An advanced delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays

In this typescript, we concerned the problem of delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays. An advanced Lyapunov–Krasovskii functional are defined, which is in triple integral form. Combining the Lyapunov–Krasovskii functional with convex combination method and free-weighting matrix approach the stability conditions are derived with the help of linear matrix inequalities (LMIs). Some available software collections are used to solve the conditions. Lastly, two numerical examples and their simulations are conferred to indicate the feasibility of the theoretical concepts

Stability Analysis and Control of Several Classes of Logical Dynamic Systems and the Applications in Game Theory

With the rapid development of complex networks, logical dynamic systems have been commonly used mathematical models for simulating Genetic Regulatory Networks (GRNs) and Networked Evolutionary Games (NEGs), which have attracted considerable attention from biology, economy and many other fields. By resorting to the Semi-Tensor Product (STP) of matrices, logical dynamic systems can be equivalently converted into discrete time linear systems with algebraic forms. Based on that, this thesis analyzes the stability and studies the control design problems of several classes of logical dynamic systems. Moreover, the obtained results are applied to investigate the control and optimization problems of NEGs. The main results of this thesis are the following. • The stability and event-triggered control for a class of k-Valued Logical Networks (KVLNs) with time delays are studied. First, some necessary and sufficient con- ditions are obtained to detect the stability of Delayed k-Valued Logical Networks (DKVLNs). Second, the global stabilization problem under event-triggered control is considered, and some necessary and sufficient conditions are presented for the sta- bilization of Delayed k-Valued Logical Control Networks (DKVLCNs). Moreover, an algorithm is proposed to construct all the event-triggered state feedback controllers via antecedence solution technique. • The robust control invariance and robust set stabilization problems for a class of Mix- Valued Logical Control Networks (MVLCNs) with disturbances are studied. First, a calculation method for the Largest Robust Control Invariant Set (LRCIS) contained in a given set is introduced. Second, based on the Robust Control Invariant Subset (RCIS) obtained, the robust set stabilization of MVLCNs is discussed, and some new results are presented. Furthermore, the design algorithm of time-optimal state feedback stabilizers via antecedence solution technique is derived. • The robust set stability and robust set stabilization problems for a class of Probabilis- tic Boolean Control Networks (PBCNs) with disturbances are studied. An algorithm to determine the Largest Robust Invariant Set (LRIS) with probability 1 of a given set for a Probabilistic Boolean Network (PBN) is proposed, and the necessary and sufficient conditions to detect whether the PBN is globally finite-time stable to this invariant set with probability 1 are established. Then, the PBNs with control inputs are considered, and an algorithm for LRCIS with probability 1 is provided, based on which, some necessary and sufficient conditions for finite-time robust set stabiliza- tion with probability 1 of PBCNs are presented. Furthermore, the design scheme of time-optimal state feedback stabilizers via antecedence solution technique is derived. • The stabilization and set stabilization problems for a class of Switched Boolean Con- trol Networks (SBCNs) with periodic switching signal are studied. First, algebraic forms are constructed for SBCNs with periodic switching signal. Second, based on the algebraic formulations, the stabilization and set stabilization of SBCNs with peri- odic switching signal are discussed, and some new results are presented. Furthermore, constructive procedure of open loop controllers is given, and the design algorithms of switching-signal-dependent state feedback controllers via antecedence solution tech- nique are derived. • The dynamics and control problems for a class of NEGs with time-invariant delay in strategies are studied. First, algebraic forms are constructed for Delayed Networked Evolutionary Games (DNEGs). Second, based on the algebraic formulations, some necessary and sufficient conditions for the global convergence of desired strategy pro- file under a state feedback event-triggered controller are presented. Furthermore, the constructive procedure and the number of all valid event-triggered state feedback controllers are derived, which can make the game converge globally. • The evolutionary dynamics and optimization problems of the networked evolutionary boxed pig games with the mechanism of passive reward and punishment are studied. First, an algorithm is provided to construct the algebraic formulation for the dynamics of this kind of games. Then, the impact of reward and punishment parameters on the final cooperation level of the whole network is discussed

Event-based state estimation for a class of complex networks with time-varying delays: A comparison principle approach

The paper is concerned with the state estimation problem for a class of time-delayed complex networks with event-triggering communication protocol. A novel event generator function, which is dependent not only on the measurement output but also on a predefined positive constant, is proposed with hope to reduce the communication burden. A new concept of exponentially ultimate boundedness is provided to quantify the estimation performance. By means of the comparison principle, some sufficient conditions are obtained to guarantee that the estimation error is exponentially ultimately bounded, and then the estimator gains are obtained in terms of the solution of certain matrix inequalities. Furthermore, a rigorous proof is proposed to show that the designed triggering condition is free of the Zeno behavior. Finally, a numerical example is given to illustrate the effectiveness of the proposed event-based estimator

An Embedded System in Smart Inverters for Power Quality and Safety Functionality

The electricity sector is undergoing an evolution that demands the development of a network model with a high level of intelligence, known as a Smart Grid. One of the factors accelerating these changes is the development and implementation of renewable energy. In particular, increased photovoltaic generation can affect the network’s stability. One line of action is to provide inverters with a management capacity that enables them to act upon the grid in order to compensate for these problems. This paper describes the design and development of a prototype embedded system able to integrate with a photovoltaic inverter and provide it with multifunctional ability in order to analyze power quality and operate with protection. The most important subsystems of this prototype are described, indicating their operating fundamentals. This prototype has been tested with class A protocols according to IEC 61000-4-30 and IEC 62586-2. Tests have also been carried out to validate the response time in generating orders and alarm signals for protections. The highlights of these experimental results are discussed. Some descriptive aspects of the integration of the prototype in an experimental smart inverter are also commented upon

DEGRADACIÓN ANORMAL DE P53 E INDUCCIÓN DE APOPTOSIS EN LA RED P53-MDM2 USANDO LA ESTRATEGIA DE CONTROL TIPO PIN

Este artículo presenta el control tipo “PIN” para regular la actividad de la red p53-Mdm2. Esta red considera la degradación de p53 mediada por el incremento de Mdm2, el cual perturba la respuesta de estrés normal de p53. El modelo considera tres proteínas: p53, Mdm2 y ARF. p53 es regulado a través de un ciclo de retroalimentación que involucra su gen objetivo Mdm2 y un regulador indirecto ARF. Se presentan dos escenarios. Para el primer escenario, la red responde a un incremento de Mdm2 y una baja regulación de p53 sin ninguna entrada externa; luego, en el segundo escenario apoptosis es inducido por el control tipo “PIN”. El comportamiento dinámico de la red y la efectividad del controlador propuesto son ilustrados vía simulaciones

Coordinated Science Laboratory progress report for December 1965, January, and February 1966

Studies in mechanical damping in possible gyro materials, electron scattering from surface of tungsten, and control system