Robust observer-based control of nonlinear dynamical systems with state constraints

In this paper, we design a variable structure observer-based control system that guarantees asymptotic convergence of the plant's trajectory to the equilibrium point despite matched and unmatched uncertainties in the plant dynamics. Our control laws are functions of the estimated plant state and the proposed framework allows employing any estimator or observer, such as the Walcott and Żak observer, as long as the estimated state converges asymptotically to the plant state. Barrier Lyapunov functions guarantee that the closed-loop system's trajectory verifies the state constraints. This study is the first of its kind, since recently variable structure control architectures have been adapted to account for constraints on the state space or allow output-feedback, but observer-based variable structure control in the presence of state constraints has not been attempted before. A numerical simulation involving the roll dynamics of an unstable aircraft, whose aerodynamic coefficients are unknown, illustrates our theoretical framework.