Control of Linear Plants with Actuators Subject to Hard Constraints

众所周知，实际控制问题总是受到约束的支配。 直到最近，这些约束已经明显缺席几乎所有的现代控制文献，考虑到这些约束导致硬复杂的非线性问题。 另一方面，忽略这些约束可能对控制系统的稳定性和性能有害。 有一些灾难性的例子说明了忽视约束的有害影响，如1986年切尔诺贝利核电站4号机组灾难或4月19日YF-22坠毁。 在控制工程中最常遇到的约束之一是执行器的约束和限制。 执行器的幅值和速率饱和是控制系统中最常见和最重要的约束。 在控制系统的分析和设计中考虑这样的约束极大地增加了现代控制理论的工业相关性。在90年代，我们目睹了在具有约束执行器的线性对象的控制领域中的更新和激烈的研究活动。 这一研究领域被广泛视为非线性控制理论研究的主要领域之一。 在过去的几年中，在这一领域的研究活动，包括本调查员和他的同事的工作已经引起了强大的分析和设计工具的出现，控制系统的执行器的约束。 以一种有意义的方式使用幅度和速率饱和非线性的结构，这位研究者和他的同事通过先前NSF资助的支持，完成了一系列工作，涉及（a）外部稳定性，（B）内部稳定性，（c）外部和内部稳定性，（d）输出调节，和（e）加性干扰抑制在全球和半的框架。性能和鲁棒性的问题时，执行器受到振幅和速率约束，没有处理的文献或我们的以前的工作。 因此，处理性能和鲁棒性问题是该领域研究的自然下一步，也是本提案的重点。 当执行器受到约束时，与性能和鲁棒性问题相关的问题虽然复杂且具有挑战性，但对于控制工程应用非常关键，因此应被视为非线性控制理论的基础研究问题。 该建议制定了一些研究任务，形成了这个非线性研究领域的核心。

As well known, practical control problems are always dominated by constraints. Until recently these constraints have been conspicuously absent from almost all-modern control literature, as taking such constraints into account leads to hard complex nonlinear problems. On the other hand, ignoring such constraints can be detrimental to the stability and performance of control systems. There are disastrous examples for detrimental effect of neglecting constraints such as the Chernobyl unit 4 nuclear power plant disaster in 1986 or YF-22 crash of April 19. One of the most commonly encountered constraints in control engineering is the actuator's constraint and limitations. Actuator magnitude and rate saturations are some of the most common and significant constraints in a control system. Taking such constraints in analysis and design of control systems immensely increases the industrial relevance of modern control theory.During the 90's we have witnessed renewed and intense research activity in the area of control of linear plants with constrained actuators. This research area is broadly viewed as one of the major areas of research in nonlinear control theory. In the past few years, the research activities in this area including the work of this investigator and his co-workers have given rise to the emergence of powerful analysis and design tools for control systems with actuator constraints. Using the structure of amplitude and rate saturation nonlinearity in a meaningful way, this investigator and his co-workers through the support of a prior NSF grant produced a body of work that concerns with (a) external stability, (b) internal stability, (c) external as well as internal stability, (d) output regulation, and (e) additive disturbance rejection in both global and semiglobal framework.The performance and robustness issues whenever actuators are subject to amplitude and rate constraints are not dealt with in the literature or in our prior work. Hence, dealing with performance and robustness issues is a natural next step for research in this area, and is the focus of this proposal. The problems associated with performance and robustness issues whenever actuators are constrained, though complex and challenging, are highly crucial for control engineering applications and thus should be viewed as fundamental research problems in nonlinear control theory. This proposal formulates a number of research tasks, which form the core of this nonlinear research area.