Robust Nonlinear Control: Feedback Passivation and Input Saturation Techniques

9972045 lin非线性反馈设计提供了利用真正的非线性效应的潜力，例如，用小的控制来诱导大的效应。本提案的目的是开发理论上合理，实用的基于无源的低增益和低增益和高增益控制方法，用于设计反馈控制器，以实现全局渐近稳定性，对建模不确定性的性能鲁棒性和干扰衰减，用于现有方法无法充分控制的大类非线性系统。在我们的理论发展中，一个独特的线索是系统地使用小控制和反馈钝化，其重点是在反馈设计中利用动态系统固有的主导非线性，而不是通过反馈线性化来消除非线性来设计控制器。反馈控制的目的是以鲁棒的方式稳定或调节系统，也就是说，以一种对系统中的各种扰动和结构不确定性不敏感的方式。一个统一的、基于被动的鲁棒非线性控制理论将有助于我们设计高性能的非线性控制器，能够衰减干扰和跟踪所需的轨迹，而不像传统的现代控制理论那样依赖于对系统模型或模型参数的准确描述以及对干扰信号的明确描述。许多具有实际重要性的动态系统（如机器人、电刺激肌肉、旋转机械、感应电动机、电力系统、航天飞行器、飞机、导弹等）本质上具有内在的非线性特性，这在反馈设计中是不可忽视的。更重要的是，利用其真正非线性的控制系统可能比那些没有利用的控制系统获得更好的性能。由于大多数工程系统涉及高度非线性的致动器、传感器和过程元件，因此积极研究的目标是将非线性系统转换为线性系统，使其易于应用定义良好的线性控制技术。这种方法有严重的局限性，例如对高能执行器的要求以及这种方案对参数变化和干扰缺乏鲁棒性。因此，这些技术在解决现实世界的问题方面取得的成功相对较少。本提案中的研究计划解决了反馈设计中的需求，并提出了解决一些最重要问题的方法，我们认为这些问题对非线性控制理论的进步和应用至关重要。所提出的研究的主要成果将是新的、系统的设计方法，用于控制非线性动态系统，这在现有文献中是不可用的。该建议的意义在于，它确定了阻碍非线性控制理论发展和应用的主要障碍，也描绘了固有非线性系统控制的具体问题，并提出了理论上创新和实际可行的方法来解决这些问题。一些重要和具有挑战性的开放性问题将得到解决。从长远来看，它将为未来对几个理论和实践问题的研究提供洞察力和推动力。人们相信，使用低能量控制的系统方法的好处将得到更广泛的认可，特别是在工业（例如制造业，航空航天，电力和生物医学工程）中，可以找到许多非线性控制与致动器饱和的应用。由于非线性控制方案具有重要的特征，并且包含了现实的假设，因此预计在该方案中开发的非线性控制方案将在其他工程分支中比传统控制理论找到更广泛的应用。

9972045LinNonlinear feedback designs offer the potential to take advantage of genuinely nonlinear effects, for instance, to induce large effects using small controls. The objective of this proposal is to develop theoretically-sound, practically-useful passivity-based low-gain and low-and-high gain control methods for designing feedback controllers that achieve global asymptotic stability, performance robustness against modeling uncertainty, and disturbance attenuation, for a large class of nonlinear systems which cannot be adequately controlled by existing methods. A unique thread in our theoretical development would be the systematic use of small controls and feedback passivation, which focus on ways to exploit the inherently dominant nonlinearities of the dynamic system in the feedback design, rather than to design controllers by canceling the nonlinearities via feedback linearization. The purpose of a feedback control is to stabilize or regulate the system globally and do so in a robust fashion, that is, in a manner that is not sensitive to various perturbations and structural uncertainties in the system. A unified, passivity-based theory of robust nonlinear control would contribute to our ability to design high performance nonlinear controllers capable of attenuating disturbances and tracking desired trajectories, without relying as much on an accurate description of the system model or model parameters and on explicit descriptions of the disturbance signals as does conventional modern control theory.Many dynamic systems of practical importance (e.g. robotics, electrically stimulated muscles, rotating machines, induction motors, power systems, aerospace vehicles, aircraft, missiles and so on) have essentially inherent nonlinear characteristics that cannot be ignored in feedback design. More importantly, control systems that exploit their genuine nonlinearities are likely to achieve better performance than those that do not. Because most engineering systems involve highly nonlinear actuators, sensors and process elements, a goal of active research is to transform a nonlinear system into a linear system for which well-defined linear control techniques are readily applicable. This approach has serious limitations, e.g. the requirement of high energy actuators and the lack of robustness of such schemes to parameter variations and disturbances. Consequently, these techniques have had relatively little successful in solving real-world problems. The research plan in this proposal addresses the needs called for in feedback design, and it proposes approaches to tackle some of the most important issues that we believe are critical to the advancement and application of nonlinear control theory. The main outcome of the proposed research will be new, systematic design methodologies for the control of nonlinear dynamic systems, which are not available in the existing literature. The significance of this proposal is that it identifies the main barriers that hamper the advance and application of nonlinear control theory, but also delineates concrete problems for the control of inherently nonlinear systems, and suggests theoretically innovative and practically feasible methods to resolve them. A number of important and challenging open problems will be solved. In the long term, it will provide insight and thrust for future investigations into several theoretical and practical issues. It is believed that the benefits to a systematic approach towards using low energy control will be becoming more widely appreciated, particularly in industries (e.g. manufacturing, aerospace, power and biomedical engineering) where many applications of nonlinear control with actuator saturation can be found. It is also expected that the nonlinear control schemes to be developed in this program will find much broader applications in other branches of engineering than traditional control theory, due to their significant features and the inclusion of realistic assumptions.