Improved decentralized prescribed performance control for non-affine large-scale systems with uncertain actuator nonlinearity

Abstract

Abstract This work considers a decentralized control problem for non-affine large-scale systems with non-affine functions possibly being discontinuous. A semi-bounded condition for non-affine functions is presented to guarantee the controllability, and the non-affine system is transformed to an equivalent pseudo-affine one based on the mild condition. Different from conventional control schemes on specific actuator nonlinearity, the controller proposed in this paper can deal with a series of actuator nonlinearities such as backlash and deadzone nonlinearity. A time-varying stable manifold involving the tracking error and its high-order derivatives is utilized to handle the high-order dynamics of each subsystem. Besides an improved prescribed performance controller independent of the initial condition is constructed to ensure the finite-time convergence of the error manifold to a predefined region. The boundedness and convergence of the closed-loop system are proved by Lyapunov theory and the counter-evidence method. Two examples are performed to verify the theoretical findings.