Integrated structure design of a process and its control system

A graph-theoretic method for integration of process and control system (IPCS) syntheses with different controllability notions has been proposed in the present paper. The foundation of this integration is a well-established, graph-theoretic approach to process synthesis in conjunction with the analysis of structural controllability based on digraph-type process models. Unambiguous structural representation of the resultant integrated process and control systems, IPXS structures in brief, has been introduced for unambiguous representation of a process structure, it is rendered possible as an extension of the directed bipartite graph, the P-graph. Different set of axioms are proposed for describing the case of disturbance-rejective regulable and the combinatorially feasible and controllable structures in the special cases considered: the case of structural controllability and the case of fault-tolerant controllability. These axioms make the synthesis computationally more effective by considering very simple engineering knowledge. The maximal controllable structure of an IPXS synthesis problem has been defined as the union of combinatorially feasible and controllable IPXS structures. Thus, the mathematical programming model, e.g. MINLP model, of an IPXS synthesis problem can be and should be derived from the maximal controllable structure. Different versions of a fundamental polynomial time, combinatorial algorithm are presented for identifying the maximal controllable structure. The resultant IPXS structures are compared with the structures synthesized without considering their control systems.     

Structured system models Part 3. An application to feedback compensator design

The controllability and observability indices are studied and applied to the feedback compensator design. The compensator design method uses polynomial matrices as system models. As the main result, a new algorithm is introduced for the construction of a first candidate for the feedback compensator. A new algorithm is also given for constructing a state-space model from polynomial matrix models. Such a realization is needed if there is originally only a polynomial matrix model for the system.     

Further results on pole-shifting using output feedback

Some previous results concerning eigenvalue assignment using constant output feedback arc extended. Necessary and sufficient conditions for an output feedback solution to exist lire shown to be equivalent to conditions imposed by the controllability and observability indices of the given system. An example is provided to illustrate the procedures described.     

Controllability indices of sampled-data systems

The controllability of the sampled-data system derived from a controllable continuous-time system is considered. In particular, some relations between the controllability indices of the original continuous-time system and those of the sampled-data system are studied. Examples are given to illustrate the results, and similar results for observability are also indicated.     

Controllability and observability of linear time-invariant compartmental models

The problems of complete controllability and complete observability of linear time-invariant compartmental models with general input-output structures are considered. The analysis of these problems is based largely on graph-theoretic methods and the properties of polynomial matrices. Specifically, statements on complete controllability and complete observability are proven by using graphical constructions which do not change the basic properties of controllability and observability. The major results of this paper are: 1) A unique decomposition of the digraph of a compartmental model into sources, sinks, and transits. 2) A theorem which states that a compartmental model with closed sinks is completely observable if and only if the matrix [C^{T}, A^{T}] is full rank, and a corollary which provides a sufficient condition for complete observability of all other linear time-invariant compartmental models. 3) A theorem which states that a single sink compartmental model is completely controllable if and only if a compartment from each source is controlled. 4) A controllability algorithm which provides sets of excitations which are sufficient for complete controllability of any linear time-invariant compartmental model.     

Absolute controllability of predicates in discrete event systems

The absolute controllability of predicates in discrete event systems is studied in this paper. A predicate is absolutely controllable if it is control-invariant and the states specified by it are mutually reachable via legal states. It is shown that there is a global state feedback such that the resultant closed-loop system is strongly connected if and only if the predicate is absolutely controllable. The weakest absolutely controllable predicate stronger than the given predicate is shown to exist with respect to the given initial state. Based on the notion of the dual automaton a graph-theoretic algorithm is given to compute the set of weakest absolutely controllable predicates stronger than the given predicate. Application of the concept of absolutely controllable predicate to a class of optimal control problem is discussed. Examples are given to illustrate the results     

Graph-theoretic characterisations of structural controllability for multi-agent system with switching topology

This article considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems is a generalisation of the traditional controllability concept for dynamical systems, and purely based on the communication topologies among agents. The main contributions of this article are graph-theoretic characterisations of the structural controllability for multi-agent systems. It turns out that the multi-agent system with switching topology is structurally controllable if and only if the union graph 𝒢 of the underlying communication topologies is connected (single leader) or leader–follower connected (multi-leader). Finally, this article concludes with several illustrative examples and discussions of the results and future work.     

