Tracking control for strict-feedback nonlinear systems with time-varying full state constraints

Abstract

This paper focuses on the tracking control problem for strict-feedback nonlinear systems subject to asymmetric time-varying full state constraints. Time-varying asymmetric barrier Lyapunov functions are employed to ensure time-varying constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. High-order coupling terms caused by backstepping are cancelled through a novel variable substitution for the first time. Besides the normal case, where the full knowledge of the system is available, we also handle scenarios of parametric uncertainties. Asymptotic tracking is achieved without violation of any constraints, and all signals in the closed-loop system are ultimately bounded. State-constrained systems with input saturation and bounded disturbances are also considered; the tracking error converges to a bounded set around zero. The performance of the asymmetric-barrier-Lyapunov-function-based control is illustrated through a numerical example.

Adaptive tracking control for nonlinear time-delay systems with time-varying full state constraints

“…Both time delay and time-varying full state constraints for uncertain nonlinear systems are considered in the paper. The proposed control method is more applicable than the methods in the aforementioned works (Li and Li, 2017; Liu et al, 2017; Wang et al, 2018a, 2019).…”

“…Remark 5: In the work of Liu et al (2017) and Wang et al (2018a, 2019), BLFs are employed to deal with time-varying state constraints. However, f ( · ) in system (1) is parametric uncertain and the time delay is not considered.…”

“…The unknown control gain functions are taken into account in the nonlinear time-delay systems with full state constraints. However, control methods in Liu et al (2017) and Wang et al (2018a, 2019) require control gain functions to be known.…”

Optimal Model Reference Control Scheme Design for Nonlinear Strict-Feedback Systems

“…In this work, the proposed controller makes the system output tracks the reference model in order to converge to achieve the desired performance. To facilitate the discussion of the main results, the following assumptions and theorems are made [16,17]. the model reference trajectory should be continuous and differentiable function up to the order.…”

Adaptive back‐stepping cancer control using Legendre polynomials

“…Thus, it is more flexible in designing controllers for high-order non-linear system models [32]. This control approach has been applied to various non-linear important systems such as missile systems [33][34][35], power systems [36], vehicle systems [37,38], pure and strictfeedback non-linear systems [39][40][41], and many other systems. This paper applies back-stepping design procedure to propose a controller for cancer treatment.…”