< p>Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. Chaos appears in the system which is very sensitive to initial condition. Study of chaos dynamic systems has quickly spread in the last three decades, and it has become a very attractive area of research to remove dynamic chaotic behaviors and make nonlinear systems stable. Stabilization has been considered as a high usage tool to eliminate aberrant behaviors of chaotic system and can be divided into two categories, regulation and tracking. In regulation stabilizing, system becomes stable by designing proper control signals to one of the available balance points or one of the alternate unstable paths on strange absorbers in chaos system. Another set of chaos systems stabilizing is tracking. In this type of stabilization, a reference signal varying with time and a control frame are considered in the way the system responses follow that signal. In this thesis, both regulation and tracking stabilizing are considered, first without chaos and then with chaos. For this purpose, smart and powerful adaptive neuro fuzzy inference system (ANFIS) technic is used. The proposed method is examined by a famous example of a chaos system called the Lorenz system. The simulation results show the ability of the proposed method. Our proposed approach is ANFIS which is designed for Lorenz chaotic system. it is compare with PID controller in the system . Manuscript profile

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximation will be compared respect to accuracy. Then the Hamilton-Jacobi-Belman (HJB) equation, obtained in nonlinear optimal approach, is considered and an analytical approximation of the solution of it using the Adomian decomposition method is presented. Manuscript profile

One of the main problems of car-like robot is robust path following in the presence of sliding effect. To tackle this problem, a robust mix H2/H∞ static state feedback control method is selected. This method is the well-known linear robust controller which is robust against external disturbance as well as model uncertainty. In this paper, the path following problem is formulated as linear matrix inequality for the kinematic model of car-like robot, which includes sliding effect. The robustness and path following performance of the proposed controller are investigated based on the comparison of suggested controller with an optimal proportional integral controller. The simulation results, which have been performed by MATLAB Simulink, shows the presented controller is able to follow various paths including simple, linear and more complex function path like square, and sine function path even in the presence of sliding effect. In addition, the robustness and correctness of closed-loop system in the simulations are demonstrated based on the nonlinear analysis of equilibrium point. Manuscript profile

This paper describes a low computational direct approach for optimal motion planning and obstacle avoidance of Omni-directional mobile robots within velocity and acceleration constraints on the robot motion. The main purpose of this problem is the minimization of a quadratic cost function while limitation on velocity and acceleration of robot is considered and collision with any obstacle in the robot workspace is avoided. This problem can be formulated as a constraint nonlinear optimal control problem. To solve this problem, a direct method is utilized which employs polynomials functions for parameterization of trajectories. By this transforming, the main optimal control problem can be rewritten as a nonlinear programming problem (NLP) with lower complexity. To solve the resulted NLP and obtain optimal trajectories, a new approach with very small run time is used. Finally, the performance and effectiveness of the proposed method are tested in simulations and some performance indexes are computed for better assessment. Furthermore, a comparison between proposed method and another direct method is done to verify the low computational cost and better performance of the proposed method. Manuscript profile

خودترمیمی ضروری ترین ویژگی جهت بازیابی شبکه توزیع هوشمند در هنگام بروز خطا است. جزیره سازی منطقه دچار خطا را می توان هم به صورت آفلاین و هم به صورت آنلاین انجام داد. با استفاده از روش جزیره سازی آنلاین برای بازیابی سرویس در منطقه خطادار، می توان مرز ریزشبکه های جزیره ای و تعداد ریزشبکه ها را به صورت بهینه، حین وقوع خطا تعیین نمود. در این مطالعه، یک روش ریاضی دو مرحله ای جدید جهت بازیابی خودترمیمی هنگام وقوع خطا ارائه شده است. در لایه اول آرایش بهینه سیستم در ناحیه دچارخطا، توسط یک مدل ریاضی جدید تعیین می شود. سپس در لایه دوم مسئله مشارکت واحدها در سیستم توزیع هوشمند حل می شود. کاهش یا قطع بار برنامه ریزی مجدد منابع تولید پراکندۀ غیرقابل توزیع و برنامه‌ریزی بهینه سیستم‌های ذخیره ساز انرژی تعیین می‌شوند. زمان اجرای کم و راه حل بهینه از مهم ترین مزایای طرح پیشنهادی است. ابزارهایی مانند کاهش هوشمند بار و برنامه های پاسخ گویی به تقاضا نیز جهت بازیابی بهینه سیستم استفاده شده است. سیستم توزیع 33 شینه IEEE برای اعتبارسنجی روش پیشنهادی استفاده می شود. نتایج مطالعات موردی اثربخشی روش پیشنهادی را نشان می‌دهد. Manuscript profile

