Robust stability of time-varying uncertain systems with rational dependence on the uncertainty

Robust stability of time-varying uncertain systems is a key problem in automatic control. This note considers the case of linear systems with rational dependence on an uncertain time-varying vector constrained in a polytope, which is typically addressed in the literature by using the linear fractional representation (LFR). A novel sufficient condition for robust stability is derived in terms of a linear matrix inequality (LMI) feasibility test by exploiting homogeneous polynomial Lyapunov functions, the square matrix representation and an extended version of Polya's theorem which considers structured matrix polynomials. It is shown that this condition is also necessary for second-order systems, and that this condition is less conservative than existing LMI conditions based on the LFR for any order. © 2010 IEEE.published_or_final_versio

Hysteresis and bi-stability by an interplay of calcium oscillations and action potential firing

Many cell types exhibit oscillatory activity, such as repetitive action potential firing due to the Hodgkin-Huxley dynamics of ion channels in the cell membrane or reveal intracellular inositol triphosphate (IP$_3$) mediated calcium oscillations (CaOs) by calcium-induced calcium release channels (IP$_3$-receptor) in the membrane of the endoplasmic reticulum (ER). The dynamics of the excitable membrane and that of the IP$_3$-mediated CaOs have been the subject of many studies. However, the interaction between the excitable cell membrane and IP$_3$-mediated CaOs, which are coupled by cytosolic calcium which affects the dynamics of both, has not been studied. This study for the first time applied stability analysis to investigate the dynamic behavior of a model, which includes both an excitable membrane and an intracellular IP$_3$-mediated calcium oscillator. Taking the IP$_3$ concentration as a control parameter, the model exhibits a novel rich spectrum of stable and unstable states with hysteresis. The four stable states of the model correspond in detail to previously reported growth-state dependent states of the membrane potential of normal rat kidney fibroblasts in cell culture. The hysteresis is most pronounced for experimentally observed parameter values of the model, suggesting a functional importance of hysteresis. This study shows that the four growth-dependent cell states may not reflect the behavior of cells that have differentiated into different cell types with different properties, but simply reflect four different states of a single cell type, that is characterized by a single model.Comment: 29 pages, 6 figure

Direct torque control for cable conduit mechanisms for the robotic foot for footwear testing

© 2018 Elsevier Ltd As the shoe durability is affected directly by the dynamic force/pressure between the shoe and its working environments (i.e., the contact ground and the human foot), a footwear testing system should replicate correctly this interaction force profile during gait cycles. Thus, in developing a robotic foot for footwear testing, it is important to power multiple foot joints and to control their output torque to produce correct dynamic effects on footwear. The cable conduit mechanism (CCM) offers great advantages for designing this robotic foot. It not only eliminates the cumbersome actuators and significant inertial effects from the fast-moving robotic foot but also allows a large amount of energy/force to be transmitted/propagated to the compact robotic foot. However, CCMs cause nonlinearities and hysteresis effects to the system performance. Recent studies on CCMs and hysteresis systems mostly addressed the position control. This paper introduces a new approach for modelling the torque transmission and controlling the output torque of a pair of CCMs, which are used to actuate the robotic foot for footwear testing. The proximal torque is used as the input signal for the Bouc–Wen hysteresis model to portray the torque transmission profile while a new robust adaptive control scheme is developed to online estimate and compensate for the nonlinearities and hysteresis effects. Both theoretical proof of stability and experimental validation of the new torque controller have been carried out and reported in this paper. Control experiments of other closed-loop control algorithms have been also conducted to compare their performance with the new controller effectiveness. Qualitative and quantitative results show that the new control approach significantly enhances the torque tracking performance for the system preceded by CCMs

Discontinuities and hysteresis in quantized average consensus

We consider continuous-time average consensus dynamics in which the agents' states are communicated through uniform quantizers. Solutions to the resulting system are defined in the Krasowskii sense and are proven to converge to conditions of "practical consensus". To cope with undesired chattering phenomena we introduce a hysteretic quantizer, and we study the convergence properties of the resulting dynamics by a hybrid system approach.Comment: 26 pages, 7 figures. Accepted for publication in Automatica. v4 is minor revision of v

Adaptive Control

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems