Zhao Lu

On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization

Abstract This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen’s system illustrate the effectiveness of the proposed approach.

Non-Mercer hybrid kernel for linear programming support vector regression in nonlinear systems identification

As a new sparse kernel modeling method, support vector regression (SVR) has been regarded as the state-of-the-art technique for regression and approximation. In [V.N. Vapnik, The Nature of Statistical Learning Theory, second ed., Springer-Verlag, 2000], Vapnik developed the @?-insensitive loss function for the support vector regression as a trade-off between the robust loss function of Huber and one that enables sparsity within the support vectors. The use of support vector kernel expansion provides us a potential avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, in the standard quadratic programming support vector regression (QP-SVR), its implementation is often computationally expensive and sufficient model sparsity cannot be guaranteed. In an attempt to mitigate these drawbacks, this article focuses on the application of the soft-constrained linear programming support vector regression (LP-SVR) with hybrid kernel in nonlinear black-box systems identification. An innovative non-Mercer hybrid kernel is explored by leveraging the flexibility of LP-SVR in choosing the kernel functions. The simulation results demonstrate the ability to use more general kernel function and the inherent performance advantage of LP-SVR to QP-SVR in terms of model sparsity and computational efficiency.

Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks

In the realm of nonlinear control, feedback linearization via differential geometric techniques has been a concept of paramount importance. However, the applicability of this approach is quite limited, in the sense that a detailed knowledge of the system nonlinearities is required. In practice, most physical chaotic systems have inherent unknown nonlinearities, making real-time control of such chaotic systems still a very challenging area of research. In this paper, we propose using the recurrent high-order neural network for both identifying and controlling unknown chaotic systems, in which the feedback linearization technique is used in an adaptive manner. The global uniform boundedness of parameter estimation errors and the asymptotic stability of tracking errors are proved by the Lyapunov stability theory and the LaSalle-Yoshizawa theorem. In a systematic way, this method enables stabilization of chaotic motion to either a steady state or a desired trajectory. The effectiveness of the proposed adaptive control method is illustrated with computer simulations of a complex chaotic system.

Linear programming support vector regression with wavelet kernel: A new approach to nonlinear dynamical systems identification

Wavelet theory has a profound impact on signal processing as it offers a rigorous mathematical framework to the treatment of multiresolution problems. The combination of soft computing and wavelet theory has led to a number of new techniques. On the other hand, as a new generation of learning algorithms, support vector regression (SVR) was developed by Vapnik et al. recently, in which e-insensitive loss function was defined as a trade-off between the robust loss function of Huber and one that enables sparsity within the SVs. The use of support vector kernel expansion also provides us a potential avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, for the support vector regression with the standard quadratic programming technique, the implementation is computationally expensive and sufficient model sparsity cannot be guaranteed. In this article, from the perspective of model sparsity, the linear programming support vector regression (LP-SVR) with wavelet kernel was proposed, and the connection between LP-SVR with wavelet kernel and wavelet networks was analyzed. In particular, the potential of the LP-SVR for nonlinear dynamical system identification was investigated.

Linear Programming SVM-ARMA

As an emerging non-parametric modeling technique, the methodology of support vector regression blazed a new trail in identifying complex nonlinear systems with superior generalization capability and sparsity. Nevertheless, the conventional quadratic programming support vector regression can easily lead to representation redundancy and expensive computational cost. In this paper, by using the l1 norm minimization and taking account of the different characteristics of autoregression (AR) and the moving average (MA), an innovative nonlinear dynamical system identification approach, linear programming SVM-ARMA2K, is developed to enhance flexibility and secure model sparsity in identifying nonlinear dynamical systems. To demonstrate the potential and practicality of the proposed approach, the proposed strategy is applied to identify a representative dynamical engine model.

_{\rm 2K}

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

With Application in Engine System Identification

The output tracking for a general family of nonlinear systems presents formidable technical challenges. In this paper, we present a novel scheme for tracking control of a class of affine nonlinear systems with multi-inputs. This effective procedure is based on a new sliding mode design for tracking control of such nonlinear systems. The construction of an optimal sliding mode is a difficult problem and no systematic and efficient method is currently available. Here, we develop an innovative approach that utilizes a chaotic optimizing algorithm, which is then successfully applied to obtain the optimal sliding manifold. The existing efficient reaching law approach is then utilized to synthesize the sliding mode control law. The sliding mode control scheme proposed here is particularly appropriate for robust tracking of the chaotic motion trajectory.

Multiscale Asymmetric Orthogonal Wavelet Kernel for Linear Programming Support Vector Learning and Nonlinear Dynamic Systems Identification

Air charge estimation is an essential task for gasoline engine control, as its performance determines that of the air-fuel-ratio control and torque control, thereby dictating the fuel economy and emissions of the vehicle. While the problem of air charge estimation has been addressed by the automotive and control communities for many years, assuring adaptivity and robustness of air charge estimation continues to be a challenge, especially as performance requirements become more stringent. In this paper, we propose a new air system model based on Support Vector Regression (SVR). The model leads to a new parameterization which facilitates effective adaptation with simple update laws. Simulation and experiment results demonstrate its real-time implementation performance, computational efficiency, and calibration simplicity.

TRACKING CONTROL OF NONLINEAR SYSTEMS: A SLIDING MODE DESIGN VIA CHAOTIC OPTIMIZATION *

As a critical tool that facilitates control strategy design, performance analysis and overall systems integration, dynamical engine models play important roles in developing advanced powertrain and vehicle technologies. Methodologies for effective engine modeling and strategy calibration are in high demand to meet stringent performance specifications under time/cost constraints. Recently, we explored the use of support vector machine (SVM) for engine modeling and identified several challenging issues in capitalizing this powerful tool for powertrain applications. In this paper, we exploited the regressor structure of the SVM to separate the auto-regression (AR) from the moving average (MA) in an attempt to build a concise engine model with reduced computational effort. The new structure allows us to use different kernel functions for the AR and MA to characterize their roles, thereby providing more flexibility in the model structure. The linear programming SVM-ARMA2K is developed and then successfully applied to identify a representative dynamical engine model. A simulation study demonstrates the potential and practicability of the proposed approach.

Parametrization and adaptation of gasoline engine air system model via linear programming Support Vector Regression

This paper proposes an Adaptive Fuzzy Classifier Approach (AFCA) to local edge detection in order to address the challenges of detecting latent fingerprint in severely degraded images. The proposed approach adapts classifier parameters to different parts of input images using the concept of reference neighborhood. Three variants of AFCAs, namely K-means-clustering AFCA, Entropy-based AFCA, and Statistical AFCA, were developed. Experiments were conducted both on synthetic images and on real fingerprint images to compare these AFCAs and Canny edge detection. The presented results show that Statistical AFCA is the best performer with latent images.