Necessary Conditions For Controllability Research Articles

Improved multi-agent controllability processing technique based on equitable partition

In this paper, we study the controllability of multi-agent systems by equitable partition and automorphism. For the case that cells are incompletely connected outside but completely connected inside, a necessary condition for controllability is given from the perspective of the rank of connection matrix. For the case of multiple cells being completely connected outside and incompletely connected inside, in terms of the eigenvalues and eigenvectors of L and Lπ, several sufficient and necessary conditions for controllability are presented. Once the quotient graph is controllable under single input or all nodes in nontrivial cells are leaders, the lower bound of controllable subspace is determined. Finally, we give the gap between the necessary condition and the sufficient condition for controllability from the aspect of equitable partition. One highlight of the results in this paper is that we show sufficient conditions to judge controllability by equitable partition and automorphism, which, for specific cases, provides one method that how to break through the defect that equitable partition can only obtain necessary conditions.

Controllability of networked systems with heterogeneous dynamics

Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976) established necessary and sufficient conditions for the controllability of homogeneous networked systems where the individual nodes are linear time-invariant (LTI) systems and the network topology matrix is diagonalizable. In this paper, we consider a class of heterogeneous networked systems having triangularizable network topology. Here, we establish a result which gives necessary and sufficient conditions for controllability of a class of heterogeneous systems, which generalizes the result of Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976). Also, we provide some necessary conditions for the controllability of general heterogeneous networked systems having some restrictions on the network topology matrix. Theoretical results are illustrated with numerical examples.

КОНЦЕПТУАЛЬНІ ЗАСАДИ ПОБУДОВИ УПРАВЛІНСЬКОГО ОБЛІКУ ЦЕНТРІВ ВІДПОВІДАЛЬНОСТІ ПРИ БЮДЖЕТУВАННІ НА ОЛІЙНО-ЖИРОВИХ ПІДПРИЄМСТВАХ УКРАЇНИ

Анотація. Проаналізовано управлінський облік центрів відповідальності, що утворюють специфічні об’єкти обліку витрат, а саме бюджетні центри відповідальності. Представлена система управлінського поопераційного обліку витрат відповідає вимогам бюджетування і стає необхідною умовою контролю за рівнем дотримання нормативів та забезпечує обґрунтоване формування виробничої собівартості продукції з технологічних переділів на олійно-жирових підприємствах. Інформаційним підґрунтям процесу складання бюджету є управлінський облік. Більше того, управлінський облік забезпечує потрібну інформацію для планування бюджету, контролю та аналізу виконання бюджету, а також є однією зі складових процесу бюджетування. Оцінка центрів відповідальності є корисною для розуміння циклів економічної діяльності, економічних процесів і структурних підрозділів у рамках створення бюджетів. Система управлінського обліку на основі операцій переважно відповідає вимогам бюджетування, що стає необхідною умовою контролю за стандартними умовами ведення обліку. Для одержання більш деталізованої інформації для аналізу і контролю пропонується організацію обліку витрат здійснювати за операціями-функціями технологічних процесів, що дає можливість аналітикам знаходити вузькі місця в технології через виявлення зайвих технологічних функцій і операцій та посилити контроль за дотриманням доведених бюджетів кожному «центру відповідальності». Облік центрів відповідальності має на меті оцінити управлінську діяльність окремого центру відповідальності, надати звіт про відповідальність та інформаційний звіт для оцінки вищого керівництва. Це метод управлінського обліку, який вимірює результати кожного центру відповідальності, що дозволяє кожному керівникові усвідомлювати відповідальність у своїй галузі, що стосується обліку витрат і бюджетування. Ключові слова: управлінський облік, центри відповідальності, технологічні переділи, бюджетування, звіт центру відповідальності, гнучкі бюджети. Формул: 0; рис.: 0; табл.: 2; бібл.: 14.

Multibody Analysis and Control of a Full-Wrist Exoskeleton for Tremor Alleviation.

