China 
Africa 
Explore chapters and articles related to this topic
Special Types of Closed-Loop Drug Input Controllers
Published in Robert B. Northrop, Endogenous and Exogenous Regulation and Control of Physiological Systems, 2020
System parameters were chosen to give a quick response without overshoot. Figure 5.20 shows the turn-on transient for the IPFM/PID-controlled system. The spikes at the bottom of the plot are y(t), trace 2 is x2(t), trace 4 is ne(t), and the set point is trace 1. Note that there is a modest ripple due to the bolus injections from the IPFM controller. Because the closed-loop system is type 1, there is zero average steady-state error. If Do is made smaller than 0.2, the ripple is smaller and the system is slower. In Figure 5.21, we have set the derivative and integral gains to zero, creating a second-order type 0 system; the proportional gain, c, was left at 1. Note that there is a huge average steady-state error and that the basic equilibrium frequency is lower, giving a large peak-to-peak ripple on x2. In Figure 5.22, we set a = b = 0 and c = 5. There is still a large average steady-state error, and the higher gain causes an initial overshoot and erratic behavior of ne(t).
Special, Second, and Higher-Order Equations
Published in L.M.B.C. Campos, Higher-Order Differential Equations and Elasticity, 2019
The solution of first-order differential equations, whether or not they have special integrals, is facilitated if the equation can be solved for the slope, or for one of the variables (section 5.4). If a first-order differential equation is not solvable, it may happen that its dual equation is simpler (section 5.5). A second-order differential equation, in which one of the variables or the slope is missing, can always be reduced to a first order differential equation (section 5.6). An ordinary differential equation of order more than two may, in some cases, be reduced to a first-order equation; more often, it may be possible to depress the order of a differential equation (section 5.7), for example if it is an exact differential, or can be factorized (section 5.8), or is homogeneous (section 5.9). The homogeneous differential equation of order N is a generalization of the homogeneous first-order type; in the linear case, it reduces to Euler's equation with power coefficients and homogeneous derivatives (sections 1.6–1.8), that together with the case of constant coefficients (sections 1.3–1.5) is a generally solvable class of differential equations of N-th order (chapter 1). The non-linear homogeneous differential equation of order N can be transformed into an equation of order N − l by means of a change of variable; this transformation, like others indicated in this section, is only useful if it leads to a differential equation simpler to solve than the original.
Mangasarian-type second- and higher-order duality for mathematical programs with complementarity constraints
Published in Optimization, 2022
In this paper, we have presented Mangasarian-type second-order and higher-order dual problems for MPCC. Under η-bonvexity and higher-order type I condition, we have obtained several duality theorems for second and higher order duality in MPCC problems, respectively, including the weak duality, strong duality, converse duality, and strict converse duality theorems. Examples have been given to verify these theorems and illustrate that second-order duality may provide tighter bound than first-order duality. For future work, it is of interest to consider these theorems by using another second-order generalized convexities characterized in [30]. Another matter is to propose efficient numerical methods for MPCC based on the second-order duality.
A robust control scheme for synchronizing fractional order disturbed chaotic systems with uncertainty and time-varying delay
Published in Systems Science & Control Engineering, 2022
Hai Gu, Jianhua Sun, Hadi Imani
Fractional order systems are one of the most important fields of research related to chaos theory (Yousefpour et al., 2020). In fact, well-known chaotic systems such as Lorenz, Chen, and etc. show a fractional order dynamic behaviour. Due to the ability of fractional order systems to express more accurately than the integer order type. They are able to describe and model application systems more precisely and are used in a wide range of applications, from signal and image processing to automation, robotic control and quantum (Ahmad et al., 2019; Khan et al., 2017; Sohail et al., 2018; Tripathi et al., 2010). Therefore, chaos theory requests additional evaluation and development in this area.
Second-order multi-objective non–differentiable Schaible type model and its duality relation under (K xQ)–C–type–I functions
Published in International Journal of Modelling and Simulation, 2021
Rajnish Kumar, Khursheed Alam, Ramu Dubey
In this article, we introduced the definition of second-order --type-I functions and also constructed a nontrivial numerical example for justifying the existence such types of functions. In section 4, a second-order non-differentiable multi-objective Schaible type optimization problem over arbitrary cones has been considered and obtains duality results with second-order --type-I functions.