Continuous Finite-Time Output Regulation of Nonlinear Systems With Unmatched Time-Varying Disturbances

In this letter, a new continuous nonlinear controller ensuring finite-time output regulation is proposed for a class of nonlinear systems subject to unmatched time-varying disturbances. The controller is developed in a composite manner which combines invariant manifold principle, feedback domination and
disturbance observation techniques. A key idea is to realize the finite-time estimation of system steady states by means of finite-time disturbance observers. A feedback domination approach with dynamic disturbance compensation in each step of virtual control design is then developed by using the tool of adding a power integrator. Finite-time stability of the closed loop
system is established by means of Lyapunov theories, which shows that finite-time convergence of output tracking error is guaranteed even in the presence of time-varying disturbances subject to mismatching condition. The claimed performances of the proposed method are validated by a simulation example.