Number Of Adaptive Parameters Research Articles

Realization of trajectory precise tracking for hypersonic flight vehicles with prescribed performances

This work attempts to achieve precise tracking control for the longitudinal dynamics of hypersonic flight vehicles (HFVs) without adopting universal approximators (e.g., fuzzy logic systems, neural networks, etc.). To this purpose, the system nonlinearities are well constrained to be bounded within some compact sets and are tackled by means of adaptation technique. Apart from achieving precise tracking, some prescribed performances (e.g., convergence rate, maximum steady tracking error, etc.) of the tracking errors of velocity, altitude, flight path angle, angle of attack, and pitch rate are also preserved. The proposed method is complexity-reduced and structurally simple in the sense that the time derivatives of the virtual control laws are no longer required and that the number of adaptation parameters have been reduced to only five due to the absence of universal approximators. Barbalat lemma is combined with Lyapunov theory to prove the closed-loop stability, while guaranteeing that the tracking errors eventually converge to zero through choosing appropriate design parameters. The effectiveness of the proposed control scheme is demonstrated by comparative numerical simulations.

Decentralized finite-time adaptive fault-tolerant synchronization tracking control for multiple UAVs with prescribed performance

This paper is concerned with the decentralized finite-time fault-tolerant attitude synchronization tracking control problem for multiple unmanned aerial vehicles (multi-UAVs) with prescribed performance. Failure to counteract actuator faults in the formation flight of multi-UAVs in a limited time may lead to catastrophic consequences. By integrating the prescribed performance functions into the synchronization tracking errors, a new set of errors is defined. Based on the transformed errors, a finite-time attitude synchronization tracking control scheme is developed by using neural networks and finite-time differentiator techniques. The neural networks are utilized to identify the unknown nonlinear terms induced by uncertainties and actuator faults. To reduce the computational burden caused by estimating the weight vectors, the norms of weight vectors are used for the estimation, such that the number of adaptive parameters is significantly reduced and independent from the number of neurons. The finite-time differentiators are utilized to estimate the intermediate control signals and their derivatives. Moreover, auxiliary dynamic signals with explicit consideration of differentiator estimation errors are introduced into the control scheme to guarantee the finite-time convergences of the synchronized tracking errors. Furthermore, it is shown that by using the Lyapunov method, all UAVs can track their individual attitude references, while the synchronized tracking errors among UAVs are all bounded in finite time and confined within the prescribed performance bounds. Finally, comparative simulation studies on multi-UAVs are conducted to verify the effectiveness of the proposed scheme.

Fuzzy Adaptive DSC Design for an Extended Class of MIMO Pure-Feedback Non-Affine Nonlinear Systems in the Presence of Input Constraints

A novel adaptive fuzzy dynamic surface control (DSC) scheme is for the first time constructed for a larger class of (multi-input multi-output) MIMO non-affine pure-feedback systems in the presence of input saturation nonlinearity. First of all, the restrictive differentiability assumption on non-affine functions has been canceled after using the piecewise functions to reconstruct the model for non-affine nonlinear functions. Then, a novel auxiliary system with bounded compensation term is firstly introduced to deal with input saturation, and the dynamic system employed in this work designs a bounded compensation term of tangent function. Thus, we successfully relax the strictly bounded assumption of the dynamic system. Additionally, the fuzzy logic systems (FLSs) are used to approximate unknown continuous systems functions, and the minimal learning parameter (MLP) technique is exploited to simplify control design and reduce the number of adaptive parameters. Finally, two simulation examples with input saturation are given to validate the effectiveness of the developed method.

