Peter X. Liu

Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises

For pseudo-linear regression identification models corresponding output error systems with colored measurement noises, a difficulty of identification is that there exist unknown inner variables and unmeasurable noise terms in the information vector. This paper presents an auxiliary model based multi-innovation extended stochastic gradient algorithm by using the auxiliary model method and by expanding the scalar innovation to an innovation vector. Compared with single innovation extended stochastic gradient algorithm, the proposed approach can generate highly accurate parameter estimates. The simulation results confirm this conclusion.

Gradient based and least-squares based iterative identification methods for OE and OEMA systems

Gradient based and least-squares based iterative identification algorithms are developed for output error (OE) and output error moving average (OEMA) systems. Compared with recursive approaches, the proposed iterative algorithms use all the measured input-output data at each iterative computation (at each iteration), and thus can produce highly accurate parameter estimation. The basic idea of the iterative methods is to adopt the interactive estimation theory: the parameter estimates relying on unknown variables are computed by using the estimates of these unknown variables which are obtained from the preceding parameter estimates. The simulation results confirm theoretical findings.

Parameter Identification and Intersample Output Estimation for Dual-Rate Systems

In this paper, we derive a mathematical model for dual-rate systems and present a stochastic gradient identification algorithm to estimate the model parameters and an output estimation algorithm to compute the intersample outputs based on the dual-rate input-output data directly. Moreover, we investigate convergence properties of the parameter and intersample estimation, and we test the proposed algorithms with example systems, including an experimental water-level system.

Multiinnovation Least-Squares Identification for System Modeling

A multiinnovation least-squares (MILS) identification algorithm is presented for linear regression models with unknown parameter vectors by expanding the innovation length in the traditional recursive least-squares (RLS) algorithm from the viewpoint of innovation modification. Because the proposed MILS algorithm uses p innovations (not only the current innovation but also past innovations) at each iteration (with the integer p > 1 being an innovation length), the accuracy of parameter estimation is improved, compared with that of the RLS algorithm. Performance analysis and simulation results show that the proposed MILS algorithm is consistently convergent. Moreover, a new interval-varying MILS algorithm is proposed, for which the key is to dynamically change the interval in order to deal with cases where some measurement data are missing. Furthermore, an auxiliary-model-based MILS algorithm is derived for pseudolinear models corresponding to output error moving average systems with colored noises. Finally, the proposed algorithms are applied to model an experimental water level control system.

Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems

This paper presents synthesis approaches for synchronization and secure communications of chaotic systems by using fuzzy model-based design methods. Many well-known continuous and discrete chaotic systems can be exactly represented by T-S fuzzy models with only one premise variable. According to the applications on synchronization and signal modulation, the general fuzzy models may have either i) common bias terms; or ii) the same premise variable and driving signal. Then we propose two types of driving signals, namely, fuzzy driving signal and crisp driving signal, to deal with the asymptotical synchronization and secure communication problems for cases i) and ii), respectively. Based on these driving signals, the solutions are found by solving LMI problems. It is worthy to note that many well-known chaotic systems, such as Duffing system, Chuas circuit. Rasslers system, Lorenz system, Henon map, and Lozi map can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either the fuzzy driving signal or the crisp driving signal. Finally, several numerical simulations are shown to verify the results.

LMI-based fuzzy chaotic synchronization and communications

Addresses synthesis approaches for signal synchronization and secure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities (LMIs). By introducing a fuzzy modeling methodology, many well-known continuous and discrete chaotic systems can be exactly represented by Takagi-Sugeno (T-S) fuzzy models with only one premise variable. Following the general form of fuzzy chaotic models, the structure of the response system is first proposed. Then, according to the applications of synchronization to the fuzzy models that have common bias terms or the same premise variable of drive and response systems, the driving signals are developed with four different types: fuzzy, character, crisp, and predictive driving signals. Synthesizing from the observer and controller points of view, all types of drive-response systems achieve asymptotic synchronization. For chaotic communications, the asymptotical recovering of messages is ensured by the same framework. It is found that many well-known chaotic systems can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either one type of driving signals or all. Several numerical simulations are shown with expected satisfactory performance.

A Force-Reflection Algorithm for Improved Transparency in Bilateral Teleoperation With Communication Delay

The problem of stable force-reflecting teleoperation with time-varying communication delay is addressed in this paper. A new force-reflection (FR) algorithm is presented, where the environmental force reflected on the master side can be altered depending on the forces applied by the human operator. This alteration is not felt by the human operator; however, it makes the FR safe in the sense it does not destroy the stability of the teleoperator system. In particular, using input-to-output stability small gain approach, it is shown that the overall stability in the teleoperator system with the force-reflecting algorithm proposed can be achieved theoretically for arbitrarily low damping on the master side and arbitrarily high FR gain. The simulation results presented confirm that the proposed FR algorithm significantly improves the stability/performance characteristics of the force-reflecting teleoperator system in the presence of time-varying communication delays.

Backstepping Control for Nonlinear Systems With Time Delays and Applications to Chemical Reactor Systems

The state feedback control problem is addressed for a class of nonlinear time-delay systems. The time delays appear in all state variables of the nonlinear system, which brings a challenging issue for controller design. With an introduced new Lyapunov-Krasovskii functional, we develop a novel control strategy. With the help of a backstepping method, we design a memoryless state feedback controller, which does not need the precise knowledge of time delays. It is rigorously proved that the closed-loop system is asymptotically stable. Chemical reactor plants are typical nonlinear systems with time delays. We apply the developed method to the control design of a two-stage chemical reactor with delayed recycle streams, and the simulation results verify the effectiveness of the main results.

Robust Control of Four-Rotor Unmanned Aerial Vehicle With Disturbance Uncertainty

This paper addresses the stability and tracking control problem of a quadrotor unmanned flying robot vehicle in the presence of modeling error and disturbance uncertainty. The input algorithms are designed for autonomous flight control with the help of an energy function. Adaptation laws are designed to learn and compensate the modeling error and external disturbance uncertainties. Lyapunov theorem shows that the proposed algorithms can guarantee asymptotic stability and tracking of the linear and angular motion of a quadrotor vehicle. Compared with the existing results, the proposed adaptive algorithm does not require an a priori known bound of the modeling errors and disturbance uncertainty. To illustrate the theoretical argument, experimental results on a commercial quadrotor vehicle are presented.

Convergence analysis of estimation algorithms for dual-rate stochastic systems

Identification is to estimate the unknown parameters of systems by using the measured input–output data {u(t), y(t)}. Most existing identification approaches assume that the input–output {u(t), y(t)} is available at each sampling instant t. This paper focuses on a class of dual-rate sampled-data systems in which all inputs u(t) are available, but only scarce outputs {y(qt)} are available (q > 1 being an integer). We derive a mathematical model for such dual-rate systems by using a polynomial transformation technique, and present new algorithms for parameter identification and intersample output estimation using directly the dual-rate input–output data {u(t), y(qt)}, and study in detail convergence properties of the algorithms in the stochastic framework by using the stochastic process theory and stochastic martingale theory. We show that (1) the parameter estimation error consistently converges to zero under the persistent excitation condition; (2) the intersample output estimation error is uniformly bounded. Finally, we illustrate and test the proposed algorithms with example systems, including an experimental water-level system.