Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

Target Controllability of Multi-Layer Networks With High-Dimensional Nodes

This paper studies the target controllability of multilayer complex networked systems,in which the nodes are highdimensional linear time invariant(LTI)dynamical systems,and the network topology is directed and weighted.The influence of inter-layer couplings on the target controllability of multi-layer networks is discussed.It is found that even if there exists a layer which is not target controllable,the entire multi-layer network can still be target controllable due to the inter-layer couplings.For the multi-layer networks with general structure,a necessary and sufficient condition for target controllability is given by establishing the relationship between uncontrollable subspace and output matrix.By the derived condition,it can be found that the system may be target controllable even if it is not state controllable.On this basis,two corollaries are derived,which clarify the relationship between target controllability,state controllability and output controllability.For the multi-layer networks where the inter-layer couplings are directed chains and directed stars,sufficient conditions for target controllability of networked systems are given,respectively.These conditions are easier to verify than the classic criterion.

Input Structure Design for Structural Controllability of Complex Networks

This paper addresses the problem of the input design of large-scale complex networks.Two types of network components,redundant inaccessible strongly connected component(RISCC)and intermittent inaccessible strongly connected component(IISCC)are defined,and a subnetwork called a driver network is developed.Based on these,an efficient method is proposed to find the minimum number of controlled nodes to achieve structural complete controllability of a network,in the case that each input can act on multiple state nodes.The range of the number of input nodes to achieve minimal control,and the configuration method(the connection between the input nodes and the controlled nodes)are presented.All possible input solutions can be obtained by this method.Moreover,we give an example and some experiments on real-world networks to illustrate the effectiveness of the method.

Polarization characteristics and controllability mechanism of passive scattering elements

Polarization feature is one of the important features of radar targets,which has been used in many fields.In this paper,the grid models of some typical foreign moving targets are constructed on the simulation platform,such as glider,cruiser,fixed wing aircraft,and rotorcraft.The electromagnetic scattering characteristics of the moving platforms under the incidence of circular polarization waves are calculated.The typical polarization characteristics which the orthogonal and in-phase components have in the echoes are analyzed and proved.Based on the polarization scattering matrix(PSM)theory,from the point of view of the physical reproduction,the technical status quo that the existing technical approaches are difficult to realize the passive simulation of polarization characteristic of the target is summarized.To solve this problem,combined with the vector synthesis law,the realization mechanism of controllable polarization characteristic of target echoes is proposed,the analytical expressions of polarization control matrix and polarization ratio are deduced,and the controllability of polarization ratio feature in the case of circular polarization is verified by simulation calculation.

ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES

In this paper,we study the controllability of compressible Navier-Stokes equations with density dependent viscosities.For when the shear viscosityμis a positive constant and the bulk viscosityλis a function of the density,it is proven that the system is exactly locally controllable to a constant target trajectory by using boundary control functions.

Optimization of robustness of network controllability against malicious attacks

As the controllability of complex networks has attracted much attention recently, how to design and optimize the robustness of network controllability has become a common and urgent problem in the engineering field. In this work, we propose a method that modifies any given network with strict structural perturbation to effectively enhance its robustness against malicious attacks, called dynamic optimization of controllability. Unlike other structural perturbations, the strict perturbation only swaps the links and keeps the in- and out-degree unchanged. A series of extensive experiments show that the robustness of controllability and connectivity can be improved dramatically. Furthermore, the effectiveness of our method is explained from the views of underlying structure. The analysis results indicate that the optimization algorithm makes networks more homogenous and assortative.

Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.

Nonlocal controllability for semilinear problems in Banach spaces

If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.

Effect of degree correlation on edge controllability of real networks

We use the controllability limit theory to study impact of correlation between in- and out-degrees (degree correlation) on edge controllability of real networks. Simulation results and analytic calculations show that the degree correlation plays an important role in the edge controllability of real networks, especially dense real networks. The upper and lower controllability limits hold for all kinds of real networks. Any edge controllability in between the limits is achievable by properly adjusting the degree correlation. In addition, we find that the edge dynamics in some real networks with positive degree correlation may be difficult to control, and explain the rationality of this anomaly based on the controllability limit theory.

Approximate controllability of infinite dimensional linear systems in nonreflexive state spaces

This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p（[0, T], U）, 1≤p〈∞ is obtained,where L^p（ [0, T], U） is the control function space.

EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.

Semi-tensor product approach to controllability and stabilizability of finite automata

Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.

EXISTENCE AND CONTROLLABILITY FOR NONLINEAR FRACTIONAL CONTROL SYSTEMS WITH DAMPING IN HILBERT SPACES

In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces.Our first step is to give the representation of mild solution for this control system by utilizing the general method of Laplace transform and the theory of(α, γ)-regularized families of operators. Next, we study the solvability and controllability of nonlinear fractional control systems with damping under some suitable sufficient conditions. Finally, two examples are given to illustrate the theory.

