On using least-squares updates without regressor filtering in identification and adaptive control of nonlinear systems

In continuous-time system identification and adaptive control the least-squares parameter estimation algorithm has always been used with regressor filtering, which adds to the dynamic order of the identifier and affects its performance. We present an approach for designing a least-squares estimator that uses an unfiltered regressor. We also consider a problem of adaptive nonlinear control and present the first least-squares-based adaptive nonlinear control design that yields a complete Lyapunov function. The design is presented for linearly parametrized nonlinear control systems in 'normal form'. A scalar linear example is included which adds insight into the key ideas of our approach and allows showing that, for linear systems, our Lyapunov-LS design with unfiltered regressor, presented in the note for unnormalized least-squares, can also be extended to normalized least-squares.