As humans, we are intuitively familiar with the process of optimization because of our constant exposure to it. For instance, in business investments we seek to maximize our profits; in recreational games we seek to maximize our own score or minimize that of our opponent. It is not surprising that optimizaStion plays a key role in engineering and many other fields. In circuit design we may want to maximize power transfer, in motor design we may want to design for the highest possible torque delivery for a given amount of current, or in communication system design we may want to. | Stable Adaptive Control and Estimation for Nonlinear Systems Neural and Fuzzy Approximator Techniques. Jeffrey T. Spooner Manfredi Maggiore Raul Ordonez Kevin M. Passino Copyright 2002 John Wiley Sons Inc. ISBNs 0-471-41546-4 Hardback 0-471-22113-9 Electronic Chapter 1r Optimization for Training Approximators Overview As humans we are intuitively familiar with the process of optimization because of our constant exposure to it. For instance in business investments we seek to maximize our profits in recreational games we seek to maximize our own score or minimize that of our opponent. It is not surprising that optimization plays a key role in engineering and many other fields. In circuit design we may want to maximize power transfer in motor design we may want to design for the highest possible torque delivery for a given amount of current or in communication system design we may want to minimize the probability of error in signal transmission. Indeed in the design of control systems we have the field of optimal control where one objective might be to minimize tracking error and control effort energy while stabilizing a system. Here as in many adaptive control methods the adaptive schemes are designed to search for a parameter set which minimizes a cost function while maintaining or seeking to achieve certain closed-loop properties . stability of the adaptive system. For instance we may seek to adjust the parameters of a neural network or fuzzy system which we treat as approximators so that the neural network or fuzzy system approximator nonlinearity matches that of the plant and then this synthesized nonlinearity is used to specify a controller that reduces the tracking error. Optimization then forms a fundamental foundation on which all the approaches rest. It is for this reason that we provide an introduction to optimization here. The reader who is already familiar with optimization methods can skip or skim this chapter and go to the next one. 73 74 .