Uncontrollable shaking in the human wrist, caused by pathological tremor, can significantly undermine the power and accuracy in object manipulation. In this paper, the design of a tremor alleviating wrist exoskeleton (TAWE) is introduced. Unlike the works in the literature that only consider the flexion/extension (FE) motion, in this paper, we model the wrist joint as a constrained three-dimensional (3D) rotational joint accounting for the coupled FE and radial/ulnar deviation (RUD) motions. Hence TAWE, which features a six degrees-of-freedom (DOF) rigid linkage structure, aims to accurately monitor, suppress tremors, and provide light-power augmentation in both FE and RUD wrist motions. The presented study focuses on providing a fundamental understanding of the feasibility of TAWE through theoretical analyses. The analytical multibody modeling of the forearm-TAWE assembly provides insight into the necessary conditions for control, which indicates that reliable control conditions in the desired workspace can be acquired by tuning the design parameters. Nonlinear regressions are then implemented to identify the information that is crucial to the controller design from the unknown wrist kinematics. The proposed analytical model is validated numerically with V-REP and the result shows good agreement. Simulations also demonstrate the reliable performance of TAWE under controllers designed for tremor suppression and movement assistance.

The Graphical Conditions for Controllability of Multiagent Systems Under Equitable Partition.

In this article, by analyzing the eigenvalues and eigenvectors of Laplacian L , we investigate the controllability of multiagent systems under equitable partitions. Two classes of nontrivial cells are defined according to the different numbers of links between them, which are completely connected nontrivial cells (CCNCs) and incompletely connected nontrivial cells. For the system with CCNCs, a necessary condition for controllability is found to be choosing leaders from each nontrivial cell, the number of which should be one less than the cardinality of the cell. It is shown that the controllability is affected by three factors: 1) the number of the links between nontrivial cells; 2) the rank of the connection matrix; and 3) the odevity of the capacity of the nontrivial cells. In the case of nontrivial cells under the equitable partition, there are automorphisms of interconnection graph G , which induce the eigenvectors of L with zero entries. For the system with automorphisms, by taking advantage of the property of eigenvectors associated with L , we propose several graphical necessary conditions for controllability. In addition, by the PBH rank criterion, the controllable subspaces of the system with different classes of nontrivial cells are compared. Finally, a necessary and sufficient condition for controllability under minimum inputs is given.

Strongly Uncontrollable Network Topologies

In this paper, we present a class of network topologies under which the Laplacian consensus dynamics exhibits undesirable controllability properties under a broadcast control signal. Specifically, the networks we characterize are uncontrollable for any subset of the nodes chosen as control inputs and that emit a common control signal. We provide a sufficient condition for a network to contain this strong uncontrollability property and describe network perturbations that leave the uncontrollability property invariant. As a by-product, we identify non-trivial network topologies that require the control of approximately half the nodes in the network as a necessary condition for controllability.

Sufficient conditions for dispersiveness of invariant control affine systems on the Heisenberg group

The notion of dispersiveness in control systems is characterized by the absence of recursive properties. It implies uncontrollability and Poisson instability. The present manuscript exhibits sufficient conditions for an invariant control affine system on the Heisenberg group to be dispersive. For a control affine system with pairwise commutative matrices, the condition for dispersiveness is the drift not depend linearly on the controlled matrices. For a general control affine system, with bounded control range, the condition is the drift not be an affine transformation of the controlled matrices. These results consequently yield necessary conditions for controllability.

Class of controllable systems of differential equations for infinite time

In the article necessary conditions for a controllability of systems of nonlinear differential equations in an infinite time are obtained without assuming the existence of an asymptotic equilibrium for the system of linear approximation. Thus, a new class of controlled systems of differential equations is presented. The problem of controllability for an infinite time (i.e. the transfer of an arbitrary point into an arbitrary small domain of another point) comes down to choosing an operator depending on the selected control, which in turn depends on the point being transferred. Then one is to prove the existence of a fixed point for this operator. It is known that the theorems on controllability require existence of an asymptotic equilibrium for system of the first approximation. It is shown in the paper that in general case the condition of asymptotic equilibrium’s existence is not necessary for controllability of systems in an infinite time. An example on the theorem on controllability for an infinite time is given. The theorem generalizing Vazhevsky inequality is proved by implementation of Cauchy-Bunyakovsky inequality. A remark is made about the theorem’s validity for the case when the matrix and vector from the right-hand side of nonlinear differential equation are complex and x is vector with complex components. Basing on the left-hand side of the inequality in the theorem generalizing Vazhevsky inequality, the necessary conditions for controllability in an infinite time are obtained. These conditions are verified on the same example of a scalar equation that was mentioned before.

