system can be guaranteed to be uniformly bounded, and the states are uniformly asymptotically stable. By using the decentralized linear state feedback controllers, one can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large scale system. Finally, a numerical example is given to demonstrate the validity of the results.

Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections

The problem of decentralized stabilization is considered for a class of large-scale time-varying systems with delayed state perturbations in the interconnections. In this note, the upper bounds of the uncertainties in the interconnections are assumed to be unknown. The adaptation laws are proposed to estimate such unknown bounds, and by making use of their updated values, a class of decentralized memoryless state feedback controllers is constructed. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the solutions to the resulting adaptive closed-loop large-scale time-delay system can be guaranteed to be uniformly ultimately bounded. Finally, a numerical example is given to demonstrate the validity of the results.

Stable adaptive fuzzy sliding mode control of interconnected systems

The problem of stable adaptive fuzzy control for a class of interconnected systems with unknown control gains is studied in this paper. By using fuzzy modeling method, a design scheme of an adaptive fuzzy controller is proposed. The design is capable of incorporating linguistic and numerical information into controllers. By theoretical analysis, the closed-loop adaptive fuzzy control system is proved to be globally stable in the sense that all signals involved are bounded, with tracking errors converging to a neighborhood of zero.

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach.

New modal wave-front sensor: a theoretical analysis

We present a new design of a modal wave-front sensor capable of measuring directly the Zernike components of an aberrated wave front. The sensor shows good linearity for small aberration amplitudes and is particularly suitable for integration in a closed-loop adaptive system. We introduce a sensitivity matrix and show that it is sparse, and we derive conditions specifying which elements are necessarily zero. The sensor may be temporally or spatially multiplexed, the former using a reconfigurable optical element, the latter using a numerically optimized binary optical element. Different optimization schemes are discussed, and their performance is compared.

Stable adaptive control for nonlinear multivariable systems with a triangular control structure

A stable adaptive controller is developed for a class of nonlinear multivariable systems using nonlinearly parametrized function approximators. By utilizing the system triangular property, integral-type Lyapunov functions are introduced for deriving the control structure and adaptive laws without the need of estimating the "decoupling matrix" of the multivariable nonlinear system. It is shown that stability of the adaptive closed-loop system is guaranteed, and transient performance is analytically quantized by mean square and L/sub /spl infin// tracking error bound criteria.

AIRCRAFT LANDING PATH TRACKING USING THE ADAPTIVE FILTERING ALGORITHM

A proposal of an adaptive closed loop system for tracking the aircraft during the approach and landing maneuver is presented. The aircraft path is measured by the MLS integrated with the GPS systems. However, the measured path is combined with additional noise or interference signals that degrade the system performance. Then, the aircraft path should be estimated from noisy observations. In this paper, an adaptive filtering algorithm is applied rather than the Kalman filter to obtain an optimal estimate of the aircraft path to control the aircraft actuators. The adaptive filter coefficients are updated according to the least mean square adaptation algorithm. The performance of the proposed scheme is evaluated through the computer simulation during the lateral and longitudinal aircraft motion. It is concluded that the proposed scheme exhibits high convergence and tracking rates. Also, the proposed scheme produces small fluctuations during the aircraft tracking of an assigned reference path.

A hybrid adaptive control scheme using sampled data and intersampling compensation

An adaptive control problem for continuous-time systems using discrete adaptation technique is examined. We propose a hybrid adaptive scheme whose controller parameters are updated only at sampling instants using sampled data. In order to establish stability for the closed-loop adaptive system, an additional feedback loop is designed to compensate possible poor intersampling behavior. A stability analysis is given for the resulting adaptive control system. Furthermore, it is shown that the intersampling compensation can be designed such that for any given sampling rate, the asymptotic tracking performance of the closed-loop hybrid adaptive control system can be made arbitrarily close to that of the continuous adaptive control system.

Adaptive servomechanism controller with an implicit reference model

In this paper the classical servomechanism problem is resolved for the case of an unknown single-input single-output plant and an a priori uncertain command signal. Namely, it is assumed that the command signal is modelled as an output of a homogeneous dynamic system (exosystem ) of known order, but with unknown parameters. In order to provide asymptotic tracking for signals of that kind, a new closed-loop adaptive system, with an implicit reference model and original adaptive observer of the time derivatives of the command signal, is designed.

On critical stability of discrete-time adaptive nonlinear control

In this paper, we examine the global stability and instability problems for a class of discrete-time adaptive nonlinear stochastic control. The systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics, which are characterized by a nonlinear function (say, f(x)). It is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares (LS)-based adaptive control systems. To be specific, let the growth rate of f(x) be f(x)=O(/spl par/x/spl par//sup 6/) with b/spl ges/0, then it is found that b=4 is a critical value for global stability, i.e., the closed-loop adaptive system is globally stable if b<4 and is unstable in general if b/spl ges/4. As a consequence, we find an interesting phenomenon that the linear case does not have: for some LS-based certainty equivalence adaptive controls, even if the LS parameter estimates are strongly consistent, the closed-loop systems may still be unstable. This paper also indicates that adaptive nonlinear stochastic control that is designed based on, e.g., Taylor expansion (or Weierstrass approximation) for nonlinear models, may not be feasible in general.