Inherently Stable Weighted Least-Squares Estimation of Common Acoustical Poles With the Application in Feedback Path Modeling Utilizing a Kautz Filter

In adaptive feedback cancellation, the feedback path must be modeled precisely using as few adaptive parameters as possible to reduce computational complexity and enable rapid convergence. To reduce the number of adaptive parameters, the feedback path is usually modeled with a transfer function composed of an invariant component and a variable component using all-pole, all-zero, and pole-zero filters. These filters may be inefficient, requiring a large number of parameters for their specification, particularly in reverberant environments. In this letter, we present a weighted least-squares algorithm to precisely estimate the common poles of feedback paths, and we then model the invariant basis functions employing a Kautz filter. The Kautz filter is defined by a set of the fixed poles and a corresponding set of tap output weights. The fixed poles are associated with prominent peaks that are common to the measured feedback path frequency responses. The algorithm guarantees unconditionally the stability of the estimated poles of the inferred model. The experimental results using measured acoustic feedback paths from a two-microphone, behind-the-ear hearing aid show that the proposed method provides an accurate model of the feedback paths for a variety of acoustic environments that were not employed in estimating the common poles.

Reduced-order observer-based adaptive fuzzy tracking control for chaotic permanent magnet synchronous motors

This paper studies an adaptive fuzzy control method combined with reduced-order observer technology for the position tracking control of chaotic permanent magnet synchronous motor (PMSM) drive system. Fuzzy logic systems (FLSs) are introduced to solve the problem of nonlinear and unknown functions appeared in the PMSM drive system, reduced-order observer is used to calculate its angle speed. Meanwhile, adaptive backstepping mechanism is applied for the design procedure of controllers. The control technique developed in this paper can ensure that the tracking error falls into a small neighborhood of origin. Compared with the existing results, the proposed algorithm can solve the explosion of complexity issue and it does not require measuring the speed signal of motors and the number of adaptive parameters has been reduced to only one. Simulation results show that the chaos of PMSM can be successfully suppressed by the proposed method and the system can track the reference signals very well.

Distributed adaptive fault‐tolerant containment control for a class of multi‐agent systems with non‐identical matching non‐linear functions

This study considers the fault-tolerant containment control problem for linear multi-agent systems with external disturbances, non-identical matching non-linear functions and actuator faults containing stuck, outage and loss of effectiveness. A novel method is proposed to estimate the norm of weight vector in fuzzy logic systems rather than the weight vector by using the traditional method. So the difficulty that the actuator with outage or stuck fault cannot work to compensate the unknown non-linear function is solved. Furthermore, different from the traditional fault-tolerant control method to estimate the feedback gain matrix related on the fault, only the ratio of coupling weight to the failure rate is estimated. The merit of the proposed controller is that the number of adaptive parameters is only related to the number of agents, which reduces the adaptive parameters and computational burden considerably. In addition, it is proved that the proposed controller guarantees all the signals in the closed-loop systems are bounded and all followers converge asymptotically to the convex hull formed by the leaders. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

A Semidefinite Programming Approach to Min-max Estimation of the Common Part of Acoustic Feedback Paths in Hearing Aids

The convergence speed and the computational complexity of adaptive feedback cancellation algorithms both depend on the number of adaptive parameters used to model the acoustic feedback paths. To reduce the number of adaptive parameters it has been proposed to decompose the acoustic feedback paths as the convolution of a time-invariant common part and time-varying variable parts. Instead of estimating all parameters of the common and variable parts by minimizing the misalignment using a least-squares cost function, in this paper we propose to formulate the parameter estimation problem as a min-max optimization problem aiming to maximize the maximum stable gain (MSG). We formulate the min-max optimization problem as a semidefinite program and use a constraint based on Lyapunov theory to guarantee stability of the estimated common pole-zero filter. Experimental results using measured acoustic feedback paths show that the proposed min-max optimization outperforms least-squares optimization in terms of the MSG. Furthermore, the results indicate that the proposed common part decomposition is able to increase the MSG and reduce the number of variable part parameters even for unknown feedback paths that were not included in the optimization. Simulation results using an adaptive feedback cancellation algorithm based on the prediction-error-method show that the convergence speed can be increased by using the proposed feedback path decomposition.