Controllability of Boolean Control Networks With Multiple Time Delays

In this paper, the controllability of Boolean control networks (BCNs) with multiple time delays is investigated. The concept of controllability matrices for BCNs with multiple time-varying delays is proposed, and an iterative algorithm is proposed to calculate all controllability matrices. Based on this, a concise criterion for controllability is proposed, which states that a BCN with delays is controllable if and only if all elements of its controllability matrix are nonzero. The proposed method is applied to BCNs with periodic and constant delays, respectively. Sufficient and necessary conditions for controllability are presented. Finally, two examples are given to illustrate the main results.

Controllability of multi-agent systems with directed and weighted signed networks

This paper studies the controllability of multi-agent systems with signed networks, which are represented by directed weighted signed graphs. The adjacency weights of network depict the property of interactions. Positive weight means cooperative interaction while negative weight antagonistic interaction. First, by using switching equivalent transformation, the controllability of three kinds of signed networks is studied: structurally balanced, anti-balanced, and strictly unbalanced. It is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network. Then, a graph-theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks. Furthermore, some necessary and sufficient conditions are given for the controllability of generic linear multi-agent systems. In addition, several examples are presented to illustrate the theoretical results.

Almost equitable partitions and new necessary conditions for network controllability

In this paper, we consider the controllability problem for multi-agent networked control systems. The main results of the paper are new graph-theoretic necessary conditions for controllability involving almost equitable graph vertex partitions. We generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple-leaders and we also consider the broadcasted control scenario. Our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number-theoretic properties of the communities. We show via examples that our results can be used to account for a large portion of uncontrollable inducing leader-selections that could not have otherwise been accounted for using symmetry results.

Control of Large-Scale Boolean Networks via Network Aggregation

A major challenge to solve problems in control of Boolean networks is that the computational cost increases exponentially when the number of nodes in the network increases. We consider the problem of controllability and stabilizability of Boolean control networks, address the increasing cost problem by partitioning the network graph into several subnetworks, and analyze the subnetworks separately. Easily verifiable necessary conditions for controllability and stabilizability are proposed for a general aggregation structure. For acyclic aggregation, we develop a sufficient condition for stabilizability. It dramatically reduces the computational complexity if the number of nodes in each block of the acyclic aggregation is small enough compared with the number of nodes in the entire Boolean network.

Control analysis of an underactuated spacecraft under disturbance

Based on the nonlinear controllability theory, this paper analyzes the attitude controllability for an underactuated spacecraft using two or one thrusters in sequence. In order to provide a preconditional guide on designing the control law for the underactuated attitude control system in the actual case, the underactuated spacecraft with respect to the orbit frame is investigated in the presence of periodical oscillation disturbance. First, attitude dynamic model was established for an underactuated spacecraft actuated by three thrusters, one or two of which has failed separately, and the special orthogonal group (SO(3)) is deployed to describe the attitude motions. Second, Liouville theorem and Poincaré’s recurrence theorem were used to confirm that the drift field is Weakly Positively Poisson Stable (WPPS). Furthermore, the sufficient and necessary condition of controllability was obtained on the basis of Lie Algebra Rank Condition (LARC). Finally, according to the case of two available thrusters, angular velocity stabilization and three-axis attitude stabilization control laws are designed, and proved by Lyapunov stability theory and LaSalle invariant theorem. The analysis and simulation results illustrate the feasibility of the proposed control law.

Indirect Controllability of Quantum Systems; A Study of Two Interacting Quantum Bits

A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set of states that can be obtained for S with this scheme. In this paper, we study the indirect controllability of quantum systems in the finite dimensional case. After discussing the relevant definitions, we give a general necessary condition for controllability in Lie algebraic terms. We present a detailed treatment of the case where both systems, S and A, are two-dimensional (qubits). In particular, we characterize the dynamical Lie algebra associated with S + A, extending previous results, and prove that complete controllability of S + A and an appropriate notion of indirect controllability are equivalent properties for this system. We also prove several further indirect controllability properties for the system of two qubits, and illustrate the role of the Lie algebraic analysis in the study of reachable states.

