Dynamic control of a unicycle robot with double flywheels using linear quadratic regulator and linear matrix inequality

2020 ◽  
Author(s):  
Boutaina Elkinany ◽  
Mohammed Alfidi ◽  
Zakaria Chalh
Keyword(s):  
Linear Matrix Inequality ◽  
Dynamic Control ◽  
Linear Quadratic Regulator ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Quadratic

Control Simulation in Building Energy Management Systems by Linear Matrix Inequality

2011 ◽  
Vol 121-126 ◽  
pp. 745-749
Author(s):  
Yau Bin Yang ◽  
Min Der Wu ◽  
Yu Choung Chang
Keyword(s):  
Energy Consumption ◽  
Linear Matrix Inequality ◽  
Linear Quadratic Regulator ◽  
Building Energy ◽  
Current Control ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Quadratic ◽  
Total Energy Consumption ◽  
Minimization Method

The energy usage of building has occupied the large portion of total energy consumption. It is important to develop the building energy consumption minimization method. The new study adopted the thermal conservation equation for this multivariable control issue and the linear matrix inequality based on linear quadratic regulator for mixed H2&H∞ control. After substituting the obtained control gains into the original thermal systems, the asymptotically stabilities of whole systems are guaranteed. The comparison between the traditional and current control scheme are made.

Two-degree-of-freedom multi-input multi-output proportional–integral–derivative control design: Application to quadruple-tank system

2018 ◽  
Vol 233 (3) ◽  
pp. 303-319
Author(s):  
Jatin Kumar Pradhan ◽  
Arun Ghosh ◽  
Chandrashekhar Narayan Bhende
Keyword(s):  
State Feedback ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Inequality ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral

This article is concerned with designing a 2-degree-of-freedom multi-input multi-output proportional–integral–derivative controller to ensure linear quadratic regulator performance and H∞ performance using a non-iterative linear matrix inequality–based method. To design the controller, first, a relation between the state feedback gain and proportional–integral–derivative gain is obtained. As the gains of proportional–integral–derivative controller cannot, in general, be found out from this relation for arbitrary stabilizing state feedback gain, a suitable form of the matrices involved in linear matrix inequality–based state feedback design is then chosen to obtain the proportional–integral–derivative gains directly. The special structure of the above matrices allows one to design proportional–integral–derivative controller in non-iterative manner. As a result, multi-objective performances, such as linear quadratic regulator and H∞, can be achieved simultaneously without increasing the computational burden much. To enhance the reference-input-to-output characteristics, a feedforward gain is also introduced and designed to minimize certain closed-loop H∞ performance. The proposed control design method is applied for multi-input multi-output proportional–integral compensation of a laboratory-based quadruple-tank process. The performance of the compensation is studied through extensive simulations and experiments.

scholarly journals A New Robust Training Law for Dynamic Neural Networks with External Disturbance: An LMI Approach

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Choon Ki Ahn
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Exponential Stability ◽  
External Disturbance ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Lmi Approach ◽  
Dynamic Neural Networks ◽  
Numerical Examples

A new robust training law, which is called an input/output-to-state stable training law (IOSSTL), is proposed for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the IOSSTL is presented to not only guarantee exponential stability but also reduce the effect of an external disturbance. It is shown that the IOSSTL can be obtained by solving the LMI, which can be easily facilitated by using some standard numerical packages. Numerical examples are presented to demonstrate the validity of the proposed IOSSTL.

Cellular Neural Network Based on Hybrid Linear Matrix Inequality and Particle Swarm Optimization for Noise Removal of Color Image

2011 ◽  
Vol 422 ◽  
pp. 771-774
Author(s):  
Te Jen Su ◽  
Jui Chuan Cheng ◽  
Yu Jen Lin
Keyword(s):  
Neural Network ◽  
Particle Swarm Optimization ◽  
Linear Matrix Inequality ◽  
Color Image ◽  
Particle Swarm ◽  
Cellular Neural Network ◽  
Noise Removal ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Swarm Optimization

This paper presents a color image noise removal technique that employs a cellular neural network (CNN) based on hybrid linear matrix inequality (LMI) and particle swarm optimization (PSO). For designing templates of CNN, the Lyapunov stability theorem is applied to derive the criterion for the uniqueness and global asymptotic stability of the CNN’s equilibrium point. The template design is characterized as a standard LMI problem, and the parameters of templates are optimized by PSO. The input templates are obtained by employing the CNN’s property of saturation nonlinearity, which can be used to eliminate noise from arbitrary corrupted images. The demonstrated examples are compared favorably with other available methods, which illustrate the better performance of the proposed LMI-PSO-CNN methodology.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

scholarly journals LMI-Based Approach for Exponential Robust Stability of High-Order Hopfield Neural Networks with Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yangfan Wang ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Robust Stability ◽  
High Order ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Global Exponential Robust Stability

This paper studies the problems of global exponential robust stability of high-order hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential robust stability for the high-order neural networks are established, which are easily verifiable and have a wider adaptive.

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