Prescribed Finite Time Stabilization of Linear Systems With State Constraints

Abstract

This paper studies the prescribed finite time stabilization control problem of multi-input linear control systems subject to uncertainties and state constraints. Different from finite-time and fixedtime control methods, a novel switching nonsingular coordinate transformation function based on the block decomposition technique is developed, resulting in a solution that the control action is continuous and bounded based on the transformed system. Moreover, the boundedness of closed-loop system states is ensured with prescribed finite time performance. Furthermore, we incorporate the barrier Lyapunov function into the stabilization control design to restrain the amplitudes of system states. Numerical examples are provided to verify the effectiveness of the proposed prescribed finite time control strategy.

Prescribed‐time stabilisation control of differential driven automated guided vehicle

“…The main innovations of this paper in the prescribed-time control method are as follows: (1) A switching function Equation (11) with nth-order smoothing property is introduced to extend the running time of the prescribed-time control scheme to the whole time axis. Moreover, when n = 0, it becomes the case in [22]:…”

“…[16] and make it applicable to AGV motion control systems, existing works have designed time-varying piecewise functions to extend the action time of the prescribed-time controller to the entire time axis [18][19][20]. Alternatively, switching scaling functions were introduced to transform the original prescribed-time stabilisation problem into an asymptotic stabilisation [21,22]. In Ref.…”

“…[21], the switching scale function is simple in form and does not consider the delayed case of the system. In contrast to the work of [21], the literature [22] adds a reserved time for the system delay case, but its derivatives at the switching point are not continuous. These methods [18][19][20][21][22] solve to some extent the infinity problem faced by the prescribed-time controller at T moments and guarantee the continuity of the system after the prescribed time.…”

“…In contrast to the work of [21], the literature [22] adds a reserved time for the system delay case, but its derivatives at the switching point are not continuous. These methods [18][19][20][21][22] solve to some extent the infinity problem faced by the prescribed-time controller at T moments and guarantee the continuity of the system after the prescribed time. However, in the practical application of AGV, there may be switching timeout triggers or non-triggers (especially the event triggering method in Ref.…”

Online recorded data-based finite-time composite neural trajectory tracking control for underactuated MSVs

“…However, tracking errors of MSVs frequently require achieving finite time convergence. Recently, finite-time (FT) control methods have been intensively investigated and adopted for various control systems because of their advantages of fast convergence and strong robustness (Yang et al, 2021(Yang et al, , 2022a. For the FT convergence problem, scholars have proposed a large number of advanced FT control techniques, In addition to the sliding-mode-based FT control method, uniformity and the addition of a power integrator (API) are also effective methods to achieve FT stability.…”