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The purpose of this chapter is to summarize a collection of standard control design techniques for certain classes of nonlinear systems. Later we will use these control techniques to develop adaptive control approaches that are suitable for use when there is additional uncertainty in the plant dynamics. Since the linear concept | 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 Part II State-Feedback Control 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 x- unapter Pissr Control of Nonlinear Systems Overview The purpose of this chapter is to summarize a collection of standard control design techniques for certain classes of nonlinear systems. Later we will use these control techniques to develop adaptive control approaches that are suitable for use when there is additional uncertainty in the plant dynamics. Since the linear concept of phase does not carry over to the nonlinear world we will not consider many of the traditional control design techniques such as using Bode and Nyquist plots. Instead we will use Lyapunov-based design techniques where a controller is chosen to help decrease a measure of the system error. Let X y h x u v 7 define the dynamics of a system with state x E Rn input u E Rm and output y E Rp. Given a control law u v t x it is assumed that t x is locally Lipschitz in x and piece-wise continuous in t so that given the initial state rr O there exists a unique trajectory satisfying . Throughout this book we will use the notation u v z to define a control law where z t is a vector of appropriate signals for the particular application. The vector z may contain for example reference signals states dynamic signals or combinations of any of these. We will only consider controllers where the components of z are measurable signals. The purpose of the controller is typically to force y r t where r E Rp is a reference signal. When r is time-varying .