Characterization of well-posedness of piecewise linear systems

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Caratheodory. The concepts of jump solutions or of sliding modes are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multimodal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-pose

Finite-time regulation property of DNA feedback regulator

In dynamic DNA nanotechnology, the DNA strand displacement technique provides the cornerstone for the bottom-up design of a man-made DNA molecular system. Practically, a feedback controller for regulating the concentration of a target DNA strand to the desired level is indispensable for mediating the kinetic momentum of a molecular actuator. However, such a regulator system operates by consuming fuel strands and requires sufficient supplies of these consumables for its normal execution, indicating that, in practice, optimal controller design requires the period of time during which the regulator proceeds with normal operation to be as long as possible. The fact that the system is naturally high dimensional and nonlinear complicates the analysis of properties emerging during a finite-time period in terms of their theoretical aspects. In this paper, we first define the new concept of a “finite-time regulation property” of DNA systems in the regulation problem. Then, to theoretically analyze this regulation property, we present two-time-scale modeling based on the difference in the initial distribution of the abundance of DNA strands. Focusing on the fast mode as a subsystem with a positive quadratic structure, we propose a new method for analyzing the regulation property observed in a finite period of time

Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks

<p/> <p>In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.</p