Prescribed‐time control with explicit reference governor for a class of constrained cascaded systems

Abstract

Different from both finite‐time control (where the settling time depends on the initial condition) and fixed‐time control (whose settling time is subject to an upper bound but varies due to uncertainties and nonlinearities), the prescribed‐time control achieves regulation in prescribed finite time, even under uncertain nonlinearities. This article investigates the prescribed‐time regulation problem for a class of cascaded systems with integral form and control input constraints. The establishment of prescribed‐time property consists of the prescribed‐time regulation controller and prescribed‐time explicit reference governor (PT‐ERG), both of which satisfy the prespecified time requirement. For an elegant implementation, the feasibility for the separate design of controller and governor is guaranteed through a developed prescribed‐time cascaded stable theory. For the prescribed‐time controller, the proposed smooth time‐varying controller provides the prescribed‐time convergence based on a residual‐time‐dependent scaling transformation. For the PT‐ERG dealing with the control input constraints, a reference trajectory with a fixed minimum convergence rate provides an elegant compromise between performance and constraints which keeps the constraint satisfied and tracking errors in an invariant set. Both theoretical analysis and numerical simulations verify the effectiveness of the proposed control scheme.

Balanced control between performance and saturation for constrained nonlinear systems

“…Every control problem can be formed as a constrained optimization problem in MPC such that the control performance can be optimized without saturation happens. As the method termed explicit reference governor (ERG) for tacking problem developed in References 17‐20, the performance and control input constraints are converted into limitations on upper Lyapunov function (or the limitation in an invariant set), and the balance is achieved through the application of a trade‐off reference trajectory. The adaptive prescribed performance control in Reference 21 accomplishes a trade‐off between input limitations and output constraints, by relaxing the performance bounds of conventional PPC, when the saturation takes place.…”

Predefined‐time tracking control of a class of nonlinear systems via a novel C∞ performance function

“…The second category presented in References 15–25 designs a monotonically increasing time function (also called time base generator or scaling function) which approaches infinity at a predefined time. This time function is injected into controllers as a time‐varying gain so that the controllers can force the solutions of systems to converge to zero at this predefined time.…”

“…In summary, the predefined‐time control is still an open topic although the studies in References 7–28 have achieved successful and promising results. Motivated by the aforesaid research, this article introduces a novel performance function with the property of reaching its terminal value at a predefined time, and whereby develops a new predefined‐time tracking control scheme for a class of nonlinear systems, such that the system tracking error can converge to a given tolerant steady‐state error domain within a predefined time.…”

“…Our developed predefined‐time control scheme has higher compatibility compared to References 7–14 as it does not require a specific control design framework. This means that any control methods can be incorporated into our developed predefined‐time control scheme. Our developed predefined‐time control scheme does not cause the high‐gain control problem at the predefined time in References 15–25. Differing from the fractional power functions in References 26–28, our introduced performance function can directly and flexibly off‐line predefine a desired time required for the performance function to reach its terminal value, independent from its parameters. And our introduced performance function is a $$$ {C}^{\infty } $$$ function so that it is applicable to arbitrary order systems. …”

Balanced control between performance and saturation for constrained nonlinear systems

“…A flexible performance control (FPC) scheme [17], [18] introduces the modification signals into the predetermined performance function, thus features the capability of avoiding performance violation due to input saturation. As the method termed explicit reference governor (ERG) for tacking problem developed in [19]- [21], the performance and control input constraints are converted into limitations on upper Lyapunov function (or the limitation in an invariant set), and the balance is achieved through the application of a trade-off reference trajectory.…”