Parametric Lyapunov equation based event‐triggered and self‐triggered control of input constrained linear systems

Abstract

This article studies semiglobal stabilization of input constrained linear systems based on the static and dynamic event-triggered control (ETC) and self-triggered control (STC). First, a static ETC based on the parametric Lyapunov equation (PLE) is designed. Then the corresponding dynamic ETC is also proposed. The main advantage of the proposed static and dynamic ETC algorithms is that the minimum interexecution time (MIET) as a decreasing function of the parameter in the PLE is given, which allows us to find easily a trade-off between the interexecution times (IETs) and the control performance. The fact that the MIET of the dynamic ETC is never less than that of the static ETC is also guaranteed. Next, in order to avoid continuous monitoring of the states, both static and dynamic STC are designed. The influence of the parameters on IETs of the static and dynamic STC is analyzed in detail. The nonoccurrence of the Zeno phenomenon is proved in all the control algorithms. Finally, the proposed algorithms are applied to the design of spacecraft rendezvous. Numerical simulations on the original nonlinear model of the spacecraft rendezvous control system show the control system effectiveness of the algorithms.

Adaptive fault‐tolerant robust control based on radial basis function neural network for a class of mechanical systems with input constraints

“…Control problem with constrained input is a common nonlinear problem in control theory. [6][7][8][9][10] There has been a lot of research on control problems with input constraints in recent years. 11,12 Antisaturation control is a common method in which anti-saturation controller is used to compensate for the system performance degradation caused by actuator saturation when the actuator is saturated.…”

“…In a control system, the physical characteristics of the actuator or the controlled plant usually require the input magnitude of the closed‐loop system to be bounded. Control problem with constrained input is a common nonlinear problem in control theory 6–10 …”

Periodic event‐triggered control with multisource disturbances and quantized states

“…Some interesting results have been obtained for different kinds of complex system, such as nonlinear systems, 1,2 multi-agent systems, 3,4 fuzzy systems, 5,6 stochastic systems, 7,8 and so on. Meanwhile, various types of ETC strategies have been proposed, such as self-triggered control, 9,10 continuous-time event-triggered control, 11,12 discrete-time event-triggered control 13,14 and adaptive event-triggered control, 15,16 etc. More recently, periodic event-triggered (PET) control has attracted considerable attention.…”

Finite-Time Stabilization of Linear Systems With Input Constraints by Event-Triggered Control

“…The global stabilization of general linear systems with input constraints has been well achieved by the nonlinear ETC algorithm in [7]. A controller based on the general Riccati equation was designed in [8], where the event-triggered mechanism is conservative and the solution of the parameters is too complicated. Recently, a series of ETC algorithms based on the parametric Lyapunov equation (PLE) have been designed in [9], [10], where the relationship between the design parameters and the minimal inter-event time (MIET) is clearly and simple.…”