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A problem of robust control of a system with time delay

100%
Blizorukova M., Kappel F., Maksimov V.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 4
821-834
EN
A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.
2
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Robust Control of Linear Stochastic Systems with Fully Observable State

80%
Poznyak A. S., Taksar M. I.
Applicationes Mathematicae
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1996-1997
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tom 24
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nr 1
35-46
EN
We consider a multidimensional linear system with additive inputs (control) and Brownian noise. There is a cost associated with each control. The aim is to minimize the cost. However, we work with the model in which the parameters of the system may change in time and in addition the exact form of these parameters is not known, only intervals within which they vary are given. In the situation where minimization of a functional over the class of admissible controls makes no sense since the value of such a functional is different for different systems within the class, we should deal not with a single problem but with a family of problems. The objective in such a setting is twofold. First, we intend to establish existence of a state feedback linear robust control which stabilizes any system within the class. Then among all robust controls we find the one which yields the lowest bound on the cost within the class of all systems under consideration. We give the answer in terms of a solution to a matrix Riccati equation and we present necessary and sufficient conditions for such a solution to exist. We also state a criterion when the obtained bound on the cost is sharp, that is, the control we construct is actually a solution to the minimax problem.
3
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Reducing the mast vibration of single-mast stacker cranes by gain-scheduled control

80%
Hajdu S., Gáspár P.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 4
791-802
EN
In the frame structure of stacker cranes harmful mast vibrations may appear due to the inertial forces of acceleration or the braking movement phase. This effect may reduce the stability and positioning accuracy of these machines. Unfortunately, their dynamic properties also vary with the lifted load magnitude and position. The purpose of the paper is to present a controller design method which can handle the effect of a varying lifted load magnitude and position in a dynamic model and at the same time reveals good reference signal tracking and mast vibration reducing properties. A controller design case study is presented step by step from dynamic modeling through to the validation of the resulting controller. In the paper the dynamic modeling possibilities of single-mast stacker cranes are summarized. The handling of varying dynamical behavior is realized via the polytopic LPV modeling approach. Based on this modeling technique, a gain-scheduled controller design method is proposed, which is suitable for achieving the goals set. Finally, controller validation is presented by means of time domain simulations.
4
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Reliable robust path planning with application to mobile robots

80%
Pepy R., Kieffer M., Walter E.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 3
413-424
EN
This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.
5
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Iterative Learning Control - monotonicity and optimization

80%
Owens D., Daley S.
International Journal of Applied Mathematics and Computer Science
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2008
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tom 18
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nr 3
279-293
EN
The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.
6
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LPV design of fault-tolerant control for road vehicles

61%
Gáspár P., Szabó Z., Bokor J.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 1
173-182
EN
The aim of the paper is to present a supervisory decentralized architecture for the design and development of reconfigurable and fault-tolerant control systems in road vehicles. The performance specifications are guaranteed by local controllers, while the coordination of these components is provided by a supervisor. Since the monitoring components and FDI filters provide the supervisor with information about the various vehicle maneuvers and the different fault operations, it is able to make decisions about necessary interventions into the vehicle motions and guarantee reconfigurable and fault-tolerant operation of the vehicle. The design of the proposed reconfigurable and fault-tolerant control is based on an LPV method that uses monitored scheduling variables during the operation of the vehicle.
7
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Minimax LQG control

61%
Petersen I. R.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
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nr 3
309-323
EN
This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.
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