Adaptive Neural Control for a Class of Pure-Feedback Nonlinear Systems via Dynamic Surface Technique.

This brief addresses the adaptive control problem for a class of pure-feedback systems with nonaffine functions possibly being nondifferentiable. Without using the mean value theorem, the difficulty of the control design for pure-feedback systems is overcome by modeling the nonaffine functions appropriately. With the help of neural network approximators, an adaptive neural controller is developed by combining the dynamic surface control (DSC) and minimal learning parameter (MLP) techniques. The key features of our approach are that, first, the restrictive assumptions on the partial derivative of nonaffine functions are removed, second, the DSC technique is used to avoid "the explosion of complexity" in the backstepping design, and the number of adaptive parameters is reduced significantly using the MLP technique, third, smooth robust compensators are employed to circumvent the influences of approximation errors and disturbances. Furthermore, it is proved that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, the simulation results are provided to demonstrate the effectiveness of the designed method.

Basis-Based Speaker Adaptation Using Partitioned HMM Mean Parameters of Training Speaker Models

This paper presents the basis-based speaker adaptation method that includes approaches using principal component analysis (PCA) and two-dimensional PCA (2DPCA). The proposed method partitions the hidden Markov model (HMM) mean vectors of training models into subvectors of smaller dimension. Consequently, the sample covariance matrix computed using the partitioned HMM mean vectors has various dimensions according to the dimension of the subvectors. From the eigen-decomposition of the sample covariance matrix, basis vectors are constructed. Thus, the dimension of basis vectors varies according to the dimension of the sample covariance matrix, and the proposed method includes PCA and 2DPCA-based approaches. We present the adaptation equation in both the maximum likelihood (ML) and maximum a posteriori (MAP) frameworks. We perform continuous speech recognition experiments using the Wall Street Journal (WSJ) corpus. The results show that the model with basis vectors whose dimensions are between those of PCA and 2DPCA-based approaches shows good overall performance. The proposed approach in the MAP framework shows additional performance improvement over the ML counterpart when the number of adaptation parameters is large but the amount of available adaptation data is small. Furthermore, the performance of the approach in the MAP framework approach is less sensitive to the choice of model order than the ML counterpart.

ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITH UNKNOWN DISTRIBUTED TIME-VARYING DELAYS AND UNKNOWN CONTROL DIRECTIONS

In this paper, an adaptive fuzzy control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the control gains. Based on the back- stepping technique, the adaptive fuzzy controller is constructed. The main contributions of the paper are that (i) by constructing appropriate Lyapunov functionals and using the Nussbaum functions, the adaptive tracking control problem is solved for the strict-feedback unknown nonlinear systems with the unknown discrete and distributed time-varying delays and the unknown con- trol directions (ii) the number of adaptive parameters is independent of the number of rules of fuzzy logic systems and system state variables, which re- duces the computation burden greatly. It is proven that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output converges to a small neighborhood of the desired reference sig- nal. Finally, an example is used to show the effectiveness of the proposed approach.

Estimation of parameters for the elimination of an orally administered test substance with unknown absorption

Assessment of the elimination of an oral test dose based on plasma concentration values requires correction for the effect of gastric release and absorption. Irregular uptake processes should be described 'model independently', which requires estimation of a large number of absorption parameters. To limit the associated computational effort a new approach is developed with a reduced number of unknown parameters. A marginalized and regularized absorption approach (MRA) is defined, which uses for the uptake just one parameter to control rigidity of the uptake curve. For validation, elimination and absorption were reproduced using published IVIVC data and a synthetic data set for comparison with approaches using a 'model-free'--staircase function or mechanistic models to describe absorption. MRA performed almost as accurate as well specified mechanistic models, which gave the best reproduction. MRA demonstrated a 50fold increase in computational efficiency compared to other approaches. The absorption estimated for the IVIVC study demonstrated an in vivo-in vitro correlation comparable to published values. The newly developed MRA approach can be used to efficiently and accurately estimate elimination and absorption with a restricted number of adaptive parameters and with automatic adjustment of the complexity of the uptake.

