Novel Adaptive Memory Event-Triggered-Based Fuzzy Robust Control for Nonlinear Networked Systems via the Differential Evolution Algorithm

This article mainly investigates the fuzzy optimization robust control issue for nonlinear networked systems characterized by the interval type-2(IT2)fuzzy technique under a differential evolution algorithm.To provide a more reasonable utilization of the constrained communication channel,a novel adaptive memory event-triggered(AMET)mechanism is developed,where two event-triggered thresholds can be dynamically adjusted in the light of the current system information and the transmitted historical data.Sufficient conditions with less conservative design of the fuzzy imperfect premise matching(IPM)controller are presented by introducing the Wirtinger-based integral inequality,the information of membership functions(MFs)and slack matrices.Subsequently,under the IPM policy,a new MFs intelligent optimization technique that takes advantage of the differential evolution algorithm is first provided for IT2 TakagiSugeno(T-S)fuzzy systems to update the fuzzy controller MFs in real-time and achieve a better system control effect.Finally,simulation results demonstrate that the proposed control scheme can obtain better system performance in the case of using fewer communication resources.

Design of PID controller with incomplete derivation based on differential evolution algorithm

To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution （DE） algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.

Differential Hydrocarbon Enrichment and its Main Controlling Factors in Depressions of the Bohai Bay Basin Differential Hydrocarbon Enrichment and its Main Controlling Factors in Depressions of the Bohai Bay Basin

Significant differential hydrocarbon enrichment occurs in depressions in a petroliferous basin.There are multiple depressions in the Bohai Bay Basin, and each depression as a relatively independent unit of hydrocarbon generation, migration and accumulation, contains significantly different hydrocarbon generation conditions and enrichment degree. On the basis of previous documents and a large number of statistical data, this work comparatively analyzed the differential hydrocarbon enrichment and its major controlling factors in depressions of the Bohai Bay Basin. The results show that depressions in the Bohai Bay Basin have various hydrocarbon enrichment degrees, and can be categorized into four types, namely enormously oil-rich, oil-rich, oily and oil-poor depressions. In general, the enormously oil-rich and oil-rich depressions are distributed in the eastern part of the basin along the Tan-Lu and Lan-Liao faults, whereas depressions in the western part of the basin are poor in hydrocarbons. Moreover, the vertical distribution of hydrocarbons is also highly heterogeneous, with Pre-Paleogene strata rich in hydrocarbons in the northern and western depressions, Paleogene strata rich in hydrocarbons in the entire basin, and Neogene strata rich in hydrocarbons in the off-shore areas of the Bohai Bay Basin. From early depressions in onshore areas to the late depressions in offshore areas of the Bohai Bay Basin, the source rocks and source-reservoir-cap rock assemblages gradually become younger and shallower, and the hydrocarbon resource abundance gradually increases. Hydrocarbon supplying condition is the key factor constraining the hydrocarbon enrichment for different depressions,while the main source-reservoir-cap rock assemblage, sufficient hydrocarbons and the transportation capacity of faults control the vertical distribution of hydrocarbons. The main factors controlling hydrocarbon enrichment are different for different layers. The hydrocarbon supplying condition of source rocks is the key controlling factor, whereas the source-reservoir configuration, the main sourcereservoir-cap rock assemblages, and the fault transportation are the main factors of hydrocarbon enrichment in the Paleogene, Paleogene and Neogene, respectively.

Self-adapting control parameters modifieddifferential evolution for trajectoryplanning of manipulators

Control parameters of original differential evolution （DE） are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed.

