Least squares algorithm for multivariable systems: learning and prediction theory

In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochas-tic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Variable simulations examples are given, the results demonstrate that the convergence rate of the algorithm depends on the parameter dimension and output dimension.