This article first proposes a sliding flexible prescribed performance boundary-guided reinforcement learning (SFPPB-RL) control approach for input-constrained nonlinear systems (ICNSs). By designing a sliding flexible prescribed performance boundary, which not only can adaptively adjust the initial boundary according to the initial error, but also dynamically adjust the constraint relaxation according to the coupling correlation between the input constraint and the performance constraint, a novel prescribed performance control (PPC) approach is proposed. Compared with the existing "horn" shape performance boundary-based PPC methods, the limitation of having to repeatedly debug design parameters or sacrifice initial transient performance to meet different initial error requirements is eliminated. Meanwhile, the coupling effect between the input constraint and the performance constraint is also considered, and the balance between input safety and control performance is achieved by constructing an auxiliary system. Furthermore, combining identifier-critic-actor structure-based RL strategy and backstepping technique, a sliding flexible PPB-guided reinforcement learning (SFPPB-RL) optimal control algorithm is developed, which minimizes the cost function while ensuring input safety and prescribed performance indicators. The validity of the proposed algorithm is demonstrated via simulations.

Abstract This paper pays close attention to the stabilization issue for delayed uncertain semi-Markovian jumping complex-valued networks via sliding mode control. The concerned corresponding transition rates depend on a positive constant, i.e., sojourn-time, which is not required to obey the general exponential distribution. Combine the generalized Dynkin’s formula with Lyapunov stability theory as well as the characteristics of cumulative distribution functions, a few sufficient criteria are proposed to ascertain the stochastic stability of the obtained sliding mode dynamical system. In addition, design a novel sliding mode controller to ensure all state trajectories of the potential closed-loop system can reach the synthesized sliding mode switching surface in a finite time and maintain there in the subsequent time. In the end of paper, one simple example is presented to verify superiority and feasibility of the provided controller design scheme.