This paper proposes a sub-optimal Extended State-Dependent Differential Riccati Equation (ESDDRE) controller for nonlinear Reaction-Advection-Diffusion (R-A-D) Partial Differential Equation (PDE) systems with multiple delays. A State-Dependent Riccati Equation (SDRE) is a nonlinear version of Linear Quadratic Regulator (LQR) in optimal control and it is used to analyze nonlinear optimal control problems. Instead of the linearization or the Jacobin procedure, the ESDDRE technique applies a State-Dependent Coefficients (SDC) for parameterization to construct an Extended Pseudo-Linearization (EPL) representation. All of the multiple delays sections in this presentation can be located in the system matrices and input vectors. The control effort of ESDDRE method is derived based on the Hamiltonian equation and also cost function according to the PDE systems. In addition, the L_2 stability is guaranteed by Poincaré inequality and as well as Lyapunov function regarded on the ESDDRE control strategy for the closed-loop system. The simulation results for the nonlinear R-A-D partial differential equation with one and two constant delays indicate that the proposed ESDDRE controller technique is efficient. Manuscript profile

This paper presents a long term optimal control treatment of human immunodeficiency virus (HIV) infection. HIV destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney, and heart, and causes death. Unfortunately, this infectious disease currently has no cure; however, there are effective retroviral drugs for improving the patients’ health conditions. In this paper, two treatment drugs are considered to decrease the free HIV virus particles in the blood. Since excessive use of these drugs is not without harmful side effects, the prescription dosage should be minimum. Thus, we formulate an optimal control problem to reduce the HIV virus particles in the blood by using minimum drugs. To solve the obtained optimal control, direct method and spline functions are utilized. The main advantage of the direct method to the indirect method is the low computational cost of this solution. Spline functions are tools used in the direct solving approach to achieve the better solutions. Also, three different models are considered in this paper to evaluate the effectiveness of the proposed method in different conditions. In addition, in the end, we compare the results from the proposed approach with the results of the problem solving by indirect method. Furthermore, the sensitivity analysis is checked to demonstrate the performance of control system against parametric uncertainties. Manuscript profile

In this paper, an adaptive-neural free model scheme is proposed to control a widely-used nonlinear multivariable industrial system, a quadruple-tank process (QTP). The system consists of four tanks that are arranged in two upper and two lower formations. The main objective is defined as maintaining the level of the liquid in lower tanks via two pumps. Controlling this system is not an easy task since it has nonlinear dynamics, strong interaction between different channels, and highly interacted input and output variables. In the adaptive part of the proposed controller, the parameters and rules obtained from Lyapunov stability analysis, along with the estimation of nonlinear functions performed with the neural network, constitute the controller design steps. To highlight the controller's abilities, an additional object is defined, which is controlling the temperature of liquid of those two tanks by adding a heater to the QTP system as a modified system. Obviously, the interactions amongst the control loops are multiplied because the modified quadruple tank process (MQTP) system has four inputs and four outputs. One of the main contributions of this paper is the implementation of the closed-loop system. Regarding the importance of such a system in the industry and to test the controller practically, the closed-loop system is implemented in an industrial automation environment with the connection of Process Control System SIMATIC (PCS7) industrial software to MATLAB with Open Platform Communications (OPC) protocol. The effectiveness of the introduced scheme is verified by performing some experimental validation. Manuscript profile

In this study, a robust H_2/H_∞ multi-objective state-feedback controller and tracking design are presented for a mobile two-wheeled inverted pendulum (MTWIP). The proposed control has to track the desired angular velocity while keeping the mobile two-wheeled inverted pendulum balanced. First, error of output states are added to the dynamic of system for better tracking control. And uncertainties of parameters are defined by affine parameters. Next, Takagi-Sugeno (T-S) fuzzy model is used for estimating the uncertainty of nonlinear model parameters. Robust H_2/H_∞ controller is designed and analyzed for each local linear subsystem of mobile two-wheeled inverted pendulum by using a linear matrix inequalities method. To sum up, in order to calculate the whole dynamic of system from each local linear subsystem, weight average defuzzifer method is used and the total controller is designed and analyzed according to parallel distribute compensation. The simulation indicate that the proposed scheme has high accuracy, robustness, good tracking, fast transient responses and lower control effort for a mobile two-wheeled inverted pendulum despite the uncertainties and external disturbance. Manuscript profile

In this paper, a strictly passive formulation has been developed to design a passive state-observer for both time-invariant and time-varying Lipschitz nonlinear systems. During this formulation, a convergence and strictly passive state-observer is provided to have passive closed-loop system. Some definitions and charts are defined here for time-invariant and time-varying systems in different scenarios. A new interconnection between passivity of subsystems and passivity/stability of the closed-loop system has been introduced from a different point of view. All definitions are organized based on the systematic method called “virtually Euler-Lagrange” form of passivation. Utilizing this form and theses definitions, make the design process simpler and straightforward, while, some conditions of design will be released due to using these definitions. The designed controller/observer has been applied to control the hepatitis B virus infection disease. The reliability of the proposed definitions are examined by using MATLAB/SIMULINK, while, the results demonstrate the ability and power of this novel approach. Manuscript profile