Tracking control of a general class of nonlinear systems using a perceptron neural network (PNN) is presented. The basic structure of the PNN and its training law are first derived. A novel discrete-time control strategy is introduced that employs the PNN for direct online estimation of the required feedforward control input. The developed controller can be applied to both discrete- and continuous-time plants. Unlike most of the existing direct adaptive or learning schemes, the nonlinear plant is not assumed to be feedback linearizable. The stability of the neural controller under ideal conditions and its robust stability to inexact modeling information are rigorously analyzed.

The stability analysis of an adaptive control scheme for robotic manipulators, originally introduced by Horowitz and Tomizuka (1980). is presented in this paper. In the previous stability proof it was assumed that the manipulator parameter variation is negligible compared with the speed of adaptation. I t isshown that this key assumption can be removed by introducing two modifications in the adaptive control scheme: 1. Reparametrizing the nonlinear terms in dynamic equations as linear functions of unknown but constant terms. 2. Defining the Coriolis compensation term in the control law as a bilinear function of the manipulator and model reference jointvelocities, instead o f a quadratic function of the manipulator joint velocities. The modified adaptive control scheme is shown to be globally asymptotically stable.

A system that has the capability to make instantaneous changes in its mass, stiffness, or damping may be termed a state-switchable dynamical system. Such a system will display different dynamical responses dependent upon its current state. For example, state-switchable stiffness may be practically obtained through the control of the termination impedance of piezoelectric stiffness elements. If such a switchable stiffness element is incorporated as part of the spring element of a vibration absorber, the change in stiffness causes a change in the resonance frequencies of the system, thereby instantaneously "retuning" the state-switched absorber to a new frequency. This paper briefly develops the fundamental analysis tools for a Single-Degree-of-Freedom state-switchable device, and then considers the application of such a device for the purpose of vibration control in a 2-DOF system. Simulation results indicate that state-switched vibration absorbers may be advantageous over classical passive tuned vibration absorbers under certain conditions.

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley/NSK SCARA type robot arm.

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