A Discretization of the Hybrid Gradient Algorithm for Linear Regression with Sampled Hybrid Signals

We consider the problem of estimating a vector of unknown constant parameters for a linear regression model whose inputs and outputs are discretized hybrid signals – that is, they are samples of hybrid signals that exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid systems framework, we propose a hybrid gradient descent algorithm that operates during both flows and jumps. We show that this algorithm guarantees exponential convergence of the parameter estimate to the unknown parameter under a new notion of discretized hybrid persistence of excitation that relaxes the classical discrete-time persistence of excitation condition. Simulation results validate the properties guaranteed by the new algorithm.