Adaptive Observer with Enhanced Gain to Address Deficient Excitation

For joint estimation of state variables and unknown parameters, adaptive observers usually assume some persistent excitation (PE) condition. In practice, the PE condition may not be satisfied, because underlying recursive problem is ill-posed. To remedy lack condition, inspired by ridge regression, this paper proposes a regularized observer with enhanced parameter adaptation gain. Like in typical ill-posed inverse problems, regularization implies an bias, which can reduced using prior knowledge about parameters.