Use of Bilinear Structures for Modelling a Brewery Fermentation Process

This paper presents the results of an investigative study with the aim being to obtain and assess the appropriateness of bilinear model structures for replicating the characteristics of a brewery fermentation process. Based on realtime data taken from a brewery fermentation plant, it is shown that a discrete-time twin-bilinear model, which simultaneously relates temperature to specific gravity and specific gravity to temperature, provides an adequate input/output reconstruction. The ability of the twin-bilinear model structure is discussed and possibilities for its utilization with an adaptive closed loop system are considered.

On a quantitative theory of robust adaptive control: an interval plant approach

This paper considers a robust direct-model reference adaptive control scheme, where the components of the estimated controller parameter vector are constrained to vary in certain prespecified intervals. This interval constraint facilitates the quantitative analysis of the robustness of the closed-loop adaptive control system. Extending existing results from the area of robust parametric stability, a tractable procedure is developed for verifying a condition which guarantees the boundedness of all the closed-loop signals. The robustness verification using this procedure involves the calculation of worst-case shifted H/sub /spl infin// norms over certain extremal one-parameter families. This makes the condition easily verifiable, whereas otherwise one is faced with the formidable task of determining the worst-case norms over higher-dimensional compact convex sets in the plant and controller parameter spaces. A simple example is used in the paper to illustrate the theoretical development.

Review of control systems for resistance spot welding: Past and current practices and emerging trends

This review focuses on the need for, challenges to, and means of achieving effective control in resistance spot welding; beginning with the earliest single variable open loop systems, progressing to single-, then multivariable feedback and adaptive closed loop systems. The former applied a control action to a single input variable to compensate for drops in line voltage without assessing the effect on output online. The latter use feedback of either single or multiple output variables measured online to execute a preplanned control action, with adaptive systems able to selfadjust gains and/or time constants in the control law in accordance with predictable and unpredictable variations to achieve near constant output. The capabilities and shortcomings of each approach are addressed. The review ends with a discussion of emerging systems for achieving intelligent control by comparing inputs against outputs of actual versus ideal welds and executing control commands in real time based on process knowledge and learning.

Evaluation of a long-range adaptive predictive controller for computerized drug delivery systems.

A closed-loop adaptive control system, based on the generalized predictive control law with a terminal matching condition, has been developed for computerized drug delivery. The control law is a minimization of the squares of prediction errors over a small future prediction horizon plus weighted square of the prediction error at steady-state. A control-relevant, long-range identification algorithm is used for on-line parameter estimation. Since the control and identification are mutually compatible, the system truly satisfies the approximate dual control criterion. The system has been applied to the control of mean arterial pressure (MAP) by automatic infusion of sodium nitroprusside in the presence of physical and physiological constraints. Experimental evaluation on six mongrel dogs, in an ethics-approved manner, included setpoint tracking and regulation of MAP in the presence of unpredictable disturbances. The system was found to be capable of inducing hypotension in an average of 2.44 +/- 0.31 min (mean +/- standard error of mean) after probing without any overshoots in mean arterial pressure. The nitroprusside infusion was also free of any ringing. When the subjects were not disturbed, 96.2% of mean arterial pressure remained within 5 mm Hg of the target pressure. A series of disturbances introduced in the presence and absence of closed-loop control affirms the robustness and effectiveness of this control system.

Estimating The Locally-Optimal Control in Closed-Loop Adaptive Systems

There is studied & least - squares (LS) estimation in closed - loop adaptive control systems without persistent excitation. As a basis for the study are used the statement concerning the consistency of estimate projection onto the identificational subspace and the statement about existence of attracting manifold of differential equations describing slow identification in closed - loop control systems. These statements make it possible to synthesize adaptive control at which, despite Unidentifiability, the wanted locally - optimal control is yielded. Results of numerical simulation are described and their conformity to theoretical results are discussed. Peculiarities of behavior beyond theoretical bounds are revealed.

Stability of input amplitude constrained adaptive pole placement control systems

This paper presents stability analysis for discrete time pole placement control system with input saturation constraints. It is shown that the adaptive closed-loop system for a class of stable type- m plants is globally stable in the sense that all the signals in the loop remain bounded. It is also shown that certain degree of robustness with respect to modelling uncertainties and disturbances can be achieved for the adaptive control system by implementing a simple fixed dead zone in the parameter estimator. If the plant is free from modelling uncertainties and disturbances and the control input is not saturated for a finite period of time, then the closed-loop adaptive control system will asymptotically be characterized by the desired closed-loop poles within this time period.