Chapter Seven. Full-State Feedback of Uncertain Multi-Input Systems

Abstract

This chapter investigates adaptive control for uncertain multi-input LTI systems with distinct discrete actuator delays. In parallel with the single-input case in the third chapter, four types of basic uncertainties come with multi-input LTI time-delay systems. Different combinations of the four uncertainties above result in different design difficulties. For example, when the full-state measurement of the transport PDE state is available, the global stabilization is acquired, whereas when the actuator state is not measurable and the delay value is unknown at the same time, the problem is not solvable globally, since the problem is not linearly parameterized. The chapter then summarizes the different collections of uncertainties for the multi-input case. When some of the four variables are unknown or unmeasured, the basic idea of certainty-equivalence-based adaptive control is to use an estimator (a parameter estimator or a state estimator) to replace the unknown variables in the PDE-based framework in the previous chapter, and carefully select their adaptive update laws based on Lyapunov-based analysis.