Adaptive control in presence of input saturation constraint an input-output approach

The problem of controlling time-invariant linear systems subject to parametric uncertainty and input saturation constraint is considered. A cautious combination of a pole placement control design and a least squares parameter adaptation is used to this end. The global stability and convergence analysis of the involved control system is carried out by investigating the l₂-stability of an adequate nonlinear feedback system. The stability condition turns out to be positive-realness of a transfer function involving the (estimated) model and the specified closed-loop poles. Such a stability requirement is shown to be satisfied using a suitable modification of the indirect pole placement adaptive control, namely i) a suitable self-excitation capability ensuring the asymptotic admissibility of the estimated plant model, e.g. the asymtotic stability. ii) an appropriate adaptation of the regulator parameters as well as the desired closed-loop poles. Besides the closed-loop global stability, the proposed control algorithm guarantees asymptotic tracking of constant reference sequences and enforces the input control to stop saturating asymptotically.