Practical prescribed time tracking control over infinite time interval involving mismatched uncertainties and non-vanishing disturbances

Most existing prescribed time control methods are valid for finite time intervals rather than infinite time intervals, and can only achieve regulation under vanishing or no uncertainties/disturbances. In this work, a control method that achieves pre-assignable tracking precision within the prescribed time is presented for nonlinear systems in the presence of non-vanishing disturbances and mismatched uncertainties over the infinite time interval. More specifically, by introducing a novel time-varying constraining function, the original finite-time tracking control problem is converted into one with a deferred constraint on tracking error, then by stabilizing of which, the prescribed time tracking control problem is solved with the following appealing features: 1) both the settling time and the tracking accuracy can be explicitly specified in advance regardless of initial conditions and any design parameter; 2) the control gains and the control input remain bounded and continuous everywhere; 3) the system is allowed to operate continuously even after the prescribed time; and 4) the results are global in that pre-set tracking accuracy is ensured within the predefined time for states starting from anywhere within the physically possible domain.