Water Supply Networks as Cyber-physical Systems and Controllability Analysis

Cyber-physical systems (CPS) is a system of systems which consists of many subsystems that can stand alone in an individual manner and can be taken as a typical complex network. CPS can be applied in the critical infrastructures such as water supply networks, energy supply systems, and so on. In this paper, we analyze the structure of modern city water supply networks from the view of CPS theory. we use complex network theory to build an undirected and unweighted complex network model for the water supply networks to investigate the structural properties, and present the structure of the water supply networks and detect communities by a spectral analysis of the Laplacian matrix. Then, we analyze the structure and controllability of water supply networks by the structural controllability method. The results show the feasibility and effectiveness of the proposed complex network model. © 2014 Chinese Association of Automation.

Controllability of Spacecraft Attitude and Its Application in Reconfigurability Analysis

We review the controllability research on spacecraft attitude based on nonlinear geometry control theory.The existing studies on attitude controllability are mostly concerning the global controllability and small time local controllability(STLC).A presentation of study methods and connotation in both aspects is briefly carried out.As a necessary condition of reconfigurability,the controllability of the faulty attitude control system is studied.Moreover,two reconfigurability conditions based on controllability results that consider the actuator faults for a pyramid configuration spacecraft are provided.

Advances in Compact Manufacturing for Shape and Performance Controllability of Large-scale Components-A Review

Research on compact manufacturing technology for shape and performance controllability of metallic components can reanze the simplification and high-reliability of manufacturing process on the premise of satisfying the requirement of macro/micro-structure. It is not only the key paths in improving performance, saving material and energy, and green manufacturing of components used in major equipments, but also the challenging subjects in frontiers of advanced plastic forming. To provide a novel horizon for the manufacturing in the critical components is significant. Focused on the high-performance large-scale components such as bearing rings, flanges, railway wheels, thick-walled pipes, etc, the conventional processes and their developing situations are summarized. The existing problems including multi-pass heating, wasting material and energy, high cost and high-emission are discussed, and the present study unable to meet the manufacturing in high-quality components is also pointed out. Thus, the new techniques related to casting-rolling compound precise forming of rings, compact manufacturing for duplex-metal composite rings, compact manufacturing for railway wheels, and casting-extruding continuous forming of thick-walled pipes are introduced in detail, respectively. The corresponding research contents, such as casting ring blank, hot ring rolling, near solid-state pressure forming, hot extruding, are elaborated. Some findings in through-thickness microstructure evolution and mechanical properties are also presented. The components produced by the new techniques are mainly characterized by fine and homogeneous grains. Moreover, the possible directions for fin＇ther development of those techniques are suggested. Finally, the key scientific problems are first proposed. All of these results and conclusions have reference value and guiding significance for the integrated control of shape and performance in advanced compact manufacturing.

Heat exchanger network synthesis integrated with flexibility and controllability

Over the last three decades,flexibility and controllability considerations for heat exchanger networks(HENs)have received great attention,respectively.However,they should be simultaneously incorporated in HEN synthesis to allow the economic performance to be achievable in a practical operating environment.This paper proposes a method for simultaneous synthesis of flexible and controllable HEN by considering their coupling.The key idea is to add the bypasses with optimized initial fractions and positions to explore such coupling,and consequently enabling HENs to be operated successfully over a range of disturbance variations.These are implemented by identifying and quantifying disturbance propagations,and then examining the sensitivity of bypasses to the entire HEN.In this way,the superstructurebased mixed integer non-linear programming(MINLP)with objective function of minimizing the total annual cost is formulated.A case study is used to demonstrate the application of the proposed method.Quantitative measures and dynamic simulation show the ability to provide the satisfactory flexibility and controllability of the obtained HEN.

Deducing Complete Selection Rule Set for Driver Nodes to Guarantee Network’s Structural Controllability

Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make the network structurally controllable. Different from the works in complex network field where structural controllability is often used to explore the emergence properties of complex networks at a macro level,in this paper, we investigate it for control design purpose at the application level and focus on describing and obtaining the solution space for all selections of driver nodes to guarantee structural controllability. In accord with practical applications,we define the complete selection rule set as the solution space which is composed of a series of selection rules expressed by intuitive algebraic forms. It explicitly indicates which nodes must be controlled and how many nodes need to be controlled in a node set and thus is particularly helpful for freely selecting driver nodes. Based on two algebraic criteria of structural controllability, we separately develop an input-connectivity algorithm and a relevancy algorithm to deduce selection rules for driver nodes. In order to reduce the computational complexity,we propose a pretreatment algorithm to reduce the scale of network's structural matrix efficiently, and a rearrangement algorithm to partition the matrix into several smaller ones. A general procedure is proposed to get the complete selection rule set for driver nodes which guarantee network's structural controllability. Simulation tests with efficiency analysis of the proposed algorithms are given and the result of applying the proposed procedure to some real networks is also shown, and these all indicate the validity of the proposed procedure.

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.