Controllability of an underactuated spacecraft with one thruster under disturbance

For an underactuated spacecraft using only one thruster, the attitude controllability with respect to the orbit frame is studied in the presence of periodical oscillation disturbance, which provides a preconditional guide on designing control law for underactuated attitude control system. Firstly, attitude dynamic model was established for an underactuated spacecraft, and attitude motion was described using the special orthogonal group (SO (3)). Secondly, Liouville theorem was used to confirm that the flow generated by the drift vector of the underactuated attitude control system is volume-preserving. Furthermore, according to Poincare’s recurrence theorem, we draw conclusions that this drift field is weakly positively poisson stable (WPPS). Thirdly, the sufficient and necessary condition of controllability was obtained on the basis of lie algebra rank condition (LARC). Finally, the controllable conditions were analyzed and simulated in different cases of inertia matrix with the installed position of thruster.

Controllability of Multi-Rate Networked Control Systems with Short Time Delay

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems. Multi-rate networked control systems mean the sampling rates of notes in networked control systems are not the same. The controllability of multi-rate networked control systems are investigated in this paper for the first time. Based on the mathematic model of multi-rate networked control systems with short time delay, some sufficient or necessary conditions for controllability of multi-rate networked control systems are got using stochastic systems approach.

Conclusions from a dynamic population model for tsetse: response to comments

AbstractThe critique by Hargrove et al. (Popul Ecol, 2011) of our recently published paper on a tsetse population model (Barclay and Vreysen in Popul Ecol 53:89–110, 2011) has made some good points but has also misinterpreted the intent of some of our results as we presented them. Hargrove et al. rightly say that there is a mismatch between the size of the unit cells in the model (1 ha) and the iteration rate of the model (every 5 days), yielding too low a dispersal rate to simulate reality. However, they have misconstrued several of our results that we presented as examples to imply that those results were a necessary condition for control of tsetse, especially using traps and targets.

Controllability and observability for time‐varying switched impulsive controlled systems

AbstractThis paper is concerned with the controllability and observability for linear time‐varying switched impulsive systems. First, some new results about the variation of parameters for time‐varying switched impulsive systems are derived. Then less conservative sufficient conditions and necessary conditions for state controllability and observability of such systems are established. And for such system without impulsive control input, sufficient and necessary conditions for controllability and observability are derived. Furthermore, corresponding criteria applied to time‐varying impulsive systems are also discussed and examples are presented to show the effectiveness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.

Hybrid Automaton Model and Control of Hybird Systems

AbstractA hybrid automaton model is proposed in this paper for hybrid systems. The model, with particular emphasis on process control applications, is based on the dynamic features of hybrid systems. It takes into account the discrete dynamics of hybrid systems in particular and can clearly separate the controller from the closed‐loop system. The definition of controllability of hybird systems with respect to the marked regions is also given. An analyzing algorithm and sufficient and necessary condition for controllability based on the hybrid automaton model are discussed. At the same time, the property of the loops in the trajectory of the closed‐loop plant is studied. Finally, the synthesis scheme for a hybrid controller is given. In this scheme, the controller consists of two parts, the discrete supervisor and the continuous regulator. The closed‐loop plant with the controller is state‐controllable.

Chaotic dynamics in coupled microwave oscillators

Describes an investigation into possible chaotic behavior in a coupled-oscillator system and the possible control of this behavior for communications. The established mathematical models for these oscillator arrays are demonstrated to exhibit chaos when the coupling strength between oscillators is below the range for phase locking. The complexity and predictability of the array dynamics are analyzed by means of standard dynamical measures such as the Lyapunov exponents, the Kolmogorov-Sinai entropy, and the attractor dimension, the authors show that chaos in these oscillator arrays is low dimensional and well characterized; both necessary conditions for control and possible exploitation of chaos. Finally, the method of occasional proportional feedback is used to stabilize the output from the array while the array is still in the chaotic regime. Possible applications of these chaotic transmitters are also discussed.