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Constrained Stabilization of Multi-Input Linear Systems with Distinct Input Delays

机译：具有不同输入延迟的多输入线性系统的约束稳定

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Quadratic Programming (QP) has been used to combine Control Lyapunov Functions (CLF) with Control Barrier Functions (CBF) for designing controllers that stabilize nonlinear systems with constraints. In this paper, we develop a predictor-based QP design for constrained stabilization of multi-input linear systems with distinct input delays. The difficulty of compensating input delays of different lengths lies in the fact that explicit expressions for the predictor states are not usually available, especially when the nominal controller for the delay-free system is nonlinear - as the case is with the standard QP controller. In this paper, we begin with a CLF and a CBF for the delay-free system and use their predicted values over different time horizons corresponding to the different input delays to form constraints for the QP problem. The controller combining the predicted CLF and CBF achieves the same closed-loop performance as the delay-free system after the longest delay has been compensated and renders the origin of the system locally asymptotically stable. We include numerical simulations to demonstrate the effectiveness of the proposed prediction-based controller.
机译：二次编程（QP）已被用于将控制Lyapunov函数（CLF）与控制屏障功能（CBF）组合，用于设计具有约束的非线性系统的控制器。在本文中，我们开发了一种基于预测的基于QP设计，用于具有不同输入延迟的多输入线性系统的约束稳定性。补偿不同长度的输入延迟的难度在于预测器状态的显式表达式通常不可用，特别是当无延迟系统的标称控制器是非线性的 - 视情况而定为标准QP控制器。在本文中，我们从CLF和CBF开始，用于无延迟系统，并在与不同的输入延迟相对应的不同时间视野上使用预测值来形成QP问题的约束。组合预测的CLF和CBF的控制器实现了在最长延迟得到补偿之后与无延迟系统相同的闭环性能，并且使系统局部渐近稳定的原点呈现。我们包括数值模拟来证明所提出的基于预测的控制器的有效性。

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