Research Initiation Award: A State-Space Approach for Multiple Objective Synthesis of Linear Controllers

大多数控制系统设计问题涉及在竞争目标之间进行权衡。在这项研究中，我们考虑了一个综合问题，当目标是找到一个控制器，使几个设计规范共同可行时，就会出现这个问题。重点是线性工厂和控制器。我们考虑可以通过闭环图上的规范来量化的设计规范。目的是发展一个完整的状态空间理论来解决几个多目标控制问题，这些问题是由结合实际意义的性能度量和鲁棒性要求而产生的。我们对综合问题的表述具有重要意义，因为可以同时考虑诸如良好的抗扰性和跟踪性，面对植物不确定性时保证稳定性等设计规范。由于不存在针对这些问题的全面理论，因此本研究的潜在成果将增强当前对控制系统设计中一些基本权衡的理论理解。此外，由于我们可以获得比现有方法（即LQG， H-infinity等）更好的设计问题的综合方法，因此它们的使用将导致控制工程师为获得可接受的控制器设计而投入的时间显着减少。我们计划使用的方法是基于线性代数和有限维凸优化。我们的动机是可能获得有效的数值算法的控制器综合，实现在大多数计算机系统。

Most control system design problems involve making tradeoffs among competing objectives. In this research we consider a synthesis problem that arises when the goal is to find a controller such that several design specifications are jointly feasible. The focus is on linear plants and controllers. We consider design specifications that may be quantified by norms on the closed loop maps. The aim is to develop a complete state-space theory for solving several multiple objective control problems, resulting from combining performance measures and robustness requirements of practical significance. Our formulation of the synthesis problem is significant because design specifications such as good disturbance rejection and tracking, guaranteed stability in the face of plant uncertainty, etc., can be taken into account simultaneously. Since a comprehensive theory for these problems does not exist, the potential yields of this research will enhance the current theoretical understanding of some fundamental tradeoffs in the design of control systems. Further, since the synthesis methodologies we may obtain capture better aspects of the design problem than existing methods (i.e. LQG, H-infinity, etc.), their use will result in a significant reduction of the time invested by the control engineer to get an acceptable controller design. The methods we plan to use are based on linear algebra and finite-dimensional convex optimization. We are motivated by the possibility of obtaining efficient numerical algorithms for controller synthesis, implementable in most computer systems.