Dissipativity and Error Feedback Controller Design of Time-Delay Genetic Regulatory Networks

Genetic regulatory networks (GRNs) play an important role in the development and evolution of the biological system. With the rapid development of DNA technology, further research on GRNs becomes possible. In this paper, we discuss a class of time-delay genetic regulatory networks with external inputs. Firstly, under some reasonable assumptions, using matrix measures, matrix norm inequalities, and Halanay inequalities, we give the global dissipative properties of the solution of the time-delay genetic regulation networks and estimate the parameter-dependent global attraction set. Secondly, an error feedback control system is designed for the time-delay genetic control networks. Furthermore, we prove that the estimation error of the model is asymptotically stable. Finally, two examples are used to illustrate the validity of the theoretical results.

Applied Mechatronics: Designing a Sliding Mode Controller for Active Suspension System

The suspension system is referred to as the set of springs, shock absorbers, and linkages that connect the car to the wheel system. The main purpose of the suspension system is to provide comfort for the passengers, which is created by reducing the effects of road bumpiness. It is worth noting that reducing the effects of such vibrations also diminishes the noise and undesirable sound as well as the effects of fatigue on mechanical parts of the vehicle. Due to the importance of the abovementioned issues, the objective of this article is to reduce such vibrations on the car by implementing an active control method on the suspension system. For this purpose, a conventional first-order sliding mode controller has been designed for stochastic control of the quarter-car model. It is noteworthy that this controller has a significant ability to overcome the stochastic effects, uncertainty, and deal with nonlinear factors. To design a controller, the governing dynamical equation of the quarter-car system has been presented by considering the nonlinear terms in the springs and shock absorber, as well as taking into account the uncertainty factors in the system and the actuator. The design process of the sliding mode controller has been presented and its stability has been investigated in terms of the Lyapunov stability. In the current research, road surface variations are considered as Gaussian white noise. The dynamical system behavior for controlled and uncontrolled situations has been simulated and the extracted results have been presented. Besides, the effects of existing uncertainty in the suspension system and actuator have been evaluated and controller robustness has been checked. Also, the obtained quantitative and qualitative compressions have been presented. Moreover, the effect of controller parameters on the basin of attraction set and its extensiveness has been assessed. The achieved results have indicated the good performance and significant robustness of the designed controller to stabilize the suspension system and mitigate the effects of road bumpiness in the presence of uncertainty and noise factors.

Relaxation of the attainability problem for a linear control system of neutral type

The problem of control of a linear system of neutral type with impulse constraints is developed. In addition, a given system of intermediate conditions is assumed. A setting is investigated in which a vanishingly small relaxation of the mentioned restrictions is allowed. In this regard, the attainability domain (AD) at a fixed time of the end of the process is replaced by a natural asymptotic analog, the attraction set (AS). To construct the latter, we use the construction of an extension in the class of finitely additive (f.-a.) measures used as generalized controls. It is shown that the AS coincides with the AD of the system in the class of generalized controls – f.-a. measures. The structure of the mentioned AS is investigated.

Bifurcation Analysis of an Electro-Statically Actuated Nano-beam Based on the Nonlocal Theory considering Centrifugal Forces

A nonlocal elasticity theory is a popular growing technique for mechanical analysis of the micro- and nanoscale structures which captures the small-size effects. In this paper, a comprehensive study was carried out to investigate the influence of the nonlocal parameter on the bifurcation behavior of a capacitive clamped-clamped nano-beam in the presence of the electrostatic and centrifugal forces. By using Eringen’s nonlocal elasticity theory, the nonlocal equation of the dynamic motion for a nano-beam has been derived using Euler–Bernoulli beam assumptions. The governing static equation of motion has been linearized using step by step linearization method; then, a Galerkin based reduced order model have been used to solve the linearized equation. In order to study the bifurcation behavior of the nano-beam, the static non-linear equation is changed to a one degree of freedom model using a one term Galerkin weighted residual method. So, by using a direct method, the equilibrium points of the system, including stable center points, unstable saddle points and singular points have been obtained. The stability of the fixed points has been investigated drawing motion trajectories in phase portraits and basins of attraction set and repulsion have been illustrated. The obtained results have been verified using the results of the prior studies for some cases and a good agreement has been observed. Moreover, the effects of the different values of the nonlocal parameter, angular velocity and van der Waals force on the fixed points have been studied using the phase portraits of the system for different initial conditions. Also, the influence of the nonlocal beam theory and centrifugal forces on the dynamic pull-in behavior have been investigated using time histories and phase portraits for different values of the nonlocal parameter.