scholarly journals The stability of coalitional structure in differential linear-quadratic game of four persons

2021 ◽  
pp. 15-18
Author(s):  
V. I. Zhukovskiy ◽  
S. P. Samsonov ◽  
Romanova V. E.
Keyword(s):  
Linear Quadratic ◽  
Coalitional Structure ◽  
The Stability

In article coefficient criteria of the stability of coalitional structure in differential linear-quadratic positional game of 4 persons are established. Following the approach adopted in the article, it is possible to obtain coefficient criteria of the stability of coalitional structures both in games with a large number of players and for other coalitional structures

Hybrid Optimization Technique for Enhancing the Stability of Inverted Pendulum System

2021 ◽  
Vol 12 (1) ◽  
pp. 77-97
Author(s):  
M. E. Mousa ◽  
M. A. Ebrahim ◽  
Magdy M. Zaky ◽  
E. M. Saied ◽  
S. A. Kotb
Keyword(s):  
Inverted Pendulum ◽  
Optimization Technique ◽  
Linear Quadratic Regulator ◽  
Variable Structure ◽  
Grey Wolf Optimizer ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
New Variant ◽  
The Stability

The inverted pendulum system (IPS) is considered the milestone of many robotic-based industries. In this paper, a new variant of variable structure adaptive fuzzy (VSAF) is used with new reduced linear quadratic regulator (RLQR) and feedforward gain for enhancing the stability of IPS. The optimal determining of VSAF parameters as well as Q and R matrices of RLQR are obtained by using a modified grey wolf optimizer with adaptive constants property via particle swarm optimization technique (GWO/PSO-AC). A comparison between the hybrid GWO/PSO-AC and classical GWO/PSO based on multi-objective function is provided to justify the superiority of the proposed technique. The IPS equipped with the hybrid GWO/PSO-AC-based controllers has minimum settling time, rise time, undershoot, and overshoot results for the two system outputs (cart position and pendulum angle). The system is subjected to robustness tests to ensure that the system can cope with small as well as significant disturbances.

scholarly journals Takagi-Sugeno Fuzzy Modeling and PSO-Based Robust LQR Anti-Swing Control for Overhead Crane

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xuejuan Shao ◽  
Jinggang Zhang ◽  
Xueliang Zhang
Keyword(s):  
Linear Quadratic Regulator ◽  
Pso Algorithm ◽  
Fuzzy Modeling ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Overhead Crane ◽  
Linear Quadratic ◽  
Highly Nonlinear ◽  
The Stability ◽  
Takagi Sugeno

The dynamic model of overhead crane is highly nonlinear and uncertain. In this paper, Takagi-Sugeno (T-S) fuzzy modeling and PSO-based robust linear quadratic regulator (LQR) are proposed for anti-swing and positioning control of the system. First, on the basis of sector nonlinear theory, the two T-S fuzzy models are established by using the virtual control variables and approximate method. Then, considering the uncertainty of the model, robust LQR controllers with parallel distributed compensation (PDC) structure are designed. The feedback gain matrices are obtained by transforming the stability and robustness of the system into linear matrix inequalities (LMIs) problem. In addition, particle swarm optimization (PSO) algorithm is used to overcome the blindness of LQR weight matrix selection in the design process. The proposed control methods are simple, feasible, and robust. Finally, the numeral simulations are carried out to prove the effectiveness of the methods.

Disturbance Elimination of Buck-Converter with Resonant LPF via ILQ Servo-System

2014 ◽  
Vol 492 ◽  
pp. 493-498
Author(s):  
Shuhei Shiina ◽  
Sidshchadhaa Aumted ◽  
Hiroshi Takami
Keyword(s):  
Transfer Functions ◽  
Design Method ◽  
Servo System ◽  
State Equation ◽  
Buck Converter ◽  
Linear Quadratic ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
The Stability

The proposed optimal control on the basis of both current and voltage of the buck-converter is designed to be based on Inverse Linear Quadratic (ILQ) design method with the resonant low pass filter, which eliminates the disturbance by appended disturbance compensator. The designed scheme is composed of the state equation, an optimal ILQ solution, the ILQ servo-system with the disturbance elimination, the optimal basic gain, the optimal condition, the transfer functions and the disturbance compensator. Our results show the proposed strategy is the stability and robust control and has been made to improve ILQ control for the disturbance elimination of the output response, which guarantees the optimal gains on the basis of polynomial pole assignment.

