A Novel Prescribed-Time Control Approach of State-Constrained High-Order Nonlinear Systems

A novel practical prescribed-time control (PPTC) approach for high-order nonlinear systems (HONSs) subject to state constraints is studied in this article. Different from the existing methods which always require the constraint boundaries to be continuous functions, the state constraints considered in this article are discontinuous (i.e., the state constraints occur only in some time periods and not in others), which can be found in many practical systems. By designing a novel stretch model-based nonlinear mapping function (NMF), the state constraints are dealt with directly, and the limitations that the virtual control function depends upon the feasibility condition (FC) and the tracking error depends upon the constraint boundaries in the conventional schemes are removed. Meanwhile, the proposed method is a unified one, which is also effective for HONSs with conventional continuous state constraints/ deferred state constraints/ funnel constraints or constraints-free without altering the control structure. Furthermore, by designing a newly time-varying scaling transformation function (STF), a more relaxed criterion for practical prescribed-time stable (PPTS) is given, based on which a newly PPTC algorithm is designed. The result shows that the proposed algorithm can preset the upper bound of the settling time, which does not depend upon the initial state of the system and control parameters, the limitations of singularity problem and excessive initial control input in existing methods are removed. Simulation examples verify the algorithm developed.