Task-level Dexterous Manipulation with Multifingered Hand Under Modeling Uncertainties

2021 ◽  
Author(s):  
Alex Caldas ◽  
Mathieu Grossard ◽  
Maria Makarov ◽  
Pedro Rodriguez-Ayerbe
Keyword(s):  
Object Motion ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Dexterous Manipulation ◽  
Geometric Uncertainties ◽  
Multifingered Hands ◽  
Modeling Uncertainties ◽  
Robust Control Design ◽  
Definition Of ◽  
Task Level

Abstract This article presents an approach to efficiently control grippers/multifingered hands for dexterous manipulation according to a task, i.e. a predefined trajectory in the object space. The object motion is decomposed using a basis of predefined object motions equivalent to object-level coordinates couplings and leading to the definition of the task-level space. In the proposed approach, the decomposition of the motion in the task space is associated with a robust control design based on Linear Matrix Inequalities (LMIs) and Bilinear Matrix Inequalities (BMI). Eigenvalue placement ensures the robustness of the system to geometric uncertainties and eigenvector placement decouples the system according to task specifications. A practical evaluation of the proposed control strategy is provided with a two-fingers and six-DoFs robotic system manipulating an object in the horizontal plane. Results show a better trajectory tracking and the robustness of the control law according to geometric uncertainties and the manipulation of various objects.

Robust Control Design for Retarded Discrete-Time Systems

2006 ◽  
Vol 129 (1) ◽  
pp. 72-76 ◽  
Author(s):  
El Houssaine Tissir
Keyword(s):  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Synthesis Methods ◽  
Matrix Inequalities ◽  
Stabilizing Controller ◽  
Discrete Time Systems ◽  
Robust Control Design ◽  
Time Systems

This paper focuses on the analysis and synthesis of a robust stabilizing controller for linear discrete time systems with norm-bounded time varying uncertainties. Delay independent robust stability conditions are derived and two synthesis methods are presented. One method is to construct a robust memoryless state feedback control law from the solutions of linear matrix inequalities. The other method consists of designing robust observer-based output feedback controller. The results are expressed in termes of linear matrix inequalities. A comparison with μ∕LDI tests is presented. Furthermore, numerical examples are given for illustration.

Completeness on the stability criterion of fractional order LTI systems

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Yiheng Wei ◽  
Yuquan Chen ◽  
Songsong Cheng ◽  
Yong Wang
Keyword(s):  
Fractional Order ◽  
Stability Criterion ◽  
Positive Definite Matrix ◽  
Order System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
The Stability ◽  
Definition Of ◽  
And Control

AbstractThe importance of the concept of stability in fractional order system and control has been recognized for some time now. Recently, it has become evident that many conclusions were drawn, but little consensus was reached. Consequently, there is an urgent need for a much deeper understanding of such a concept. With the definition of fractional order positive definite matrix, a set of equivalent and elegant stability criteria are developed via revisiting a stability criterion we proposed before. All the results are formed in terms of linear matrix inequalities. Afterwards, a series of interesting properties of these criteria are revealed profoundly, including completeness, singularity, conservatism, etc. Eventually, a simulation study is provided to validate the effectiveness of the obtained results.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Ramalingam Sriraman ◽  
Rajendran Samidurai
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stochastic Perturbations ◽  
Practical Applications ◽  
Markovian Jump Parameters ◽  
Generalized Neural Networks ◽  
System Information ◽  
Dissipativity Analysis

Abstract This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.

scholarly journals Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 580
Author(s):  
Pavel Shcherbakov ◽  
Mingyue Ding ◽  
Ming Yuchi
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computational Mathematics ◽  
Closed Form Solutions ◽  
Monte Carlo Techniques ◽  
Control Optimization ◽  
Point Representation ◽  
Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

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