PRINCIPLE TO CLOSED LOOP CONTROL DIFFERENTIAL CYLINDER WITH DOUBLE SPEED VARIABLE PUMPS AND SINGLE LOOP CONTROL SIGNAL

To control the position of differential cylinder closed loop without usingany throttle elements, a flew idea that two speed variable pumps are used to compensate thenon-symmetric flow of differential cylinder is carried out. According to the leaking property of thesystem, a speed offset principle is also proposed to eliminate the cavitation and tension caused bythe leakage and condensation of oil, which makes the system be in the same state as a valvecontrolled circuit. This principle is explained theoretically and experimentally. Further therelationship that the pressures in cylinder chambers change with load and leakage, and therelationship between biasing speed and pre-load pressures in cylinder chambers are established. Theresearch has proved that the new system has similar technique features as those of controlled withservo valves, but due to the elimination of all the throttle lose the efficiency of system can beimproved greatly.

Application of PID controller to 2D differential geometric guidance problem

This paper presents the application of the proportional-integral-derivative （PID） controller to the flight control system （FCS） for two-dimensional （2D） differential geometric （DG） guidance and control problem. In particular, the performance of the designed FCS is investigated. To this end, the commanded angle-of-attack is firstly developed in the time domain using the classical DG formulations. Then, the classical PID controller is introduced to develop a FCS so as to form the 2D DG guidance and control system, and the PID controller parameters are determined by the Ziegler-Nichols method as well as the Routh-Hurwitz stability algorithm to guarantee the convergence of the system error. The results demonstrate that the designed controller yields a fast responding system, and the resulting DG guidance and control system is viable and effective in a realistic missile defense engagement.

Sliding Mode Control for Fractional Differential Systems with State-delay

The problem of sliding mode control for fractional differential systems with statedelay is considered.A novel sliding surface is proposed and a controller is designed correspondingly,such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point.And the stability of the proposed control design is discussed.

A Simplified Sliding Mode Controlled Electronic Differential for an Electric Vehicle with Two Independent Wheel Drives

This paper presents a simple sliding mode control strategy used for an electronic differential system for electric vehicle with two independent wheel drives. When a vehicle drives along a curved road lane, the speed of the inner wheel has to be different from that of the outer wheel in order to prevent the vehicle from vibrating and travelling an unsteady path. Because each wheel of this electrical vehicle has independent driving force, an electrical differential system is required to replace a gear differential system. However, it is difficult to analyse the nonlinear behaviour of the differential system in relation to the speed and steering angle, as well as vehicle structure. The proposed propulsion system consists of two permanent magnet synchronous machines that ensure the drive of the two back driving wheels. The proposed control structure called independent machines for speed control allows the achievement of an electronic differential which ensures the control of the vehicle behaviour on the road. It also allows to control, independently, every driving wheel to turn at different speeds in any curve. Analysis and simulation results of the proposed system are presented in this paper.

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

On the finite horizon Nash equilibrium solution in the differential game approach to formation control

The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.

Adaptive fault-tolerant control of heavy lift launch vehicle via differential algebraic observer

A novel adaptive fault-tolerant control scheme in the differential algebraic framework was proposed for attitude control of a heavy lift launch vehicle （HLLV）. By using purely mathematical transformations, the decoupled input-output representations of HLLV were derived, rendering three decoupled second-order systems, i.e., pitch, yaw and roll channels. Based on a new type of numerical differentiator, a differential algebraic observer （DAO） was proposed for estimating the system states and the generalized disturbances, including various disturbances and additive fault torques. Driven by DAOs, three improved proportional-integral- differential （PID） controllers with disturbance compensation were designed for pitch, yaw and roll control. All signals in the closed-loop system were guaranteed to be ultimately uniformly bounded by utilization of Lyapunov＇s indirect method. The convincing numerical simulations indicate that the proposed control scheme is successful in achieving high performance in the presence of parametric perturbations, external disturbances, noisy corruptions, and actuator faults.

Controllability of Neutral Impulsive Differential Inclusions with Non-Local Conditions

In this short article, we have studied the controllability result for neutral impulsive differential inclusions with nonlocal conditions by using the fixed point theorem for condensing multi-valued map due to Martelli [1]. The system considered here follows the P.D.E involving spatial partial derivatives with α-norms.

