Adaptive Prescribed Finite Time Control for Strict-Feedback Systems

An adaptive observer based output feedback prescribed‐time control of a class of nonlinear systems with unknown parameters

“…Consider the armature‐controlled DC motor system studied in Reference 55 which the relative degree is $$$ r=2 $$$, $$$$ {\displaystyle \begin{array}{ll}{R}_{\mathrm{a}}{i}_{\mathrm{a}}+{L}_{\mathrm{a}}{\dot{i}}_{\mathrm{a}}+{C}_{\mathrm{e}}\omega & =u,\\ {}J\dot{\omega}+ f\omega -{C}_{\mathrm{m}}{i}_{\mathrm{a}}& =0,\end{array}} $$$$ where $$$ {R}_{\mathrm{a}}=6\Omega, {L}_{\mathrm{a}}=0.1\mathrm{H},{C}_{\mathrm{e}}=0.132\mathrm{V}\cdotp \mathrm{s}/\mathrm{rad},{C}_{\mathrm{m}}=0.2,f=0.15\mathrm{N}\cdotp \mathrm{m}\cdotp \mathrm{s}/\mathrm{rad} $$$ and $$$ J=0.06125\mathrm{kg}\cdotp {\mathrm{m}}^2 $$$ are constants which denote resistance, inductance, back electromotive force coefficient, electromagnetic torque coefficient, friction coefficient and rotational inertia, respectively, $$$ \omega, {i}_{\mathrm{a}} $$$ are angular speed, armature current denote system variables with …”