Global Prescribed-Time Control of Nonlinear Uncertain Systems via a Novel Low-Complexity Analysis Framework

Abstract

The global prescribed-time stability problem of a class of uncertain systems is investigated. Utilizing the proposed $\gamma$-fold convergence convergence function, a novel low-complexity global prescribed-time stability analysis framework is developed. Existing virtual controllers based on time-varying transformation methods usually involve high-order derivative information of time-varying functions, posing significant challenges for stability analysis. We proposed a new stability criterion, which only involves the partial state variable on the right-hand side of the derivative inequality. The key advantage is that it eliminates the need for directly analyzing the boundedness of the virtual control gain coefficients with high-order time-varying functions. Building off this framework, we address the prescribed-time stabilization problem of multi-input multi-output (MIMO) nonlinear systems, where the Nussbaum gain function is extended to prescribed-time control to deal with time-varying sensor errors. Note that due to the infinitely divergent nature of time-varying functions at the terminal, ensuring the boundedness of the variables in the Nussbaum function is a challenge. Finally, we rigorously prove that all signals are bounded and the proposed controllers ensure that all state variables of systems converge to origin within a specified time, while the transient performance (convergence rate and specified overshoot) of the system output is also guaranteed. A simulation example is provided to illustrate the efficiency of the developed control algorithms.