Control of Linear Plants with Actuators Subject to Hard Constraints

众所周知，实际的控制问题总是受约束的支配。直到最近，这些约束在几乎所有现代控制文献中都是明显缺失的，因为考虑这些约束会导致复杂的非线性问题。另一方面，忽视这些约束可能会对控制系统的稳定性和性能造成不利影响。有一些灾难性的例子表明，忽视约束的有害影响，如1986年切尔诺贝利4号机组核电站灾难或4月19日YF-22坠毁。控制工程中最常见的约束之一是执行器的约束和限制。执行器幅度和速率饱和是控制系统中一些最常见和最重要的限制。在控制系统的分析和设计中采用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年代的S期间，我们目睹了具有约束执行器的线性对象控制领域的新的和激烈的研究活动。这一研究领域被广泛认为是非线性控制理论研究的主要领域之一。在过去的几年里，这一领域的研究活动，包括这位研究员和他的同事的工作，已经导致了具有执行器约束的控制系统的强大分析和设计工具的出现。利用幅度和速率饱和非线性的结构以一种有意义的方式，这位研究员和他的同事在先前的NSF拨款的支持下产生了一系列关于(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。因此，处理性能和健壮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来说是非常关键的，因此应该被视为非线性控制理论的基础研究问题。这一建议提出了一系列研究任务，这些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.