Marios M. Polycarpou

Stable adaptive neural control scheme for nonlinear systems

Based on the Lyapunov synthesis approach, several adaptive neural control schemes have been developed during the last few years. So far, these schemes have been applied only to simple classes of nonlinear systems. This paper develops a design methodology that expands the class of nonlinear systems that adaptive neural control schemes can be applied to and relaxes some of the restrictive assumptions that are usually made. One such assumption is the requirement of a known bound on the network reconstruction error. The overall adaptive scheme is shown to guarantee semiglobal uniform ultimate boundedness. The proposed feedback control law is a smooth function of the state.

High-order neural network structures for identification of dynamical systems

Several continuous-time and discrete-time recurrent neural network models have been developed and applied to various engineering problems. One of the difficulties encountered in the application of recurrent networks is the derivation of efficient learning algorithms that also guarantee the stability of the overall system. This paper studies the approximation and learning properties of one class of recurrent networks, known as high-order neural networks; and applies these architectures to the identification of dynamical systems. In recurrent high-order neural networks, the dynamic components are distributed throughout the network in the form of dynamic neurons. It is shown that if enough high-order connections are allowed then this network is capable of approximating arbitrary dynamical systems. Identification schemes based on high-order network architectures are designed and analyzed.

A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems

This paper presents a robust fault diagnosis scheme for abrupt and incipient faults in nonlinear uncertain dynamic systems. A detection and approximation estimator is used for online health monitoring. Once a fault is detected, a bank of isolation estimators is activated for the purpose of fault isolation. A key design issue of the proposed fault isolation scheme is the adaptive residual threshold associated with each isolation estimator. A fault that has occurred can be isolated if the residual associated with the matched isolation estimator remains below its corresponding adaptive threshold, whereas at least one of the components of the residuals associated with all the other estimators exceeds its threshold at some finite time. Based on the class of nonlinear uncertain systems under consideration, an isolation decision scheme is devised and fault isolability conditions are given, characterizing the class of nonlinear faults that are isolable by the robust fault isolation scheme. The nonconservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and of faults for which these conditions are also necessary for fault isolability. Moreover, the analysis of the proposed fault isolation scheme provides rigorous analytical results concerning the fault isolation time. Two simulation examples are given to show the effectiveness of the fault diagnosis methodology.

Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators

The design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered. The Lyapunov synthesis approach is used to develop state-feedback adaptive control schemes based on a general class of nonlinearly parametrized on-line approximation models. The key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher-order terms of the on-line approximator (with respect to the network weights) satisfy certain bounding conditions. An adaptive bounding design is used to show that the overall neural control system guarantees semi-global uniform ultimate boundedness within a neighbourhood of zero tracking error. The theoretical results are illustrated through a simulation example.

Adaptive approximation based control : unifying neural, fuzzy and traditional adaptive approximation approaches