Controllability and the theory of economic policy: a structural approach

Tinbergen's policy rule states that we must have at least as many policy instruments as the number of target variables if we wish to realize an arbitrarily fixed set of policy targets. We explore the structural characterization of the controllability of economic systems described by a set of static or dynamic equations. First, an economic system is represented as a directed graph, where the nodes stand for economic variables, while the arcs indicate the relations among these variables. Then, the main result is as follows: a static economic system is structurally controllable if and only if there exists a set of disjoint paths on the graph representation or the system which connect the set of instruments to each target. Similar graph-theoretic characterization of structural controllability is obtained for dynamic systems. Conditions for structural output controllability and structural perfect controllability are also discussed.     

Parameterized Two-Player Nash Equilibrium

We study the problem of computing Nash equilibria in a two-player normal form (bimatrix) game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement those results, by identifying three cases in which the problem becomes fixed-parameter tractable. Our results are based on a graph-theoretic representation of a bimatrix game, and on applying graph-theoretic tools on this representation.     

On the structural controllability of compartmental systems

In this paper compartmental systems are modeled by a class of linearly parameterized matrix pairs and the controllability characteristics are expressed in terms of a compartmental graph. The result gives intuitive and physical information about the controllability and it extends the well-known result on the single-sink case to the multisink case. Furthermore, this result is applied to more special models, called undirected compartmental models, by which physical systems such as a class of liquid systems and of network systems, etc., can be concisely modeled.     

时变线性切换系统的指数镇定

研究满足驻留时间条件的时变线性切换系统的指数镇定问题.在一致完全可控条件下,引入带权可控性格拉姆矩阵设计出参数化的反馈控制器,利用比较原理给出状态转移矩阵的超调估计.针对驻留时间已知和未知两种情况,通过选择设计参数消除切换产生的超调影响,建立了两个指数镇定结论.最后以仿真实例验证本文结论.     

Minimum-state realizations of linear time-varying systems

An algorithm for removing uncontrollable (unobservable) state variables from time-varying systems is presented. The algorithm makes use of the time-variable controllability (observability) matrix which is augmented with the identity matrix and transformed into Hermite normal form. In this new set of coordinates, the uncontrollable (unobservable) state variables are easily identified and removed. An example is given.     

离散线性系统鲁棒非奇异自适应控制的改进

为解决间接自适应控制系统的奇异性或不可控性问题,提出一种新的修正模型辨识参数方法,参数修正策略使系统辨识模型在适应过程中保持能控性。该修正算法同文献「１」给出的算法相比计算量大为减少,进上步提高了控制算法的实时性。     

广义动力系统的可控性与强可观性

本文研究广义状态空间系统的强可控与强可观问题。给出强可控强可观及强既约的充要判据。     

On controllability and trajectory tracking of a kinematic vehicle model

This paper presents some further results concerning the issues of controllability and trajectory tracking regarding a front-wheel drive vehicle kinematic model. A simple procedure for computing an open-loop control strategy that transfers the system between given initial and final states, is presented. In particular, the input function is computed by means of a set of linear algebraic equations. The resulting motion planning procedure allows us to present a control scheme for solving the trajectory (a time-parameterized reference signal) tracking problem. Various applications of the approach in forward and backward motions are considered, and simulation results are presented.     

Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstract second-order infinite-dimensional dynamical systems is considered. It is proved using the frequency-domain method, that approximate controllability of second-order system can be verified by the approximate controllability conditions for the corresponding simplified first-order system. General results are then applied for approximate controllability investigation of a vibratory dynamical system modeling flexible mechanical structure. Some special cases are also considered. Moreover, remarks and comments on the relationships between different concepts of controllability are given. The paper extends earlier results on approximate controllability of second-order abstract dynamical systems.     

Algebraic aspects of controllability for AR-systems

This paper examines some aspects of controllability for behaviour systems in AR-representation. The approach is based on the theory of dipolynomial modules and dipolynomial matrices. Explicit criteria for controllability in terms of the representing matrices are derived and an effective test algorithm is given. Furthermore, controllability indices are introduced for AR-systems. The new theory is compared with existing index concepts in the literature on linear systems.