We present a novel decentralized tracking control scheme for a class of large-scale nonlinear systems with partial state constraints. For the first time, backstepping design with the newly proposed BLF is incorporated to effectively deal with the control problem of nonlinear systems with interconnected constraints. To prevent the states of each subsystem from violating the constraints, we employ a special barrier Lyapunov function (BLF), which grows to infinity whenever its argument approaches some finite limits. By ensuring boundedness of the barrier Lyapunov function in the closed loop, we ensure that those limits are not transgressed. Asymptotic tracking is achieved without violation of the constraints, and all closed-loop signals remain bounded. In the end, an illustrative example is presented to demonstrate the performance of the proposed control.

The control problem of constrained systems is by far one of the most common challenges faced by control engineers. In practical physical systems, constraints are ubiquitous, such as physical stoppages, saturation, and performance and safety specifications. Violation of the constraints during operation may result in performance degradation, hazards, or system damage. Driven by practical needs and theoretical challenges, the rigorous handling of constraints in control design has become an important research topic in recent decades. Various techniques have been developed to solve the constrained control problems, namely, override control [

Integrator backstepping design was developed in [

However, despite the maturity of BLF in dealing with SISO systems, the more challenging control problem of constrained large-scale systems has received little attention, for the reason that the constrained states are distributed in the subsystems. In this paper, we tackle the tracking problem of large-scale nonlinear system with partial states constrains, motivated by the fact that full state constrains systems and output constrained systems mentioned before are subset of it. By using a BLF, new decentralized tracking control design is presented based on backstepping methodology, but more efforts are made to deal with the constrained states of the subsystems. The stability analysis shows that all closed-loop signals are ensured to be bounded, and the output tracking errors can converge to zero asymptotically. Simulation results demonstrate the effectiveness of the proposed approach.

Consider a partial constrained large-scale system comprised of

For

The reference signals

The large-scale nonlinear systems considered in this paper are more complicated than output constrains [

In this section, adaptive decentralized controller design for system (

Define the error variables

To keep the constraint

Consider the closed-loop systems (

The signals

The states

All closed-loop signals are bounded.

The output tracking errors

The properties

In this section, we consider the following large-scale system consisting of two second-order subsystems:

Based on the control scheme proposed in this paper, we have

The tracking performances are shown in Figures

Tracking performance of subsystem 1.

Tracking performance of subsystem 2.

State

Control efforts.

From Figures

The problem of tracking control for a class of interconnected large-scale systems with partial state constraints has been considered. Such systems are very common in practice due to physical/performance limitations. The main contribution of this paper is the first extension of the BLF-based backstepping control methodology to interconnected large-scale systems with distributed constrained states. Future research will focus on extending the proposed approach to a more general class of nonlinear systems.

The author declares that there is no conflict of interests regarding the publication of this paper.

This work was supported by Program for Science & Technology Innovation Talents in Universities of Henan Province (15HASTIT021), the Science and Technology Project of Henan Province (142300410114 and 112102210126), and the Foundation of Henan Educational Committee (2011B120001 and 13A520017).