Preface. 1. INTRODUCTION. 1.1 Systems and Control Terminology. 1.2 Nonlinear Systems. 1.3 Feedback Control Approaches. 1.3.1 Linear Design. 1.3.2 Adaptive Linear Design. 1.3.3 Nonlinear Design. 1.3.4 Adaptive Approximation Based Design. 1.3.5 Example Summary. 1.4 Components of Approximation Based Control. 1.4.1 Control Architecture. 1.4.2 Function Approximator. 1.4.3 Stable Training Algorithm. 1.5 Discussion and Philosophical Comments. 1.6 Exercises and Design Problems. 2. APPROXIMATION THEORY. 2.1 Motivating Example. 2.2 Interpolation. 2.3 Function Approximation. 2.3.1 Off-line (Batch) Function Approximation. 2.3.2 Adaptive Function Approximation. 2.4 Approximator Properties. 2.4.1 Parameter (Non)Linearity. 2.4.2 Classical Approximation Results. 2.4.3 Network Approximators. 2.4.4 Nodal Processors. 2.4.5 Universal Approximator. 2.4.6 Best Approximator Property. 2.4.7 Generalization. 2.4.8 Extent of Influence Function Support. 2.4.9 Approximator Transparency. 2.4.10 Haar Conditions. 2.4.11 Multivariable Approximation by Tensor Products. 2.5 Summary. 2.6 Exercises and Design Problems. 3. APPROXIMATION STRUCTURES. 3.1 Model Types. 3.1.1 Physically Based Models. 3.1.2 Structure (Model) Free Approximation. 3.1.3 Function Approximation Structures. 3.2 Polynomials. 3.2.1 Description. 3.2.2 Properties. 3.3 Splines. 3.3.1 Description. 3.3.2 Properties. 3.4 Radial Basis Functions. 3.4.1 Description. 3.4.2 Properties. 3.5 Cerebellar Model Articulation Controller. 3.5.1 Description. 3.5.2 Properties. 3.6 Multilayer Perceptron. 3.6.1 Description. 3.6.2 Properties. 3.7 Fuzzy Approximation. 3.7.1 Description. 3.7.2 Takagi-Sugeno Fuzzy Systems. 3.7.3 Properties. 3.8 Wavelets. 3.8.1 Multiresolution Analysis (MRA). 3.8.2 MRA Properties. 3.9 Further Reading. 3.10 Exercises and Design Problems. 4. PARAMETER ESTIMATION METHODS. 4.1 Formulation for Adaptive Approximation. 4.1.1 Illustrative Example. 4.1.2 Motivating Simulation Examples. 4.1.3 Problem Statement. 4.1.4 Discussion of Issues in Parametric Estimation. 4.2 Derivation of Parametric Models. 4.2.1 Problem Formulation for Full-State Measurement. 4.2.2 Filtering Techniques. 4.2.3 SPR Filtering. 4.2.4 Linearly Parameterized Approximators. 4.2.5 Parametric Models in State Space Form. 4.2.6 Parametric Models of Discrete-Time Systems. 4.2.7 Parametric Models of Input-Output Systems. 4.3 Design of On-Line Learning Schemes. 4.3.1 Error Filtering On-Line Learning (EFOL) Scheme. 4.3.2 Regressor Filtering On-Line Learning (RFOL) Scheme. 4.4 Continuous-Time Parameter Estimation. 4.4.1 Lyapunov Based Algorithms. 4.4.2 Optimization Methods. 4.4.3 Summary. 4.5 On-Line Learning: Analysis. 4.5.1 Analysis of LIP EFOL scheme with Lyapunov Synthesis Method. 4.5.2 Analysis of LIP RFOL scheme with the Gradient Algorithm. 4.5.3 Analysis of LIP RFOL scheme with RLS Algorithm. 4.5.4 Persistency of Excitation and Parameter Convergence. 4.6 Robust Learning Algorithms. 4.6.1 Projection modification. 4.6.2 &sigma -modification. 4.6.3 &epsis -modification. 4.6.4 Dead-zone modification. 4.6.5 Discussion and Comparison. 4.7 Concluding Summary. 4.8 Exercises and Design Problems. 5. NONLINEAR CONTROL ARCHITECTURES. 5.1 Small-Signal Linearization. 5.1.1 Linearizing Around an Equilibrium Point. 5.1.2 Linearizing Around a Trajectory. 5.1.3 Gain Scheduling. 5.2 Feedback Linearization. 5.2.1 Scalar Input-State Linearization. 5.2.2 Higher-Order Input-State Linearization. 5.2.3 Coordinate Transformations and Diffeomorphisms. 5.2.4 Input-Output Feedback Linearization. 5.3 Backstepping. 5.3.1 Second order system. 5.3.2 Higher Order Systems. 5.3.3 Command Filtering Formulation. 5.4 Robust Nonlinear Control Design Methods. 5.4.1 Bounding Control. 5.4.2 Sliding Mode Control. 5.4.3 Lyapunov Redesign Method. 5.4.4 Nonlinear Damping. 5.4.5 Adaptive Bounding Control. 5.5 Adaptive Nonlinear Control. 5.6 Concluding Summary. 5.7 Exercises and Design Problems. 6. ADAPTIVE APPROXIMATION: MOTIVATION AND ISSUES. 6.1 Perspective for Adaptive Approximation Based Control. 6.2 Stabilization of a Scalar System. 6.2.1 Feedback Linearization. 6.2.2 Small-Signal Linearization. 6.2.3 Unknown Nonlinearity with Known Bounds. 6.2.4 Adaptive Bounding Methods. 6.2.5 Approximating the Unknown Nonlinearity. 6.2.6 Combining Approximation with Bounding Methods. 6.2.7 Combining Approximation with Adaptive Bounding Methods. 6.2.8 Summary. 6.3 Adaptive Approximation Based Tracking. 6.3.1 Feedback Linearization. 6.3.2 Tracking via Small-Signal Linearization. 6.3.3 Unknown Nonlinearities with Known Bounds. 6.3.4 Adaptive Bounding Design. 6.3.5 Adaptive Approximation of the Unknown Nonlinearities. 6.3.6 Robust Adaptive Approximation. 6.3.7 Combining Adaptive Approximation with Adaptive Bounding. 6.3.8 Some Adaptive Approximation Issues. 6.4 Nonlinear Parameterized Adaptive Approximation. 6.5 Concluding Summary. 6.6 Exercises and Design Problems. 7. ADAPTIVE APPROXIMATION BASED CONTROL: GENERAL THEORY. 7.1 Problem Formulation. 7.1.1 Trajectory Tracking. 7.1.2 System. 7.1.3 Approximator. 7.1.4 Control Design. 7.2 Approximation Based Feedback Linearization. 7.2.1 Scalar System. 7.2.2 Input-State. 7.2.3 Input-Output. 7.2.4 Control Design Outside the Approximation Region D. 7.3 Approximation Based Backstepping. 7.3.1 Second Order Systems. 7.3.2 Higher Order Systems. 7.3.3 Command Filtering Approach. 7.3.4 Robustness Considerations. 7.4 Concluding Summary. 7.5 Exercises and Design Problems. 8. ADAPTIVE APPROXIMATION BASED CONTROL FOR FIXED-WING AIRCRAFT. 8.1 Aircraft Model Introduction. 8.1.1 Aircraft Dynamics. 8.1.2 Non-dimensional Coefficients. 8.2 Angular Rate Control for Piloted Vehicles. 8.2.1 Model Representation. 8.2.2 Baseline Controller. 8.2.3 Approximation Based Controller. 8.2.4 Simulation Results. 8.3 Full Control for Autonomous Aircraft. 8.3.1 Airspeed and Flight Path Angle Control. 8.3.2 Wind-axes Angle Control. 8.3.3 Body Axis Angular Rate Control. 8.3.4 Control Law and Stability Properties. 8.3.5 Approximator Definition. 8.3.6 Simulation Analysis. 8.4 Conclusions. 8.5 Aircraft Notation. Appendix A: Systems and Stability Concepts. A.1 Systems Concepts. A.2 Stability Concepts. A.2.1 Stability Definitions. A.2.2 Stability Analysis Tools. A.3 General Results. A.4 Prefiltering. A.5 Other Useful Results. A.5.1 Smooth Approximation of the Signum function. A.6 Problems. Appendix B: Recommended Implementation and Debugging Approach. References. Index.

