Prescribed-Time Consensus Control for Nonlinear Multi-Agent Systems With Output Constraint: A Bounded Time-Varying Gain-Based Method

Abstract

This paper explores the prescribed-time consensus control problem for a class of high-order strict-feedback nonlinear multi-agent systems with output state constraints. A distributed adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathit {C^{1}}$ </tex-math></inline-formula> smooth control scheme is developed such that the output-constrained consensus tracking is achieved within a prescribed time regardless of any initial conditions and other design parameters, although in the presence of completely unknown control gains and uncertainties. The prescribed-time control scheme is made possible for high-order systems by constructing a hybrid time-varying gain-based prescribed-time first-order filter and using the time transformation methods. Particularly, a novel uniformly switching mechanism is introduced into the time-varying gains, where the gain function is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathit {C^{1}}$ </tex-math></inline-formula> smooth and the switching time is regardless of initial conditions, ensuring that the gains are uniformly bounded for all time and thus avoiding infinite time-varying gain problem. Finally, the benefits and effectiveness of the proposed control scheme are confirmed by a numerical simulation and its application to a 2 degree of freedom robotic manipulator. Note to Practitioners—This paper investigates the distributed adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C^{1}$ </tex-math></inline-formula> smooth control problem for nonlinear multi-agent systems with high-order strict-feedback dynamics, which can model various physical systems, such as flight systems, robotic systems, and autonomous aerial vehicles. Achieving distributed prescribed-time control for high-order MASs with completely unknown control gains, output constraint, and uncertainties poses significant challenges. By introducing a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C^{1}$ </tex-math></inline-formula> smooth gain switching mechanism, a hybrid time-varying gain function is constructed to ensure uniform boundedness of the time-varying gain, which effectively avoids the high-gain implementation problem. Moreover, a prescribed-time distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C^{1}$ </tex-math></inline-formula> smooth controller, operating smoothly for all time and everywhere is also forwarded, which is more desirable in practice. As a result, the proposed control scheme demonstrates high adaptability to practical engineering requirements and exhibits enhanced generalizability, as finally validated by the numerical simulations including a dual-degree-of-freedom robotic manipulator.