标题： 具有有界输入的约束非线性系统的可证明安全控制 显示英文标题

标题： Provably Safe Control for Constrained Nonlinear Systems with Bounded Input

摘要： 在实际的控制应用中，执行器约束和输出约束（特别是在跟踪问题中）是固有的且至关重要的，以确保安全可靠的运行。然而，通常情况下，控制策略往往忽略这些物理限制，在实际系统上部署时可能导致潜在的不稳定、性能下降，甚至系统故障。本文研究了一类在执行器饱和和输出约束下非线性系统的控制设计问题。首先，提出了一种平滑不对称饱和模型（更通用的实际场景代表），用于建模执行器饱和，从而确保控制输入始终被限制在一个预定义的集合内以保证安全性。基于该模型，我们开发了一个非线性控制框架，确保输出跟踪的同时，使系统输出保持在预定义集合内。随后，我们将此设计与带约束的输出跟踪控制问题相结合，证明了系统输出通过同时满足输入和输出约束来跟踪期望轨迹。在存在输入约束的情况下实现了跟踪误差的全局稳定性，而在同时存在输入和输出约束的情况下实现了半全局稳定性。此外，我们在所提出的控制器设计下严格证明了所有闭环信号的有界性。仿真结果表明，所提出的方法在处理不对称约束的同时能够实现理想的跟踪性能。 显示英文摘要

摘要： In real-world control applications, actuator constraints and output constraints (specifically in tracking problems) are inherent and critical to ensuring safe and reliable operation. However, generally, control strategies often neglect these physical limitations, leading to potential instability, degraded performance, or even system failure when deployed on real-world systems. This paper addresses the control design problem for a class of nonlinear systems under both actuator saturation and output constraints. First, a smooth asymmetric saturation model (a more generic representative of practical scenarios) is proposed to model actuator saturation, which ensures that the control inputs always remain confined within a predefined set to ensure safety. Based on the proposed model, we develop a nonlinear control framework that guarantees output tracking while ensuring that system output remains confined to the predefined set. Later, we integrate this design with the constrained output tracking control problem, wherein we show that the system output tracks its desired trajectory by simultaneously satisfying input and output constraints. The global stabilization of the tracking error is achieved in the presence of input constraints, while semi-global stabilization is achieved in the presence of both input and output constraints. Additionally, we rigorously establish the boundedness of all closed-loop signals under the proposed design. Simulation results demonstrate the effectiveness of the proposed methods in handling asymmetric constraints while achieving desirable tracking performance.