Adaptive fault-tolerant control of nonlinear uncertain systems: an information-based diagnostic approach

This paper presents a unified methodology for detecting, isolating and accommodating faults in a class of nonlinear dynamic systems. A fault diagnosis component is used for fault detection and isolation. On the basis of the fault information obtained by the fault-diagnosis procedure, a fault-tolerant control component is designed to compensate for the effects of faults. In the presence of a fault, a nominal controller guarantees the boundedness of all the system signals until the fault is detected. Then the controller is reconfigured after fault detection and also after fault isolation, to improve the control performance by using the fault information generated by the diagnosis module. Under certain assumptions, the stability of the closed-loop system is rigorously investigated. It is shown that the system signals remain bounded and the output tracking error converges to a neighborhood of zero.

Automated fault detection and accommodation: a learning systems approach

The detection, diagnosis, and accommodation of system failures or degradations are becoming increasingly more important in modern engineering problems. A system failure often causes changes in critical system parameters, or even, changes in the nonlinear dynamics of the system. This paper presents a general framework for constructing automated fault diagnosis and accommodation architectures using on-line approximators and adaptation/learning schemes. In this framework, neural network models constitute an important class of on-line approximators. Changes in the system dynamics are monitored by an on-line approximation model, which is used not only for detecting but also for accommodating failures. A systematic procedure for constructing nonlinear estimation algorithms is developed, and a stable learning scheme is derived using Lyapunov theory. Simulation studies are used to illustrate the results and to gain intuition into the selection of design parameters. >

Command Filtered Backstepping

This article presents and analyzes a novel back-stepping feedback control implementation approach. In practical applications, implementation of the backstepping approach becomes increasingly complex as the state order increases. The main complicating factor is computation of the command derivatives. This article presents a filtering approach that significantly simplifies the backstepping implementation, analyzes the effect of the command filtering, and derives a compensated tracking error that retains the standard stability properties of backstepping approaches.

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.

Backstepping-Based Flight Control with Adaptive Function Approximation

A command filtered backstepping approach is presented that uses adaptive function approximation to control unmanned air vehicles. The controller is designed using three feedback loops. The command inputs to the airspeed and flight-path angle controller are x c , γ c , V c and the bounded first derivatives of these signals. That loop generates comand inputs μ c , α c for a wind-axis angle loop. The sideslip angle command β c is always zero. The wind-axis angle loop generates rate commands P c , Q c , R c for an inner loop that generates surface position commands. The control approach includes adaptive approximation of the aerodynamic force and moment coefficient functions. The approach maintains the stability (in the sense of Lyapunov) of the adaptive function approximation process in the presence of magnitude, rate, and bandwidth limitations on the intermediate states and the surfaces.