5 research outputs found
Discrete-time control of continuous systems with approximate decentralized fixed modes
In this paper, the discrete-time control of decentralized continuous-time systems, which have approximate decentralized fixed modes, is studied. It is shown that under certain conditions, discrete-time controllers can improve the overall performance of the decentralized control system, when a linear time-invariant continuous-time controller is ineffective. In order to obtain these conditions, a quantitative measure for different types of approximate fixed modes in a decentralized system is given. In this case, it is shown that discrete-time zero-order hold (ZOH) controllers, and in particular, that generalized sampled-data hold functions (GSHF), can significantly improve the overall performance of the resultant closed-loop system. The proposed sampled-data controller is, in fact, a linear time-varying controller for the continuous-time system
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
Time Complexity of Decentralized Fixed-Mode Verification
Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem
Complexity of checking the existence of a stabilizing decentralized controller
Given an interconnected system, this paper is
concerned with the time complexity of verifying if any given
unrepeated mode of the system is a decentralized fixed mode
(DFM). It is shown that checking the decentralized fixedness of
any distinct mode is tantamount to testing the strong connectivity
of a digraph formed based on the system. It is subsequently
proved that the time complexity of this decision problem using
the proposed approach is the same as the complexity of matrix
multiplication. This work concludes that the identification of
distinct decentralized fixed modes (by means of a deterministic
algorithm, rather than a randomized one) is computationally
very easy, although the existing algorithms for solving this
problem would wrongly imply that it is cumbersome. This paper
provides not only a complexity analysis, but also an efficient
algorithm for tackling the underlying problem