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This volume in the newly established series Advances in Delays and Dynamics (ADD@S) provides a collection of recent results on the design and analysis of Low Complexity Controllers for Time Delay Systems. A widely used indirect method to obtain low order controllers for time delay systems is to design a controller for the reduced order model of the plant. In the dual indirect approach, an infinite dimensional controller is designed first for the original plant model; then, the controller is approximated by keeping track of the degradation in performance and stability robustness measures. The present volume includes new techniques used at different stages of the indirect approach. It also includes new direct design methods for fixed structure and low order controllers. On the other hand, what is meant by low complexity controller is not necessarily low order controller. For example, Smith predictor or similar type of controllers include a copy of the plant internally in the controller, so they are technically infinite dimensional. However, they have very nice numerical properties from the point of reliable implementation. Therefore, such predictor-based controllers are considered as low complexity. This book includes new predictor-based design techniques, with several application examples.
Dynamics --- Mathematical models. --- Engineering. --- Systems theory. --- Control and Systems Theory. --- Complexity. --- Systems Theory, Control. --- Construction --- Industrial arts --- Technology --- Control engineering. --- Computational complexity. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Complexity, Computational --- Electronic data processing --- Machine theory --- Philosophy
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This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.
Mathematics. --- Systems Theory, Control. --- Mathematical and Computational Biology. --- Gene Expression. --- Control, Robotics, Mechatronics. --- Gene expression. --- Systems theory. --- Mathématiques --- Expression génique --- Gene regulatory networks -- Mathematical models. --- Gene regulatory networks. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Gene regulatory networks --- Mathematical models. --- System theory. --- Biomathematics. --- Control engineering. --- Robotics. --- Mechatronics. --- Circuits, Gene --- Gene circuits --- Gene modules --- Gene networks --- Genetic regulatory networks --- GRNs (Gene regulatory networks) --- Modules, Gene --- Networks, Gene regulatory --- Networks, Transcriptional --- Regulatory networks, Gene --- Transcriptional networks --- Genetic regulation --- Nucleotide sequence --- Genes --- Expression --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Biology --- Mathematics --- Systems, Theory of --- Systems science --- Science --- Philosophy
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