H∞ and guaranteed cost control of discrete linear repetitive processes

AbstractRepetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. In general, they cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here first we give major new results on the design of control laws using an H∞ setting and including the possibility of uncertainty in the process model. Then we give the first ever results on guaranteed cost control, i.e. including a performance criterion in the design. The designs in both cases can be computed using linear matrix inequalities. These results are for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control

Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains

This paper develops a fault-tolerant iterative learning control law for a~class of~linear time-delay differential batch processes with actuator faults using the repetitive process setting. Once the dynamics are expressed in this setting, stability analysis and control law design makes use of the generalized Kalman-Yakubovich-Popov (KYP) lemma in the form of the corresponding linear matrix inequalities (LMIs). In particular, sufficient conditions for the existence of a fault-tolerant control law are developed together with design algorithms for the associated matrices. Under the action of this control law the ILC dynamics have a monotonicity property in terms of an error sequence formed from the difference between the supplied reference trajectory and the outputs produced. An extension to robust control against structured time-varying uncertainties is also developed. Finally, a simulation based case study on the model of a~two-stage chemical reactor with delayed recycle is given to demonstrate the feasibility and effectiveness of the new designs

Robust H∞ filtering for uncertain 2-D continuous systems

This paper considers the problem of robust H∞ filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H∞ norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H∞ filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method. © 2005 IEEE.published_or_final_versio

Dissipative stability theory for linear repetitive processes with application in iterative learning control

Abstract-This paper develops a new set of necessary and sufficient conditions for the stability of linear repetitive processes, based on a dissipative setting for analysis. These conditions reduce the problem of determining whether a linear repetitive process is stable or not to that of checking for the existence of a solution to a set of linear matrix inequalities (LMIs). Testing the resulting conditions only requires computations with matrices whose entries are constant in comparison to alternatives where frequency response computations are required

Steroid-eluting epicardial pacing in children

Background: Permanent cardiac pacing is a known method of the treatment for children with bradycardia. Epicardial pacing is required in small children and in children with some congenital heart defects. Steroid-eluting leads (SEL) have been introduced to reduce implant site fibrosis and to retain permanent low-pacing threshold values. Our aim was to evaluate the pacing characteristic and follow-up of children with epicardial steroid-eluting pacing. Material and methods: We implanted steroid-eluting epicardial pacing systems in 53 children (age at implantation: 2 days - 17.5 years, mean 4.6 years), of whom 37 (70%) had congenital heart disease and 22 of these had already had cardiac surgery. These children formed group I. Group II was the control group and consisted of 29 children (age at implantation: 10 days - 13 years, mean 6.5 years) with non-steroid epicardial pacing systems; 15 patients (51%) had diagnosed congenital heart disease, and 9 of these had had cardiac surgery. The pacing threshold (PT) was obtained during implantation, before discharge, 1-3 and 6 months following implantation and then every 6 months. Results: In group I the mean PT during the implantation procedure was 1.6 V/0.4 ms and decreased significantly before discharge. In group II the PT during the implantation procedure was low and increased before discharge. In group I the PT of the atrial leads was low and stable during the follow-up period, while the PT of the ventricular leads slowly increased and four years following implantation was similar to that of group II. Conclusions: In children with permanent epicardial pacing the ventricular PT was significantly lower when steroid-eluting leads had been used then when these had not been used, but during the follow-up period the PT slowly increased, while the pacing threshold of atrial steroid-eluting leads remained stable

Elektrody nasierdziowe uwalniające sterydy w stałej stymulacji serca u dzieci

Wstęp: Stała stymulacja serca jest uznaną metodą leczenia bradyarytmii u dzieci. U małych dzieci i w niektórych patologiach układu krążenia konieczne jest zastosowanie elektrod nasierdziowych. Przyjmuje się, że sterydy uwalniane na końcu elektrod nasierdziowych, zmniejszając miejscowe włóknienie, przyczyniają się do utrzymania niskiego progu stymulacji serca. Celem pracy była ocena przebiegu stymulacji serca u dzieci z EP z elektrodami uwalniającymi sterydy. Materiał i metody: Pierwszą badaną grupę stanowiło 53 dzieci z EP z elektrodami uwalniającymi sterydy, w wieku od 2 doby życia do 17,5 roku (śr. 4,6 roku) w momencie zabiegu. U 37 (70%) z nich rozpoznano wrodzoną wadę serca, 22 przebyło operację serca. Do grupy II - kontrolnej zakwalifikowano 29 dzieci z EP niesterydowymi wszczepionymi w wieku od 10 doby życia do 13 lat (śr. 6,5 roku). U 15 (51%) rozpoznano wrodzoną wadę serca, 9 leczono kardiochirurgicznie. Przebieg stymulacji analizowano retro- i prospektywnie. Progi stymulacji (PT) mierzono w czasie wszczepienia EP, przy wypisie, po 1–3 oraz po 6 miesiącach od zabiegu, a następnie co pół roku. Wyniki: U pacjentów z I grupy PT podczas wszczepienia EP wynosił średnio 1,6 V/0,4 ms i istotnie obniżał się już w pierwszych dniach po zabiegu, natomiast u pacjentów z grupy II początkowo niski PT, później narastał. W okresie obserwacji PT elektrod przedsionkowych uwalniających sterydy były stabilne, a komorowych powoli wzrastały i po 4 latach od zabiegu były porównywalne z PT elektrod niesterydowych. Wnioski: U dzieci z EP progi stymulacji komorowej są istotnie niższe po zastosowaniu elektrod uwalniających sterydy w porównaniu z elektrodami niesterydowymi, jednak powoli się podnoszą

KYP lemma based stability and control law design for differential linear repetitive processes with applications

Repetitive processes are a class of two-dimensional systems that have physical applications, including the design of iterative learning control laws where experimental validation results have been reported. This paper uses the Kalman–Yakubovich–Popov lemma to develop new stability tests for differential linear repetitive processes that are computationally less intensive than those currently available. These tests are then extended to allow control law design for stability and performance

Experimentally verified multi-objective iterative learning control design with frequency domain specifications

This paper considers the design of multi-objective iterative learning control (ILC) schemes for discrete linear systems. In particular, a two step design approach is developed where the feedback and learning controllers are designed separately. The design procedures developed are able to impose performance specifications over selected frequency ranges to obtain the desired shapes of the sensitivity functions relevant to a particular example. This makes it possible to reject disturbances in specific frequency ranges and hence the desired performance specifications for both the transient response and error convergence speed can be achieved. All design computations required can be completed using linear matrix inequalities (LMIs). Preliminary experimental results demonstrate the effectiveness of the new design