Decentralized pole assignment for interconnected systems

Given a general proper interconnected system, this paper aims to design a LTI decentralized controller to place the modes of the closed-loop system at pre-determined locations. To this end, it is first assumed that the structural graph of the system is strongly connected. Then, it is shown applying generic static local controllers to any number of subsystems will not introduce new decentralized fixed modes (DFM) in the resultant system, although it has fewer inputoutput stations compared to the original system. This means that if there are some subsystems whose control costs are highly dependent on the complexity of the control law, then generic static controllers can be applied to such subsystems, without changing the characteristics of the system in terms of the fixed modes. As a direct application of this result, in the case when the system has no DFMs, one can apply generic static controllers to all but one subsystem, and the resultant system will be controllable and observable through that subsystem. Now, a simple observer-based local controller corresponding to this subsystem can be designed to displace the modes of the entire system arbitrarily. Similar results can also be attained for a system whose structural graph is not strongly connected. It is worth mentioning that similar concepts are deployed in the literature for the special case of strictly proper systems, but as noted in the relevant papers, extension of the results to general proper systems is not trivial. This demonstrates the significance of the present work

A Near-Optimal Decentralized Servomechanism Controller for Hierarchical Interconnected Systems

This paper is concerned with decentralized output regulation of hierarchical systems subject to input and output disturbances. It is assumed that the disturbance can be represented as the output of an autonomous LTI system with unknown initial state. The primary objective is to design a decentralized controller with the property that not only does it reject the degrading effect of the disturbance on the output (for a satisfactory steady-state performance), it also results in a small LQ cost function (implying a good transient behavior). To this end, the underlying problem is treated in two phases. In the first step, a number of modified systems are defined in terms of the original system. The problem of designing a LQ centralized controller which stabilizes all the modified systems and rejects the disturbance in the original system is considered, and it is shown that this centralized controller can be efficiently found by solving a LMI problem. In the second step, a method recently presented in the literature is exploited to decentralize the designed centralized controller. It is proved that the obtained controller satisfies the pre-determined design specifications including disturbance rejection. Simulation results elucidate the efficacy of the proposed control law

Rational Optimization using Sum-of-Squares Techniques

Motivated by many control applications, this paper deals with the global solutions of unconstrained optimization problems. First, a simple SOS method is presented to find the infimum of a polynomial, which can be handled efficiently using the relevant software tools. The main idea of this method is to introduce a perturbation variable whose approaching to zero results in a solution with any arbitrary precision. The proposed technique is then extended to the case of rational functions. The primary advantages of this approach over the existing ones are its simplicity and capability of treating problems for which the existing methods are not efficient, as demonstrated in three numerical examples

Pole Assignment With Improved Control Performance by Means of Periodic Feedback

This technical note is concerned with the pole placement of continuous-time linear time-invariant (LTI) systems by means of LQ suboptimal periodic feedback. It is well-known that there exist infinitely many generalized sampled-data hold functions (GSHF) for any controllable LTI system to place the modes of its discrete-time equivalent model at prescribed locations. Among all such GSHFs, this technical note aims to find the one which also minimizes a given LQ performance index. To this end, the GSHF being sought is written as the sum of a particular GSHF and a homogeneous one. The particular GSHF can be readily obtained using the conventional pole-placement techniques. The homogeneous GSHF, on the other hand, is expressed as a linear combination of a finite number of functions such as polynomials, sinusoidals, etc. The problem of finding the optimal coefficients of this linear combination is then formulated as a linear matrix inequality (LMI) optimization. The procedure is illustrated by a numerical example