Control of Linear Plants with Actuators Subject to Hard Constraints

众所周知，实际控制问题总是由约束支配的。直到最近，这些约束在几乎所有现代控制文献中都明显缺席，因为考虑到这些约束会导致复杂的非线性问题。另一方面，忽略这些约束可能会损害控制系统的稳定性和性能。1986年切尔诺贝利核电站4号机组事故和4月19日YF-22坠机事故都是由于忽视限制因素而造成的灾难性后果。在控制工程中最常遇到的约束之一是执行机构的约束和限制。执行器的幅度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些约束极大地增加了现代控制理论的工业相关性。在90年代，我们见证了新的和激烈的研究活动，在控制领域的线性植物与约束执行器。该研究领域被广泛认为是非线性控制理论的主要研究领域之一。在过去的几年里，在这一领域的研究活动，包括研究者和他的同事的工作，已经引起了强大的分析和设计工具的出现与执行器约束的控制系统。以一种有意义的方式使用幅度和速率饱和非线性的结构，该研究者和他的同事通过先前的NSF资助的支持，产生了一系列涉及(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，以及(e)全局和半全局框架中的加性干扰抑制的工作。每当执行器受到幅度和速率约束时，性能和鲁棒性问题在文献或我们先前的工作中没有得到处理。因此，处理性能和鲁棒性问题自然是该领域研究的下一步，也是本提案的重点。当执行器受到约束时，与性能和鲁棒性相关的问题虽然复杂且具有挑战性，但对控制工程应用至关重要，因此应被视为非线性控制理论的基础研究问题。本方案提出了若干研究任务，构成了这一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.