Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods. † Correspondence: Chung-Ming Kuan, Institute of Economics, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 115, Taiwan; ckuan@econ.sinica.edu.tw. †† I would like to express my sincere gratitude to the editor, Professor Steven Durlauf, for his patience and constructive comments on early drafts of this entry. I also thank Shih-Hsun Hsu and Yu-Lieh Huang for very helpful suggestions. The remaining errors are all mine.

Artificial neural networks

Ordinary differential equations of the first order linear differential equations complex numbers and linear algebra simultaneous linear differential equations numerical methods the descriptive theory of nonlinear differential equations mechanical systems and electric circuits Fourier series Fourier integrals and Fourier transforms the Laplace transformation partial differential equations Bessel functions and Legendre polynomials applications and further properties of matrices vector analysis the calculus of variations analytic functions of a complex variable infinite series in the complex plane the theory of residues conformal mapping.

Advanced Engineering Mathematics. By C. R. Wylie. Pp. xiv, 813. 1966. (McGraw-Hill.)

Summary This paper examines the role of the human driver as the primary control element within the traditional driver-vehicle system. Lateral and longitudinal control tasks such as path-following, obstacle avoidance, and headway control are examples of steering and braking activities performed by the human driver. Physical limitations as well as various attributes that make the human driver unique and help to characterize human control behavior are described. Example driver models containing such traits and that are commonly used to predict the performance of the combined driver-vehicle system in lateral and longitudinal control tasks are identified.

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Understanding and modeling the human driver.

The article demonstrates the implementation of a model-based vehicle estimator, which can be used for combined estimation of vehicle states and parameters. The estimator is realised using the dual extended Kalman filter (DEKF) technique, which makes use of two Kalman filters running in parallel, thus ‘splitting’ the state and parameter estimation problems. Note that the two problems cannot be entirely separated due to their inherent interdependencies. This technique provides several advantages, such as the possibility to switch off the parameter estimator, once a sufficiently good set of estimates has been obtained. The estimator is based on a four-wheel vehicle model with four degrees of freedom, which accommodates the dominant modes only, and is designed to make use of several interchangeable tyre models. The paper demonstrates the appropriateness of the DEKF. Results to date indicate that this is an effective approach, which is considered to be of potential benefit to the automotive industry.

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Dual extended Kalman filter for vehicle state and parameter estimation

Understanding the driver of an automobile has been attractive to researchers from many different disciplines for more than half a century. On the basis of their acquirements, models of the (human) driver have been developed to better understand, analyse and improve the combined couple of driver and automobile. Due to distinctive demands on the models in accordance with different kinds of applications, a variety of driver models is available. An overview of driver models is given with respect to their application and different methodical modelling approaches. The emphasis is put on the interest of engineers, who generally focus on the automobile (like design and optimization of vehicle components and the overall vehicle dynamics behaviour) by applying their approved (mathematical) methods. Nonetheless, a brief look beyond is added to better complete the view on the involved task of driving and driver modelling for automobile dynamics application.

Driver models in automobile dynamics application

This paper considers a method for estimating vehicle handling dynamic states in real-time, using a reduced sensor set; the information is essential for vehicle handling stability control and is also valuable in chassis design evaluation. An extended (nonlinear) Kalman filter is designed to estimate the rapidly varying handling state vector. This employs a low order (4 DOF) handling model which is augmented to include adaptive states (cornering stiffnesses) to compensate for tyre force nonlinearities. The adaptation is driven by steer-induced variations in the longitudinal vehicle acceleration. The observer is compared with an equivalent linear, model-invariant Kalman filter. Both filters are designed and tested against data from a high order source model which simulates six degrees of freedom for the vehicle body, and employs a combined-slip Pacejka tyre model. A performance comparison is presented, which shows promising results for the extended filter, given a sensor set comprising three accelerometers only. The study also presents an insight into the effect of correlated error sources in this application, and it concludes with a discussion of the new observer's practical viability.

/pdf/an-extended-adaptive-kalman-filter-for-real-time-state-2v37cystpq.pdf

An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics

http://www.mnwhowell.com/research/publications/Howell_2000.pdf

On-line PID tuning for engine idle-speed control using continuous action reinforcement learning automata

Two actuation mechanisms are considered for the comparison of performance capabilities in improving the yaw-sideslip handling characteristics of a road vehicle. Yaw moments are generated either by the use of single-wheel braking or via driveline torque distribution using an overdriven active rear differential. For consistency, a fixed reference vehicle system is used, and the two controllers are synthesized via a single design methodology. Performance measures relate to both open-loop and closed-loop driving demands, and include both on-centre and limit handling manoeuvres. Â© IMechE 2005.

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A comparison of braking and differential control of road vehicle yaw-sideslip dynamics

The simulator motion cueing problem has been considered extensively in the literature; approaches based on linear filtering and optimal control have been presented and shown to perform reasonably well. More recently, model predictive control (MPC) has been considered as a variant of the optimal control approach; MPC is perhaps an obvious candidate for motion cueing due to its ability to deal with constraints, in this case the platform workspace boundary. This paper presents an MPC-based cueing algorithm that, unlike other algorithms, uses the actuator positions and velocities as the constraints. The result is a cueing algorithm that can make better use of the platform workspace whilst ensuring that its bounds are never exceeded. The algorithm is shown to perform well against the classical cueing algorithm and an algorithm previously proposed by the authors, both in simulation and in tests with human drivers.

/pdf/model-predictive-driving-simulator-motion-cueing-algorithm-2a6h3n1556.pdf

Model predictive driving simulator motion cueing algorithm with actuator-based constraints

The majority of vehicle dynamics control systems currently in production utilize some form of brake or throttle intervention to generate a yaw moment and control wheel slip. Such control systems can be both intrusive and inefficient. The use of active driveline technology is therefore an attractive alternative and recent advances in controlled differential technology have served to make it a potentially viable one. Using simulation results, this paper will demonstrate the power of these devices to influence vehicle dynamics by first proposing a suitable control strategy. This is then used to illustrate how, with perfect actuation, a vehicle's handling characteristics may be modified. The actuator limitations imposed by the two main classes of contemporary controlled differentials are then discussed and imposed on the simulation model. Using the ideal results as a benchmark, the relative merits of each type are then assessed.

Matt C. Best

Papers

An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics

On-line PID tuning for engine idle-speed control using continuous action reinforcement learning automata

A comparison of braking and differential control of road vehicle yaw-sideslip dynamics

Model predictive driving simulator motion cueing algorithm with actuator-based constraints

Yaw motion control via active differentials