Exact Predictor Feedback for Multi-Input Systems

This chapter presents the exact predictor feedback for deterministic multi-input LTI systems with distinct discrete input delays. This offers a PDE-based framework for compensation for multi-input distinct delays and lays a foundation for adaptive control in later chapters. In the PDE-based framework to deal with the discrete multi-input delays, the problem is formulated as a cascade between several first-order transport PDEs (accounting for the distinct delayed inputs) and an ODE (accounting for the original plant). This problem is solved using backstepping to design a prediction-based controller. The key idea of this prediction technique is to replace future inputs involved in the state predictions computation by their closed-loop expressions.