Structured optimal and robust control with multiple criteria: a convex solution

In this paper, the design of controllers that incorporate structural and multiobjective performance requirements is considered. The control structures under study cover nested, chained, hierarchical, delayed interaction and communications, and symmetric systems. Such structures are strongly related to several modern-day and future applications including integrated flight propulsion systems, platoons of vehicles, micro-electro-mechanical systems, networked control, control of networks, production lines and chemical processes. It is shown that the system classes presented have the common feature that all stabilizing controllers can be characterized by convex constraints on the Youla-Kucera parameter. Using this feature, a solution to a general optimal performance problem that incorporates time domain and frequency domain constraints is obtained. A synthesis procedure is provided which at every step yields a feasible controller together with a measure of its performance with respect to the optimal. Convergence to the optimal performance is established. An example of a multinode network congestion control problem is provided that illustrates the effectiveness of the developed methodology.     

On l∞ and l2 robustness of spatially invariant systems

We consider spatiotemporal systems and study their l_∞ and l₂ robustness properties in the presence of spatiotemporal perturbations. In particular, we consider spatially invariant nominal models and provide necessary and sufficient conditions for system robustness for the cases when the underlying perturbations are linear spatiotemporal varying, and nonlinear spatiotemporal invariant, unstructured or structured. It turns out that these conditions are analogous to the scaled small gain condition (which is equivalent to a spectral radius condition and a linear matrix inequality for the l_∞ and l₂ cases, respectively) derived for standard linear time‐invariant models subject to time‐varying linear and time‐invariant nonlinear perturbations. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal controllers for spatially invariant systems with delayed communication requirements

We consider the problem of optimal design of semi-decentralized controllers for a special class of spatially distributed systems. This class includes spatially invariant and distributed discrete-time systems with an inherent temporal delay in the interaction of neighboring sites. We consider the problem of optimal design of distributed controllers that have the same information passing delay structure as the plant. We show how for stable plants, the YJBK parameterization of such stabilizing controllers yields a convex parameterization for this class. We then show how the optimal problem can be solved.     

Diagonal stabilization of linear multivariable systems

A new procedure is presented for the synthesis of diagonal compensators for N × N linear multivariable systems that are free of fixed modes with respect to constant diagonal output feedbacks. The synthesis procedure employs simple polynomial algebra and it is in the form of an N-step algorithm. The geometric configurations 2N- and 2^N-cells in N-space are shown to be especially suitable for visualizing diagonal feedback and aiding the application of the synthesis algorithm.     

A convex characterization of distributed control problems in spatially invariant systems with communication constraints

In this paper we consider the problem of distributed controller design in spatially invariant systems for which communication among sites is limited. In particular, the controller is constrained so that information is propagated with a delay that depends on the distance between subsystems—a structure we refer to as “funnel” causality. We show that the problem of optimal design can be cast as a convex problem provided that the plant has a similar funnel-causality structure, and the propagation speeds in the controller are at least as fast as those in the plant. As an example, we consider the case of the wave dynamics with limited propagation speed control.