Basic Predictor Feedback
In this chapter we introduce the basic idea of a PDE backstepping design for systems with input delay.We treat the input delay as a transport PDE, an elementary first–order hyperbolic PDE. Our design yields a classical control formula obtained through various other approaches–modified Smith predictor (mSP), finite spectrum assignment (FSA), and the Artstein–Kwon–Pierson “reduction“ approach. The backstepping approach is distinct because it provides a construction of an infinitedimensional transformation of the actuator state, which yields a cascade system of transformed stable actuator dynamics and stabilized plant dynamics. Our design results in the construction of an explicit Lyapunov–Krasovskii functional and an explicit exponential stability estimate.
KeywordsLyapunov Function Exponential Stability Smith Predictor Stability Proof Adaptive Control Design
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