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相互竞争的目标之间进行权衡。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，使得几个设计规范是联合可行的。重点放在线性对象和控制器上。我们考虑可以通过闭环图上的规范来量化的设计规范。其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，其结果是将性能指标和鲁棒性要求相结合，具有实际意义。我们对综合问题的表述意义重大，因为可以同时考虑设计指标，例如良好的干扰抑制和跟踪、在面对对象的不确定性时保证稳定性等。由于对这些问题还没有一个全面的理论，这项研究的潜在成果将加强目前对控制系统设计中一些基本权衡的理论理解。此外，由于我们可能获得的综合方法比现有方法(如LQG、H-无穷大等)更好地捕捉设计问题的方面，它们的使用将显著减少控制工程师为获得可接受的控制器设计而投入的时间。我们计划使用的方法是基于线性代数和有限维凸优化。我们的动机是获得用于控制器综合的高效数值算法的可能性，该算法可在大多数计算机系统中实现。

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.