Jay A. Farrell

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.

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.

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.

Cooperative Control of Multiple Nonholonomic Mobile Agents

This paper considers two cooperative control problems for nonholonomic mobile agents. In the first problem, we discuss the design of cooperative control laws such that a group of nonholonomic mobile agents cooperatively converges to some stationary point under various communication scenarios. Dynamic control laws for each agent are proposed with the aid of sigma-processes and results from graph theory. In the second problem, we discuss the design of cooperative control laws such that a group of mobile agents converges to and tracks a target point which moves along a desired trajectory under various communication scenarios. By introducing suitable variable transformations, cooperative control laws are proposed. Since communication delay is inevitable in cooperative control, in each of the above cooperative control problems, we analyze the effect of delayed communication on the proposed controllers. As applications of the proposed results, formation control of wheeled mobile robots is discussed. It is shown that our results can be successfully used to solve formation control problem. To show effectiveness of the proposed approach, simulation results are included.

Associative memories via artificial neural networks

Several design techniques that can be used for continuous-time and discrete-time neural networks to realize associative memories are presented. Associative memory is discussed, and neural network models are presented. Some stability concepts are outlined. The applicability of these techniques is demonstrated by means of specific examples that illustrate strengths and weaknesses.<<ETX>>

Filament-Based Atmospheric Dispersion Model to Achieve Short Time-Scale Structure of Odor Plumes

This article presents the theoretical motivation, implementation approach, and example validation results for a computationally efficient plume simulation model, designed to replicate both the short-term time signature and long-term exposure statistics of a chemical plume evolving in a turbulent flow. Within the resulting plume, the odor concentration is intermittent with rapidly changing spatial gradient. The model includes a wind field defined over the region of interest that is continuous, but which varies with location and time in both magnitude and direction. The plume shape takes a time varying sinuous form that is determined by the integrated effect of the wind field. Simulated and field data are compared. The motivation for the development of such a simulation model was the desire to evaluate various strategies for tracing odor plumes to their source, under identical conditions. The performance of such strategies depends in part on the instantaneous response of target receptors; therefore, the sequence of events is of considerable consequence and individual exemplar plume realizations are required. Due to the high number of required simulations, computational efficiency was critically important.

Moth-inspired chemical plume tracing on an autonomous underwater vehicle

This paper presents a behavior-based adaptive mission planner (AMP)to trace a chemical plume to its source and reliably declare the source location. The proposed AMP is implemented on a REMUS autonomous underwater vehicle (AUV)equipped with multiple types of sensors that measure chemical concentration,the flow velocity vector, and AUV position, depth, altitude, attitude, and speed. This paper describes the methods and results from experiments conducted in November 2002 on San Clemente Island, CA, using a plume of Rhodamine dye developed in a turbulent fluid flow (i.e., near-shore ocean conditions). These experiments demonstrated chemical plume tracing over 100 m and source declaration accuracy relative to the nominal source location on the order of tens of meters. The designed maneuvers are divided into four behavior types: finding a plume,tracing the plume, reacquiring the plume, and declaring the source location. The tracing and reacquiring behaviors are inspired by male moths flying up wind along a pheromone plume to locate a sexually receptive female. All behaviors are formulated by perception and action modules and translated into chemical plume-tracing algorithms suitable for implementation on a REMUS AUV. To coordinate the different behaviors, the subsumption architecture is adopted to define and arbitrate the behavior priorities. AUVs capable of such feats would have applicability in searching for environmentally interesting phenomena, unexploded ordnance, undersea wreckage, and sources of hazardous chemicals or pollutants.

Command Filtered Adaptive Backstepping

As the order of the system increases, implementation of adaptive backstepping controllers becomes increasingly complex due to the necessity to calculate analytically the partial derivatives of certain stabilizing functions with respect to the system state. To remove the burden of computation, in this paper we propose a command filtered adaptive backstepping design method. In the proposed controller design method, analytic calculation of partial derivatives is not required. The control law and the update law become succinct. The stability properties of the controllers is analyzed through a sequence of theorems. Effectiveness of the proposed method is shown by simulation results.

Battery state-of-charge estimation

This paper discusses the problem of lead acid battery state-of-charge estimation for (hybrid) electric vehicles. The problem is to accurately estimate the remaining battery capacity for both driver notification and automated energy management. The article presents a review of the problem, existing solution methods, presentation of a new solution method, and experimental analysis of the performance of that method.

Chemical plume tracing via an autonomous underwater vehicle

Olfactory-based mechanisms have been hypothesized for biological behaviors including foraging, mate-seeking, homing, and host-seeking. Autonomous underwater vehicles (AUVs) capable of such chemical plume tracing feats would have applicability in searching for environmentally interesting phenomena, unexploded ordinance, undersea wreckage, and sources of hazardous chemicals or pollutants. This article presents an approach and experimental results using a REMUS AUV to find a chemical plume, trace the chemical plume to its source, and maneuver to reliably declare the source location. The experimental results are performed using a plume of Rhodamine dye developed in a turbulent, near-shore, oceanic fluid flow.