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到使 竞争目标之间的权衡。 在这项研究中，我们考虑一个综合问题， 当目标是找到一个控制器， 多个设计规范是共同可行的。 的 重点是线性设备和控制器。 我们认为 可通过规范量化的设计规范 在闭环地图上。 目的是发展一个 完备状态空间理论求解多重 目标控制问题，由于结合 性能指标和稳健性要求 现实意义 我们对综合问题的表述是有意义的 由于设计规范，如良好的干扰， 拒绝和跟踪，保证稳定的脸 工厂的不确定性，等等，可以考虑 同步 由于一个全面的理论， 这些问题并不存在，潜在的收益率 这项研究将加强目前的理论 理解一些基本的权衡， 控制系统的设计。 此外，由于合成 我们可以获得的方法捕捉更好的方面， 设计问题比现有的方法（即LQG， H-infinity等），它们的使用将导致 减少控制工程师投入的时间 以获得可接受的控制器设计。 我们计划使用的方法基于线性 代数和有限维凸优化。 我们的动力来自于 用于控制器综合的有效数值算法， 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.