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The prescribed‐time stabilization problem for a general class of uncertain nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed‐time stabilization objective requires convergence of the state vector to the origin in a finite time interval that can be arbitrarily picked (i.e., "prescribed") by the control system designer irrespective of the system's initial condition. The class of systems considered is allowed to have general nonlinear uncertain terms throughout the system dynamics as well as uncertain appended dynamics (that effectively generate a time‐varying non‐vanishing disturbance signal input into the nominal system). The control design is based on a nonlinear transformation of the time scale, dynamic high‐gain scaling, adaptation dynamics with temporal forcing terms, and a composite control law that includes two components. The first component in the composite control law is analogous to prior dynamic high‐gain scaling‐based control designs, but with a time‐dependent function in place of the unknown input gain, while the second component has a non‐smooth form with time‐dependent terms that ensure prescribed‐time convergence in spite of the unknown input gain and the disturbances. The efficacy of the proposed control design is illustrated through numerical simulation studies on two example systems (a "synthetic" fifth‐order system and a "real‐world" electromechanical system). [ABSTRACT FROM AUTHOR]

In this paper, we propose a dynamic high-gain scaling technique and solutions to coupled Lyapunov equations leading to results on state-feedback, output-feedback, and input-to-state stable (ISS) appended dynamics with nonzero gains from all states and input. The observer and controller designs have a dual architecture and utilize a single dynamic scaling. A novel procedure for designing the dynamics of the high-gain parameter is introduced based on choosing a Lyapunov function whose derivative is negative if either the high-gain parameter or its derivative is large enough (compared to functions of the states). The system is allowed to contain uncertain terms dependent on all states and uncertain appended ISS dynamics with nonlinear gains from all system states and input. In contrast, previous results require uncertainties to be bounded by a function of the output and require the appended dynamics to be ISS with respect to the output, i.e., require the gains from other states and the input to be zero. The generated control laws have an algebraically simple structure and the associated Lyapunov functions have a simple quadratic form with a scaling. The design is based on the solution of two pairs of coupled Lyapunov equations for which a constructive procedure is provided. The proposed observer/controller structure provides a globally asymptotically stabilizing output-feedback solution for the benchmark open problem proposed in our earlier work with the provision that a magnitude bound on the unknown parameter be given. Index Terms--Adaptive, high-gain, input-to-state stable (ISS), nonlinear, output feedback, scaling.

Summary: The prescribed‐time output‐feedback stabilization (ie, regulation of the state and control input to zero within a "prescribed" time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict‐feedback‐like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state‐dependent nonlinear functions throughout the system dynamics. We show that prescribed‐time output‐feedback stabilization (ie, both prescribed‐time state estimation and prescribed‐time regulation) is achieved through a novel output‐feedback control design involving specially designed dynamics of an adaptation state variable and a high‐gain scaling parameter in combination with a temporal transformation and a dual high‐gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high‐gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high‐gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval. [ABSTRACT FROM AUTHOR]