Global Tracking Control for a Class of Uncertain Nonlinear SISO Systems

Abstract This paper investigates the problem of global tracking control for a class of nonlinear systems with unknown system functions. The key features of the proposed algorithm are given as follows. First, a novel nth-order smoothly switching function is presented, and therefore an energy-efficient controller is obtained. Second, only a neural network is employed to compensate for all the unknown parts in each backstepping design procedure to reduce the number of adaptive parameters, so that a more simplified controller is proposed. Finally, the overall controller ensures that all the signals in the closed-loop system are globally uniformly ultimately bounded (GUUB) and the output of the system converges to a small neighborhood of the reference trajectory by properly choosing the design parameters. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive fuzzy-neural tracking control for uncertain nonlinear discrete-time systems in the NARMAX form

In this paper, an adaptive fuzzy-neural control scheme is investigated for a class of single-input single-output (SISO) discrete-time nonlinear systems in the presence of bounded disturbances. The SISO systems are in the form of the nonlinear autoregressive moving average with exogenous input (NARMAX), which has received much attention in the discrete control field. In order to realize the stability, the systems are first transformed into a causal state space description, and an ideal controller is obtained. The desired controller is approximated by using the fuzzy-neural networks. Compared with the previous results for controlling NARMAX, the number of adaptation parameters is less, and thus, it reduces the computational burden. Finally, the feasibility of this theory is proven in a simulation.

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov–Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.

Rejection and tracking of an unknown broadband source in a two-element array through least square approximation of inter-element delay

A new algorithm to reject and track an unknown broadband source by approximating the inter-element delay in a two-element adaptive array is investigated. Essentially, by constraining the response of the L-tap processing filter to a delay in the least squares sense, the number of adaptive parameters is reduced to merely an unknown gain and delay, which can then be adjusted to reject the unknown source by using the LMS algorithm. Compared with the conventional LMS algorithm, the new algorithm has the advantage that, at about the same complexity, an estimate for the source location is available and the convergence speed is significantly improved.

Adaptive allpass filtering for nonminimum-phase system identification

Efficient algorithms for the recursive identification of nonminimum-phase systems using an adaptive allpass filter together with an adaptive transversal filter are introduced. Both the output and input sequences are assumed to be available, and the proposed technique basically uses a linear predictor at the output of the system to equalise its magnitude response and an allpass filter to match its phase response. The mirror image property of the numerator and denominator polynomials in an allpass transfer function reduces the number of adaptive parameters needed compared to an unconstrained recursive identification scheme. Computer simulations are used to support the claims made in the paper.

A general method of deriving a discrete normalized system of orthogonal functions and its application to adaptive digital filters

AbstractThe system of orthogonal functions is very useful in science and engineering, and the theory on the orthogonal function system in the continuous time domain has been established. On the other hand, with the advance in digital signal processing, a need for processing the signal in the discrete time domain is acute. With this background, a general derivation of the orthogonal function system in the discrete time domain is desired. This paper proposes a general method for deriving the orthogonal function system in the discrete time domain from the already established orthogonal function system in the continuous time domain. First, the orthogonal function system in the continuous time domain is presented. Next, by the bilinear information of its transfer function, the system is transferred to the discrete time domain. However, in general, the orthogonality in the discrete time domain is destroyed by the bilinear transformation. It is shown that the orthogonality can be maintained in the discrete time domain and the orthonormal function system can be constructed by an appropriate processing. Further, the digital filter using this orthonormal function system is applied to the adaptive digital filter and the number of adaptive parameters is reduced. Finally, by computer simulation, the effectiveness of the adaptive filter configuration by means of the orthonormal function system is proven.