Petros G. Voulgaris

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 convexproblem 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.

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.

Optimal H ∞ and H 2 control of hybrid multirate systems

The problem of using a synchronous multirate digital controller for a continuous-time plant is considered. The performance objectives considered are the H∞ and the H2 norms of the periodically time-varying continuous-time input-output behavior of the closed loop system. A continuous-time lifting technique is used to solve these hybrid sampled-data problems. This approach yields equivalent purely discrete-time problems while preserving the multirate causality of the systems. The later problems can then be solved using known techniques.

H ∞ and H 2 -optimal controllers for periodic and multirate systems

In this paper we present the solutions to the optimal l2 to l2 disturbance rejection problem (H∞) as well as to the LQG (H2) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H∞ problem is solved using Neharis theorem whereas in the H2 problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.

A convex characterization of classes of problems in control with specific interaction and communication structures

We present a list of optimal disturbance rejection problems in systems in which the overall control scheme is required to have a certain structure. These structures correspond to various classes of controlled systems which include what we refer to as nested, chained, hierarchical, delayed interaction and communication, and, symmetric systems. The common thread in all of these classes is that by taking an input-output point of view we can characterize all stabilizing controllers in terms of convex constraints in the Youla-Kucera parameter. The disturbance rejection problem can therefore be casted as a convex, yet nonstandard, model matching problem. Approaches that solve this problem are presented for various optimality criteria.

Optimal and robust controllers for periodic and multirate systems

The problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time periodic systems. The solution consists of solving an equivalent time-invariant standard l/sup 1/ optimization problem subject to an additional constraint. This constraint assures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard l/sup 1/ problem. Also, it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems. Finally, the results are applied to the problem of robust stabilization of periodic and multirate systems. >

Control of nested systems

This paper presents an input-output point of view for the problem of optimal command following and disturbance rejection of systems which are comprised of subsystems that affect each other in a nested manner. In such a nested manner, a subsystem affects the subsystems that are exterior to it but not the subsystems that are interior to it. By using model matching methods the problem is shown to be convex. Techniques to solve this convex yet non-standard problem are discussed.

Smart Icing Systems for Aircraft Icing Safety

Ice accretion affects the performance and control of an aircraft and in extreme situations can lead to incidents and accidents. However, changes in performance and control are difficult to sense. As a result, the icing sensors currently in use sense primarily ice accretion, not the effect of the ice. No processed aircraft performance degradation information is available to the pilot. In this paper, the Smart Icing System research program is reviewed and progress towards its development reported. Such a system would sense ice accretion through traditional icing sensors and use modern system identification methods to estimate aircraft performance and control changes. This information would be used to automatically operate ice protection systems, provide aircraft envelope protection and, if icing was severe, adapt the flight controls. All of this would be properly communicated to and coordinated with the flight crew. In addition to describing the basic concept, this paper reviews the research conducted to date in three critical areas; aerodynamics and flight mechanics, aircraft control and identification, and human factors. In addition, the flight simulation development is reviewed, as well as the Twin Otter flight test program that is being conducted in cooperation with NASA Glenn Research Center.

Control of asynchronous sampled data systems

This paper is concerned with the problem of controller design in the case of asynchronous sampled data systems. Optimal LQG controllers are obtained for the class of two-rate systems where all the control inputs are held at a rate which is asynchronously related to the rate with which all of the outputs are sampled. Furthermore for this class, a parameterization of all stabilizing controllers is provided. >

Parameter identification for inflight detection and characterization of aircraft icing

Abstract Increasing interest in aircraft icing has motivated the proposal of a new ice management system that would provide inflight monitoring of ice accretion effects. Since these effects are manifested in the flight dynamics, parameter identification is a critical element of ice detection. In particular, identification must provide timely and accurate parameter estimates under normal operational input in the presence of disturbances and measurement noise. This paper evaluates a batch least-squares algorithm, an extended Kalman filter, and an H∞ algorithm in the context of icing detection. Simulation results show that only the H∞ method provides a timely and accurate icing indication.