Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Performance limitations of piezoelectric and force feedback electrostatic transducers in different applications

Current limitations in piezoelectric and electrostatic transducers are discussed. A force-feedback electrostatic transducer capable of operating at bandwidths up to 20 kHz is described. Advantages of the proposed design are a linearised operation which simplifies the feedback control aspects and robustness of the performance characteristics to environmental perturbations. Applications in nanotechnology, optical sciences and acoustics are discussed.

Achieving or exceeding maximum available feedback

A feedback system for control or electronics should have high loop gain, so that its output is close to its desired state, and the effects of changes in the system and of disturbances are minimised. Bode proposed a method for single loop feedback systems to obtain the maximum available feedback, defined as the largest possible loop gain over a bandwidth pertinent to the system, with appropriate gain and phase margins. The method uses asymptotic approximations, and this paper describes some novel adjustments to the asymptotes, so that the final system often exceeds the maximum available feedback. The implementation of the method requires the cascading of a series of lead-lag element. This paper describes a new way to determine how many elements should be used.

Parallelism in control

A parallel structure is suggested for feedback control systems. Such a technique can be applied to either single or multi-sensor environments and is ideally suited for parallel processor implementation. The control input actually applied is based on a weighted summation of the different parallel controller values, the weightings being either fixed values or chosen by an adaptive decision-making mechanism. The effect of different controller combinations is a field now open to study.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.

A critique of neural networks for discrete-time linear control

This paper discusses the use of multi-layer perceptron networks for linear or linearizable, adaptive feedback.control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parametrization. A comparison is made with standard, non-perceptron algorithms, e.g. self-tuning control, and it is shown how gross over-parametrization can occur in the neural network case. Because of the resultant heavy computational burden and poor controller convergence, a strong case is made against the use of neural networks for discrete-time linear control.

The control of dynamical systems by neural networks

In this paper the use of neural networks for the control of dynamical systems is considered. Both identification and feedback control aspects are discussed as well as the types of system for which neural networks can provide a useful technique. Multi-layer Perceptron and Radial Basis function neural network types are looked at, with an emphasis on the latter. It is shown how basis function centre selection is a critical part of the implementation process and that multivariate clustering algorithms can be an extremely useful tool for finding centres.