Adaptive Nonlinear Prescribed-Time Control With Filterless Least Squares

For linearly parametrized nonlinear systems in normal form, we first develop a new prescribed-time (PT) least-squares identification scheme (abbreviated PT-LS) characterized by a blow-up function, and then design a new PT adaptive controller which ensures that the plant state is regulated to zero in the prescribed time and the parameter estimate converges to a vector-valued constant in the same PT. Under a moderate interval excitation (IE) condition where the IE is fulfilled at the time strictly before the terminal time and we maintain the presence of IE in the estimator until the terminal time, even though the regressor may have lost the excitation, we redesign a new PT-LS estimator by introducing a novel term characterized by the blow-up function, online historical data and instant data, which not only ensures that the plant state is regulated to zero in PT, but also that the parameter estimation is strongly consistent in the same PT, i.e., the estimator PT-converges to the parameter's true value. Finally, two simulation examples are given to illustrate the PT-LS and adaptive control designs.