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This paper proposes a new model-following adaptive control design technique for a class of non-affine and nonsquare nonlinear systems using neural networks. An appropriate stabilizing controller is assumed available for a nominal system model. This nominal controller may not be able to guarantee stability/satisfactory performance in the presence of unmodeled dynamics (neglected algebraic terms in the mathematical model) and/or parameter uncertainties present in the system model. In order to ensure stable behavior, an online control adaptation procedure is proposed in this paper. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture matched unmodeled (neglected) dynamics or model uncertainties due to parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a desired nominal model. The neural network weight update rule is derived using Lyapunov theory, which guarantees both stability of the error dynamics (in a practical stability sense) and boundedness of the weights of the neural networks. A desirable characteristic of the adaptation procedure presented in this paper is that it is independent of the technique used to design the nominal controller; and hence can be used in conjunction with any known control design technique. Numerical results for two challenging illustrative problems are presented in this paper which demonstrate these features and clearly bring out the potential of the proposed approach.

This paper proposes a new model-following adaptive control design technique for nonlinear systems that are nonaffine in control. The adaptive controller uses online neural networks that guarantee tracking in the presence of unmodeled dynamics and/or parameter uncertainties present in the system model through an online control adaptation procedure. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture the unmodeled (neglected) dynamics or model uncertainties due to parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a reference model. This method is tested using a three degree of freedom model of a UAV. Numerical results which demonstrate these features and clearly bring out the potential of the proposed approach are presented in this paper.

This paper presents a neural network model for a three-dimensional ultrasonic position estimation system that uses the di erence in the time of arrivals of waves from a transmitter to various receivers. Even though a linearized analytical model for the three-dimensional system exists and is currently being used to estimate the position of the transmitter, its accuracy is highly dependent on complex and time consuming signal conditioning. A neural network approach is developed to train the system based on unconditioned training sets obtained directly from the receivers. It is proposed to use the nal trained system to estimate the three-dimensional position in real time using these raw signals, thereby simplifying the hardware and the computational software as well as increasing the update rate. The weights of the neural network are obtained from a traditional backpropagation method and by using genetic algorithms. Results for one-, two-and three-dimensional systems are presented as proof of concept. The performance of the neural network model using the raw signals is shown to be comparable to the analytical model using conditioned signals. Further, it is shown that the neural network model is extremely robust in terms of providing accurate position estimates, even after loss of information from multiple receivers. This work has signi cant applications in robotics, autonomous systems, virtual reality and image-guided surgery.

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