scholarly journals Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sutrima Sutrima ◽  
Christiana Rini Indrati ◽  
Lina Aryati
Keyword(s):  
Control Systems ◽  
Approximate Controllability ◽  
Null Controllability ◽  
Control Problems ◽  
Output Stability ◽  
Sturm Liouville ◽  
Exact Null Controllability ◽  
Analysis Of Stability ◽  
The Stability ◽  
Controllability And Observability

In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated C0-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.

Lack of null controllability of viscoelastic flows

2019 ◽  
Vol 25 ◽  
pp. 60
Author(s):  
Debayan Maity ◽  
Debanjana Mitra ◽  
Michael Renardy
Keyword(s):  
Approximate Controllability ◽  
Momentum Equation ◽  
Null Controllability ◽  
Viscoelastic Flow ◽  
Viscoelastic Flows ◽  
Relaxation Mode ◽  
Maxwell Fluids ◽  
Linear Viscoelastic ◽  
Exact Null Controllability

We consider controllability of linear viscoelastic flow with a localized control in the momentum equation. We show that, for Jeffreys fluids or for Maxwell fluids with more than one relaxation mode, exact null controllability does not hold. This contrasts with known results on approximate controllability.

scholarly journals Stability Analysis of Systems with Fuzzy PI Controllers Applied to Electric Drives

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1246
Author(s):  
Constantin Voloşencu
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Fuzzy Controller ◽  
Stability Domain ◽  
Input Output ◽  
Electric Drives ◽  
Output Stability ◽  
Pi Controllers ◽  
The Stability ◽  
Internal And External Stability

This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers.

scholarly journals Exact Null Controllability of KdV-Burgers Equation with Memory Effect Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Rajagounder Ravi Kumar ◽  
Kil To Chong ◽  
Jong Ho Park
Keyword(s):  
Burgers Equation ◽  
Null Controllability ◽  
Carleman Estimates ◽  
External Control ◽  
Observability Inequality ◽  
Exact Null Controllability ◽  
Controllability Property ◽  
The Stability ◽  
With Memory

This paper is concerned with exact null controllability analysis of nonlinear KdV-Burgers equation with memory. The proposed approach relies upon regression tool to prove controllability property of linearized KdV-Burgers equation via Carleman estimates. The control is distributed along with subdomainω⊂Ωand the external control acts on the key role of observability inequality with memory. This description finally showed the exact null controllability guaranteeing the stability.

Design of robots driven by linear servo systems

Robotica ◽  
1992 ◽  
Vol 10 (4) ◽  
pp. 361-368 ◽  
Author(s):  
P. Minotti ◽  
P. Pracht
Keyword(s):  
Numerical Simulations ◽  
Control Systems ◽  
Dynamic Behavior ◽  
Robotic Manipulators ◽  
Control Problems ◽  
Servo Systems ◽  
Dynamic Decoupling ◽  
Non Linear ◽  
The Stability

SUMMARYThe performance of robotic manipulators is limited by the nature of the control systems which do not satisfactorily integrate the non-linear phenomena associated with the dynamic behavior of the mechanisms. The significant variations in the axial inertias lead to control problems and require an optimization of the mechanical structures in order to improve the stability of the manipulators. This paper proposes mechanical solutions in the domain of dynamic decoupling of robots and demonstrates, using numerical simulations the value of these solutions in terms of control.

Analysis of Stability Control Systems for Single-Unit Commercial Vehicles

2011 ◽  
Author(s):  
Dan T. Horak
Keyword(s):  
Control Problem ◽  
Control Systems ◽  
Single Unit ◽  
Dynamic Models ◽  
Stability Control ◽  
Performance Limits ◽  
Commercial Vehicles ◽  
Rollover Stability ◽  
Analysis Of Stability ◽  
The Stability

The stability control problem of single-unit commercial vehicles, from large pickup trucks to motorcoaches, is analyzed. Detailed dynamic models of four baseline vehicles are used to estimate the feasibility and the performance limits of rollover stability and directional stability control systems for such vehicles on dry and wet roads.

scholarly journals On the Lyapunov equation in Banach spaces and applications to control problems

2002 ◽  
Vol 29 (3) ◽  
pp. 155-166 ◽  
Author(s):  
Vu Ngoc Phat ◽  
Tran Tin Kiet
Keyword(s):  
Control Systems ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Lyapunov Equation ◽  
Null Controllability ◽  
Control Problems ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Linear Differential Systems ◽  
Linear Differential

By extending the Lyapunov equationA*Q+QA=−Pto an arbitrary infinite-dimensional Banach space, we give stability conditions for a class of linear differential systems. Relationship between stabilizability and exact null-controllability is established. The result is applied to obtain new sufficient conditions for the stabilizability of a class of nonlinear control systems in Banach spaces.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

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