Exponential Stabilization for a Class of Strict-Feedback Nonlinear Time Delay Systems via State Feedback Control Scheme

Abstract

This paper considers the exponential stabilization problem for a class of strict-feedback nonlinear systems with multiple time-varying delays, whose nonlinear terms satisfy the linear growth condition. The state feedback controller that relies on a positive parameter to be determined is constructed to deal with nonlinear terms. By tactfully introducing the Lyapunov–Krasovskii functional with an exponential function and selecting the applicable parameter to be determined, the implementable state feedback controller can be obtained to guarantee that the closed-loop system is exponentially stable. The proposed state feedback control scheme is finally applied to the control design of two-stage chemical reactor system, which illustrates the effectiveness of the control method.

Reinforcement learning event-triggered output feedback control for uncertain nonlinear discrete systems

“…Bai et al (2019) resolved the RL control problem for some uncertain nonlinear systems, where utility function and dynamic uncertainties were estimated by the critic and actor NN scheme. In addition, backstepping technique has been well developed and applied in the control issue for strictfeedback nonlinear systems (Kong and Liu, 2022;Wen et al, 2018Wen et al, , 2020. In the work by Wen et al (2020), the tracking control of nonlinear strict-feedback systems with unknown dynamics was tackled using the RL mechanism with the backstepping strategy, where the uncertainties were estimated by actor-critic NNs.…”

“…1. Compared with the state-feedback control proposed in the work by Kong and Liu (2022) and Sun et al (2023) (2019), when the controllers are sampled at all discrete instants, an ET mechanism is adopted to sample the input signal, which can realize the energy consumption in transmission.…”

“…In the work by Wen et al (2020), the tracking control of nonlinear strict-feedback systems with unknown dynamics was tackled using the RL mechanism with the backstepping strategy, where the uncertainties were estimated by actor-critic NNs. Applying the backstepping methodology, Kong and Liu (2022) developed a state-feedback control policy for strict-feedback nonlinear systems with numerous time-varying delays. In the work by Wen et al (2018), the RL-based optimized tracking control for strict-feedback systems was addressed in light of backstepping method.…”

“…Compared with the state-feedback control proposed in the work by Kong and Liu (2022) and Sun et al (2023), the RL-based output feedback tracking problem has been further addressed for uncertain strict-feedback nonlinear discrete-time systems, where a dynamic state observer is developed in view of the actor NN. The presented state observer can ensure the state estimation errors are semi-global uniformly ultimately bounded (SGUUB).…”