On the Output-Feedback Regulation for a Second-Order System with Unknown Parameters: An I&I and MRAC Based Approach

We propose an adaptive stabilization solution for a linear second-order system with unknown parameters, where only the position and the sign of the constant associated with the control input are known. The control strategy consists in proposing a filter system with its whole state available and having the same structure as the uncertain system. Then, based on the Immersion & Invariance approach, and the Model Reference method, we design an adaptive controller to stabilize the filter system. Finally, using the backstepping approach, we stabilize the original uncertain system. We carry out the convergence analysis using the traditional Lyapunov method, in conjunction with the Barbalat’s Lemma. The obtained control strategy is simple and easy to implement. We assess the effectiveness of our adaptive control strategy through numerical simulations.