Stability analysis of a noise control system in a duct by using delay differential equation

The paper deals with the criteria for the closed- loop stability of a noise control system in a duct. To study the stability of the system, the model of delay differential equation is derived from the propagation of acoustic wave governed by a partial differential equation of hyperbolic type. Then, a simple feedback controller is designed, and its closed- loop stability is analyzed on the basis of the derived model of delay differential equation. The obtained criteria reveal the influence of the controller gain and the positions of a sensor and an actuator on the closed-loop stability. Finally, numerical simulations are presented to support the theoretical results.

Novel Control Vector Parameterization Method with Differential Evolution Algorithm and Its Application in Dynamic Optimization of Chemical Processes

Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution （DE） algorithm and control vector parameteri- zation （CVP） is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the oroposed methods.

Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem

In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.

Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

Controlling factors of marine shale gas differential enrichment in southern China

Based on the exploration and development practice of marine shale gas in Fuling, Weiyuan, Changning, Luzhou and Southeast Chongqing in southern China, combined with experiments and analysis, six factors controlling differential enrichment of marine shale gas are summarized as follows:(1) The more appropriate thermal evolution and the higher the abundance of organic matter, the higher the adsorption and total gas content of shale will be.(2) Kerogen pyrolysis and liquid hydrocarbon cracking provide most of the marine shale gas.(3) The specific surface area and pore volume of organic matter rich shale increased first and then decreased with the increase of thermal evolution degree of organic shale. At Ro between 2.23% and 3.33%, the shale reservoirs are mainly oil-wet, which is conducive to the enrichment of shale gas.(4) The thicker the roof and floor, the higher the shale gas content. The longer the last tectonic uplift time and the greater the uplift amplitude, the greater the loss of shale gas will be.(5) The buried depth and dip angle of the stratum have different controlling and coupling effects on shale gas in different tectonic positions, resulting in two differential enrichment models of shale gas.(6) The effective and comprehensive matching of source, reservoir and preservation conditions determines the quality of shale gas accumulation. Good match of effective gas generating amount and time, moderate pore evolution and good preservation conditions in space and time is essential for the enrichment of shale gas.

Differential Correspondences and Control Theory

When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differential extension N in order to define the new differential extensions L∩M and the smallest differential field (L,M ) ⊂ N containing both L and M. Such a result allows to generalize the use of complex numbers in classical algebra. Having now two finitely generated differential modules L and M over the non-commutative ring D = K [d1,...,dn] = K [d] of differential operators with coefficients in K, we may similarly look for a differential module N containing both L and M in order to define L∩M and L+M. This is exactly the situation met in linear or non-linear OD or PD control theory by selecting the inputs and the outputs among the control variables. However, in many recent books and papers, we have shown that controllability was a built-in property of a control system, not depending on the choice of inputs and outputs. The purpose of this paper is thus to revisit control theory by showing the specific importance of the two previous problems and the part plaid by N in both cases for the parametrization of the control system. An important tool will be the study of differential correspondences, a modern name for what was called Bäcklund problem during the last century, namely the elimination theory for groups of variables among systems of linear or nonlinear OD or PD equations. The main difficulty is to revisit differential homological algebra by using noncommutative localization as a way to generalize the symbolic calculus in the style of Heaviside and Mikusinski. Finally, when M is a D-module, this paper is using for the first time the fact that the system R = homK (M,K) is a D-module for the Spencer operator acting on sections, avoiding thus behaviours, trajectories and signal spaces in a purely formal way, contrary to a few recent works on this difficult subject.

Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control

The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The Lyapunov theorem and the unique solvability result for the first-order linear hyperbolic PDE are used to obtain some sufficient conditions for ensuring the finite-time consensus of the leaderless and leader-following MASs driven by first-order linear hyperbolic PDEs.Finally,two numerical examples are provided to verify the effectiveness of the proposed methods.