ON THE STABILITY OF THE BEST REPLY MAP FOR NONCOOPERATIVE DIFFERENTIAL GAMES

2012 ◽  
Vol 10 (02) ◽  
pp. 113-132 ◽  
Author(s):  
ALBERTO BRESSAN ◽  
ZIPENG WANG
Keyword(s):  
Present Note ◽  
Nonlinear Perturbations ◽  
Linear Quadratic ◽  
Infinite Time ◽  
Feedback Controls ◽  
Affine Functions ◽  
The Stability ◽  
Discounted Costs ◽  
Noncooperative Differential Games ◽  
Linear Quadratic Games

Consider a differential game for two players in infinite time horizon, with exponentially discounted costs. A pair of feedback controls [Formula: see text] is Nash equilibrium solution if [Formula: see text] is the best strategy for Player 1 in reply to [Formula: see text], and [Formula: see text] is the best strategy for Player 2, in reply to [Formula: see text]. The aim of the present note is to investigate the stability of the best reply map: [Formula: see text]. For linear-quadratic games, we derive a condition which yields asymptotic stability, within the class of feedbacks which are affine functions of the state x ∈ ℝn. An example shows that stability is lost, as soon as nonlinear perturbations are considered.

scholarly journals Design and Implementation of a Quadcopter Based on a Linear Quadratic Regulator (LQR)

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Amevi Acakpovi ◽  
François-Xavier Fifatin ◽  
Maurel Aza-Gnandji ◽  
François Kpadevi ◽  
Justice Nyarko
Keyword(s):  
Coastal Zone Management ◽  
Linear Quadratic Regulator ◽  
Control Measures ◽  
The Internet ◽  
Linear Quadratic ◽  
Infrastructure Monitoring ◽  
Zone Management ◽  
Forestry Management ◽  
The Stability ◽  
And Control

This paper presents the design and construction and control of a quadcopter drone for Aerial Data Collection (ADC). The frame of the drone was designed using CadDian Software and the parts were printed using a 3D printer. The flight controller was based on Arduino board using an Atmega328p microprocessor with GSM, GPS and GPRS for sending data over the internet and also enhancing long range flight. A feedback control system was developed and tested to control the stability of drone. The proposed control strategy of the drone was tested for a case of pursuit of trajectory and also for speed of response and the findings were very positive confirming the appropriateness of the control measures for independent and autonomous flying with promising precision. This Unmanned Aerial Vehicle (UAV) fitted with IoT has the capability of collecting and sending data over the internet and therefore can be used in many applications including risk assessment, forestry management, urban planning, coastal zone management, infrastructure monitoring, post-disaster damage assessment and delivery of medical supplies.

scholarly journals Stabilized controller of a two wheels robot

2020 ◽  
Vol 9 (4) ◽  
pp. 1357-1363
Author(s):  
Ahmad Fahmi ◽  
Marizan Sulaiman ◽  
Indrazno Siradjuddin ◽  
I Made Wirawan ◽  
Abdul Syukor Mohamad Jaya ◽  
...  
Keyword(s):  
Control Method ◽  
Control Function ◽  
Balance Control ◽  
Linear Quadratic Regulator ◽  
Zero Point ◽  
Stability Control ◽  
Pole Placement ◽  
Linear Quadratic ◽  
Balancing Robot ◽  
The Stability

The Segway Human Transport (HT) robot, it is dynamical self-balancing robot type. The stability control is an important thing for the Segway robot. It is an indisputable fact that Segway robot is a natural instability framework robot. The case study of the Segway robot focuses on running balance control systems. The roll, pitch, and yaw balance of this robot are obtained by estimating the Kalman Filter with a combination of the pole placement and the Linear Quadratic Regulator (LQR) control method. In our system configuration, the mathematical model of the robot will be proved by Matlab Simulink by modelling of the stabilizing control system of all state variable input. Furthermore, the implementation of this system modelled to the real-time test of the Segway robot. The expected result is by substitute the known parameters from Gyro, Accelero and both rotary encoder to initial stabilize control function, the system will respond to the zero input curve. The coordinate units of displacement response and inclination response pictures are the same. As our expected, the response of the system can reach the zero point position. 

scholarly journals Improve Linear Quadratic Regulator by Particle Swarm Optimization Algorithms for Two Wheeled Self Balancing Mobile robot

2017 ◽  
Vol 13 (2) ◽  
pp. 173-179
Author(s):  
Ekhlas Karam ◽  
Noor Mjeed
Keyword(s):  
Particle Swarm Optimization ◽  
Numerical Method ◽  
Control Method ◽  
Particle Swarm ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Balancing Robot ◽  
The Stability ◽  
Multivariable Feedback

