A Hamiltonian-based solution to the mixed sensitivity optimization problem for stable pseudorational plants

This paper considers the mixed sensitivity optimization problem for a class of infinite-dimensional stable plants. This problem is reducible to a two- or one-block H^∞ control problem with structured weighting functions. We first show that these weighting functions violate the genericity assumptions of existing Hamiltonian-based solutions such as the well-known Zhou–Khargonekar formula. Then, we derive a new closed form formula for the computation of the optimal performance level, when the underlying plant structure is specified by a pseudorational transfer function.     

Dwell time-based stabilisation of switched linear delay systems using clock-dependent Lyapunov–Krasovskii functionals

ABSTRACT

Dwell time stability conditions of the switched delay systems are derived using multiple clock-dependent Lyapunov–Krasovskii functionals. The corresponding conditions are approximated by both using piecewise linear functions and sum of squares polynomials. The upper bound of the dwell time is minimised using a combination of a bisection and a golden section search algorithm. Using the results obtained in the stability case, synthesis of dwell time minimiser controllers are presented. Some numerical examples are given to illustrate effectiveness of the proposed method, and its performance is compared with the existing approaches. The resulting values of the dwell time via the proposed technique show that the novel approach outperforms the previous ones.     

Dwell time-based stabilisation of switched delay systems using free-weighting matrices

In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov–Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities , dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.     

Neural network-based modelling of subsonic cavity flows

A fundamental problem in the applications involved with aerodynamic flows is the difficulty in finding a suitable dynamical model containing the most significant information pertaining to the physical system. Especially in the design of feedback control systems, a representative model is a necessary tool constraining the applicable forms of control laws. This article addresses the modelling problem by the use of feedforward neural networks (NNs). Shallow cavity flows at different Mach numbers are considered, and a single NN admitting the Mach number as one of the external inputs is demonstrated to be capable of predicting the floor pressures. Simulations and real time experiments have been presented to support the learning and generalization claims introduced by NN-based models.     

Modeling and control of biological systems with multiple afferent and efferent transmission delays

Biological systems are highly nonlinear, have at least one pair of muscles actuating every degree of freedom at any joint, and possess neural transmission delays in their feedforward (efferent) and feedback (afferent) paths. The modeling and control of such systems for nominally small trajectories, such that linear analysis applies, is the subject of this article. In these systems, coactivation of pairs of muscles for every degree of freedom stabilizes the system: therefore the open loop system is stable. The purpose of feedback is to decouple the links, coordinate the movement of the linkages, execute tasks under relatively large delays, and control the pole positions. Robustness and insensitivity to disturbance are other attributes of feedback that are also considered in this article. Robots of the future may have similar delays in their feedback and feedforward paths. The robotic delays are primarily computational, and have two major sources. The first source is computational delays brought about by better vision and tactile systems in the robot and the integration of all sensory modalities. The second source of delays is due to computations needed for indirect measurements of desired physical attributes and quantities. The main results of this paper, therefore, can be extended to robots whose capabilities extend beyond the robots of today, and are capable of more sophisticated tasks including communication and collaboration with humans. © 2000 John Wiley & Sons, Inc.     

Complexity issues in robust stability of linear delay-differential systems

In this paper the following stability problems concerning linear delay-differential systems are shown to beN P-hard: (i) asymptotic stability independent of delay, and (ii) robust asymptotic stability, when each delay is known to lie in an interval. The main results are based on theN P-hardness of complex bilinear programming over the polydisk ⁿ which also shows that the purely complexμ computation, analysis/synthesis problems areN P-hard even if there are no repeated blocks. Another side result of the paper is that checking robust nonsingularity, robust Hurwitz stability, and robust Schur stability of a disk matrix areN P-hard problems. This work was supported by the Ohio State University and DISC (Dutch Institute of Systems and Control). This work was completed while the first author was at the Faculty of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.     

Development and Validation of a Rapid Method for Identification and Quantitation of Benzophenone and Related 17 Derivatives in Paper and Cardboard Packaging Materials by Gas Chromatography–Mass Spectrometry

Benzophenone (BP) and its derivates are photoinitiators widely used in food packaging to cure inks or lacquers with ultraviolet light on cardboards and papers. Although there is no specific European legislation covering printing inks for food contact use, the European Food Safety Authority published recommendations of a limit of 0.6 mg/kg for the sum of BP and 4‐methylbenzophenone. In this study, a method has been devised to test migration levels of BP and BP derivates in foodstuffs. Eleven different paper or cardboard materials were analysed for their BP and derivative contents. The qualitative and quantitative analyses of BP and other 17 derivatives for the first time were performed by gas chromatography–mass spectrometry system. The method was evaluated by validation parameters such as linearity, repeatability, accuracy and precision values. According to results, maximum values by specific migration test (at 40°C for 10 days, using TENAX) were 10.83 mg/l for BP, 0.53 mg/l for 1‐hydrocyclohexylphenylketone, 0.47 mg/l for 4‐methylbenzophenone, 0.22 mg/l for 2,2‐dimethoxy‐2‐phenylacetophenone and 0.4 mg/l for methyl‐2‐benzoylbenzoate.     

Decentralised robust flow controller design for networks with multiple bottlenecks

Decentralised rate-based flow controller design in multi-bottleneck data-communication networks is considered. An ?^∞ problem is formulated to find decentralised controllers which can be implemented locally at the bottleneck nodes. A suboptimal solution to this problem is found and the implementation of the decentralised controllers is presented. The controllers are robust to time-varying uncertain multiple time-delays in different channels. They also satisfy tracking and weighted fairness requirements. Lower bounds on the actual stability margins are derived and their relation to the design parameters is analysed. A number of simulations are also included to illustrate the time-domain performance of the proposed controllers.