Adaptive Observer with Parametric Uncertainty in the System Dynamics and Output: An Initial Excitation Approach

In this paper, an adaptive observer is designed, which addresses the problem of joint estimation of state and the unknown parameters that emerge in the system dynamics as well as the output equation of a multi-input multi-output (MIMO) plant. Conventional adaptive observers ensure parameter convergence when the input-output signals are significantly ‘energy-rich’ to satisfy the persistence of excitation (PE). The proposed work develops a two-layered filter adaptive observer architecture based on initial excitation (IE), which relaxes the stringent PE condition in terms of excitation requirement and online verifiability. The unknown initial condition of the state is strategically appended with the vector of the unknown parameter, which essentially results in a higher dimensional estimator. This extended parameter estimator proves to be instrumental in ensuring uniformly global exponential stability (UGES) of the estimation error, applicable in a delayed sense. As far as the authors are aware this is the first work where a ‘relaxed’ excitation condition is utilized for simultaneous estimation of states and the unknown parameters which appear both in the state dynamics and the output. To validate the efficacy of the performance of the adaptive observer proposed, a simulation study has been undertaken on a remotely piloted aircraft model.