The aim of this paper is to suggest a methodical smooth control method for improving the stability of two wheeled self-balancing robot under effect disturbance. To promote the stability of the robot, the design of linear quadratic regulator using particle swarm optimization (PSO) method and adaptive particle swarm optimization (APSO). The computation of optimal multivariable feedback control is traditionally by LQR approach by Riccati equation. Regrettably, the method as yet has a trial and error approach when selecting parameters, particularly tuning the Q and R elements of the weight matrices. Therefore, an intelligent numerical method to solve this problem is suggested by depending PSO and APSO algorithm. To appraise the effectiveness of the suggested method, The Simulation result displays that the numerical method makes the system stable and minimizes processing time.

Robust Observer-Based Load Extenuation Control for Wind Turbines

2019 ◽  
Author(s):  
M. Hung Do ◽  
Dirk Söffker
Keyword(s):  
Wind Turbines ◽  
Large Scale ◽  
Linear Models ◽  
Simulation Software ◽  
Control Algorithms ◽  
Linear Quadratic ◽  
Robust Observer ◽  
Wind Turbine Control ◽  
Speed Regulation ◽  
The Stability

Abstract Wind energy is currently the fastest growing electricity source. To meet the output demand, wind turbines are becoming larger and more flexible leading to the problems of structural load especially in case of offshore turbines. Advanced control algorithms are developed to reduce the load, allowing to build larger turbines, and expand their lifetime. Observer-based control algorithms such as Linear-Quadratic-Gaussian LQG control which uses LQR to calculate the optimal observer and controller gains are commonly applied to wind turbines in literature. However the approach requires to calculate the observer and control gains separately. In addition, linear models used for parameter calculation may have errors with respect to the nonlinearities of wind turbines and induced to unmodeled dynamical properties. These modeling errors need to be considered to to guarantee the stability of the controlled system. Alternatively a robust design assuming bounds and limits of models have to be realized to guarantee stability while ignoring details of modeling. This paper proposes an optimal robust observer-based state feedback controller for large-scale wind turbines to realize multi objectives, including structural load mitigation and rotor speed regulation. The novel contribution is that the observer gain parameters, control gains, and integral action are optimized at the same time within H∞ mixed sensitivity framework to achieve desired performance with respect to power regulation, structural load mitigation, and also robustness for the wind turbine control system. The control performances have been verified by a high fidelity simulation software and are compared to those of a classical baseline controller.

A Linear Quadratic Integral Design Approach for the Automatic Control System of a Launch Vehicle

2015 ◽  
Vol 772 ◽  
pp. 410-417 ◽  
Author(s):  
Adrian Mihail Stoica ◽  
Cristian Emil Constantinescu ◽  
Silvia Nechita
Keyword(s):  
Control System ◽  
Flight Control ◽  
Launch Vehicle ◽  
Design Approach ◽  
Flight Control System ◽  
Linear Quadratic ◽  
Atmospheric Disturbances ◽  
Modeling Uncertainties ◽  
Quadratic Integral ◽  
The Stability

This paper presents a design approach for the automatic flight control system of a launch vehicle using a linear quadratic integral technique together with a fixed gain Kalman filter. Its purpose is to analyse the stability and tracking robustness performances of the control system designed via this approach when atmospheric disturbances, modeling uncertainties and structural flexible modes of the launcher are taken into account.

Delayed Reference Control of a Two-Mass Elastic System

2004 ◽  
Vol 10 (1) ◽  
pp. 135-159 ◽  
Author(s):  
P Gallina ◽  
Alberto Trevisani
Keyword(s):  
Elastic System ◽  
Linear Quadratic Regulator ◽  
Primary Concern ◽  
Linear Quadratic ◽  
Mass System ◽  
Control Scheme ◽  
Optimal Linear ◽  
Reference Parameter ◽  
The Stability

An innovative non-time-based control scheme for path tracking and vibration control of a two-mass system is introduced in this paper. The basic idea of the scheme, called delayed reference control (DRC), is to make the path reference of the system be a function of an action reference parameter which depends both on time and a variable which plays the role of a time delay. By suitably computing the value of the delay on the basis of the vibration measured, such vibration can be actively suppressed while an independent position regulator ensures an accurate tracking of the desired path. The DRC scheme is therefore suitable for those applications, in particular in the robotic field, where a pre-defined path through space must be followed precisely while the time taken to carry out the task is not a primary concern. In this paper the stability of the system is investigated, and numerical results are provided to assess the performance of the proposed method, compared to that of an optimal linear quadratic regulator.

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