An Adaptive Observer Design for 2 × 2 Semi-linear Hyperbolic Systems using Distributed Sensing

We design an adaptive model-based observer for state and parameter estimation in 2 × 2 semi-linear hyperbolic systems with uncertain parameters where we assume that one of the two distributed states is available through distributed sensing. The uncertainties appear in the equation for the unmeasured distributed state and may be non-linear in the unmeasured state, although linearly parameterized. The adaptive law is designed using a Lyapunov approach and expressed in terms of known signals by utilizing the specific model structure which gives rise to a general solution strategy valid for a large class of non-linear source terms.