The Saturated Delayed Design For Linear And Nonlinear Multiple Integrators

Actuator saturation phenomena are often found in engineering practice and consequently, saturated designs have been paid attention for a long time. Using the saturation approach, Teel and Sussmann had ever presented stabilization designs for the chain of integrators. Recently, the related research even becomes a hot issue of nonlinear control, the algorithms of multiple integrators have been extended to the case of the nonlinear situation. There are a lot of nonlinear feedforward systems, whose input-constrained stabilization problem have been considerably studied, while taking into account the input amplitude constraints and the input delays of the systems, that is, designing the saturated delay control law of the feedforward systems, is more challenging. Along this line of research, the main works in this paper are stated as follows.1. This paper addresses the robust stabilization of a chain of integrators with a delay and an additive perturbation in the input. In principle, the design in this paper admits arbitrarily large time delay and perturbation. As for the stabilization in the unperturbed case is concerned, the proposed design admits a larger time delay than the existing nested method when the order of the chain of integrators is high and the control amplitude is a certain constant.2. This paper presents two kinds of saturated delayed controls for nonlinear multiple integrators that are in a feedforward form, guaranteeing that the states of the closed-loop system are globally asymptotically stable, at the same time, the design in this paper admits arbitrarily large time delay. The main strategy of the design is: suggested algorithm depends on suitable normal forms rather than the homogeneity of multiple integrators, the small parameter in suitable normal forms is set into the saturated delayed controls, by adjusting this parameter, we can compensate for any input delays.3. This paper investigates the decentralized stabilization with saturated delayed feedback laws for a class of large-scale feedforward systems. Firstly, upon specifications to the centralized feedforward systems, we obtain a new class of saturated delayed controllers for the single-input feedforward nonlinear systems, then; this design scheme is generalized to the setting of decentralized large-scale feedforward systems using saturated time-delayed feedback. As a by-product, the obtained results extend the existing centralized design, and we also have extended the previous decentralized design to the time-delayed case.