Robust estimation‐free decentralized prescribed performance control of nonaffine nonlinear large‐scale systems

Abstract

SummaryIn this paper, a low-complexity robust estimation-free decentralized prescribed performance control scheme is proposed and analyzed for nonaffine nonlinear large-scale systems in the presence of unknown nonlinearity and external disturbance. To tackle the high-order dynamics of each tracking error subsystem, a time-varying stable manifold involving the output tracking error and its high-order derivatives is constructed, which is strictly evolved within the envelope of user-specialized prescribed performance. Sequentially, a robust decentralized controller is devised for each manifold, under which the output tracking error and its high-order derivatives are proven to converge asymptotically to a small residual domain with prescribed fast convergence rate. Additionally, no specialized approximation technique, adaptive scheme, and disturbance observer are needed, which alleviates the complexity and difficulty of robust decentralized controller design dramatically. Finally, 3 groups of illustrative examples are used to validate the effectiveness of the proposed low-complexity robust decentralized control scheme for uncertain nonaffine nonlinear large-scale systems.

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

“…The inequality constraint only depicts a general variation of with x i + 1 , which has no special requirement for each specific point on the nonlinear curve. Figure B is an illustration of the common assumption utilized in other works . The conventional controllability condition of nonaffine functions is , which requires the nonaffine function to be differentiable and its partial derivative to keep positive all the time.…”

“…The past decades have witnessed a great amount of studies on control for nonaffine systems where the control inputs take their actions through a nonlinear and implicit way . There are many systems falling into this category featured with nonaffine structure, such as mechanical systems, biochemical process, and aircraft flight control system .…”

“…Most notably, mean value theorem is typically used to build a transformational model for nonaffine system under the condition that ∂f ( x , u )/ ∂u is bounded, and then, control approaches such as adaptive fuzzy control, adaptive neural network control, and prescribed performance control can be constructed on the basis of the transformational model. Moreover, Taylor series expansion is also utilized to construct an equivalent system under the hypothesis that ∂f ( x , u )/ ∂u is bounded, and then, adaptive fuzzy controllers can be designed based on the pseudoaffine system …”

“…Many constraint control schemes have been utilized to cope with output constraint control problems such as Barrier Lyapunov function, funnel control (FC), and prescribed performance control (PPC) . Moreover, PPC, as an alternative method of FC, is proposed for nonlinear systems of higher relative degree .…”

Second-Order Sliding Mode Disturbance Observer-Based Adaptive Fuzzy Tracking Control for Near-Space Vehicles with Prescribed Tracking Performance

“…In [28], a fault-tolerant controller guaranteeing prescribed tracking performance has been proposed for a class of nonlinear uncertain systems. Moreover, the prescribed performance controllers for the cascade systems [29] and the nonaffine nonlinear large scale systems [30] have also been developed.…”