共查询到20条相似文献，搜索用时 46 毫秒
1.
《Journal of The Franklin Institute》2023,360(3):1706-1732
One of the drawbacks of the controllability theory for nonlinear systems is that most existing controllability criteria are not algebraically verifiable, which makes them difficult to apply especially if the system dimension is high. Thus, it is a significant task to seek algebraically verifiable controllability criteria for nonlinear systems. In this paper, we study controllability of discrete-time inhomogeneous bilinear systems. In the classical results on controllability of such systems, a necessary condition is that the linear part has to be controllable. However, we will show that this condition is in fact not necessary for controllability. Specifically, we first define the spectrum for discrete-time inhomogeneous bilinear systems and reveal that the spectrum is a fundamental property which is very useful in investigating the controllability problems. We then present controllability criteria for the systems with real spectrum, which are algebraically verifiable. Furthermore, we also provide algorithms for the controllable systems to compute the exact or approximated control inputs to achieve the transition between any given pair of states. The presented controllability criteria and algorithms work for the systems in any finite dimension and are easy to implement. More importantly, through our controllability criteria, we reveal that controllability of the linear part is not necessary for discrete-time inhomogeneous bilinear systems to be controllable. Examples are given to illustrate the presented algebraic controllability criteria. 相似文献
2.
J.E. Rubio 《Journal of The Franklin Institute》1980,309(5):301-308
Control problems in Hilbert spaces are treated in a measure-theoretical framework; instead of dealing with a set of admissible trajectory-control pairs, a set of measures defined by the boundary conditions and the differential equations of the problem are considered. The concept of weak controllability is introduced; a system has this property if every pair of initial and final points, (ta,xa) and (tb,xb) can be weakly joined; this is possible if a set of linear equalities involving measures has a solution. In turn, this is shown to be equivalent to the possibility of extending a linear functional in a positive manner. Necessary and sufficient conditions for controllability are derived, and applied to the study of a finite-dimensional system with the control appearing linearly. 相似文献
3.
In this paper, we consider the H∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l2-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l2-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results. 相似文献
4.
This paper investigates the optimal control problem for a class of Boolean control networks, called singular Boolean control networks (SBCNs), which consist of two parts: difference equations and algebraic equations. By constructing the truth matrix of Ledley solution, necessary and sufficient conditions are provided for the solvability of SBNs (or SBCNs). Then an effective algorithm is presented to design an optimal control sequence by using the controllability matrix of normalized Boolean control networks. 相似文献
5.
As a basic concept in modern control theory, controllability reveals the fundamental structural characteristics of a dynamic system, and it also plays an important part in the analysis and control of a dynamic system. With the increasing complexity of multi-agent systems, the multi-agent networks can be divided into some subnetworks in terms of time scales. This paper concentrates on the group controllability of two-time-scale multi-agent networks, establishes the necessary and sufficient criterion of group controllability based on singular perturbation methods, and deduces easy-to-use group controllability criteria by using matrix theory and graph theory. Lastly, a simulation example is presented to illustrate the effectiveness of the proposed methods. 相似文献
6.
Jiangrong Li Zhiguang Feng Yuxin Zhao Juan Shi 《Journal of The Franklin Institute》2018,355(13):5721-5735
The problem of reachable set estimation is studied for discrete-time bilinear system in this paper. Time-varying delays and bounded input disturbances are both considered in bilinear system. The aim is to find reachable set that converges from all the states of system with initial conditions. By constructing Lyapunov–Krasovskii functional, sufficient delay-dependent less conservative stable conditions of reachable set estimation are obtained for bilinear delay system via the reciprocally convex combination and delay partition approaches. The derived theorem can guarantee that all the states of system with initial conditions from some domain are bounded in an ellipsoid and all the states from other domain are converged exponentially within a ball. One simulation example is presented to illustrate the correctness of the derived result in this paper. 相似文献
7.
Yongyuan Yu Jun-e Feng Biao Wang Peihe Wang 《Journal of The Franklin Institute》2018,355(12):5324-5335
Derived from a simplified intelligent traffic control system, sampled-data controllability and stabilizability of Boolean control networks are considered. Compared with the existing case of uniform (periodic) sampling in Boolean control networks, the nonuniform one is more general. Using linear span with integral coefficients, the distribution of sampling points can be obtained. Then by constructing novel systems, some necessary and sufficient conditions are proposed to determine sampled-data controllability and stabilizability. Finally, two illustrative examples, which are on apoptosis networks and traffic control systems, respectively, are worked out to show the effectiveness of the obtained results. 相似文献
8.
In this paper, sufficient conditions for the approximate controllability of mixed stochastic Volterra–Fredholm type integrodifferential systems are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the theory. 相似文献
9.
Artur Babiarz Adam Czornik Alexander Konyukh Michał Niezabitowski 《Journal of The Franklin Institute》2017,354(13):5131-5144
In this paper, we give the necessary and sufficient conditions for a function f to be a lower Bohl function of a diagonal discrete linear time-varying systems. 相似文献
10.
P. Muthukumar 《Journal of The Franklin Institute》2009,346(1):65-80
In this paper, the approximate controllability of nonlinear stochastic evolution time-varying delay systems with preassigned responses is studied. The necessary conditions for controllability results of nonlinear systems are not associated with linear systems. No compactness assumptions are imposed in the main results. 相似文献
11.
In this paper we consider a problem of controllability of discrete time linear system with randomly jumping parameters which can be described by finite state Markov chain. Necessary and sufficient conditions for existence of control which governs the system from any initial conditions to zero, from zero initial condition to any final value and from any initial condition to any final value in given time and with probability one are given. The relations between such kinds of controllability and stochastic stabilizability are discussed. 相似文献
12.
Richard L. Derr 《Information processing & management》1983,19(5):273-278
The necessary and sufficient conditions for saying that X has a need for certain information are identified. It is concluded that an information need is a condition in which certain information contributes to the achievement of a genuine or legitimate information purpose. Information need is a relationship which obtains between information and information purposes: it is not a psychological state. Implications for research and practice are drawn from the conceptual analysis. 相似文献
13.
In this paper sufficient conditions for the complete controllability of nonlinear stochastic integrodifferential system are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the technique. 相似文献
14.
In this paper, the stability, L1-gain analysis and asynchronous L1-gain control problems of uncertain discrete-time switched positive linear systems (DSPLSs) with dwell time are investigated. First, several convex and non-convex conditions on dwell time stability of DSPLSs with interval and polytopic uncertainties are presented, and the relation between these conditions is revealed. Then, via a switched dwell-time-dependent co-positive Lyapunov functions (SDTLFs) approach, convex sufficient conditions on L1-gain analysis and asynchronous L1-gain control of DSPLSs with interval uncertainties are derived. Meanwhile, via the switched parameter-dwell-time-dependent co-positive Lyapunov functions (SPDTLFs) approach, the L1-gain analysis and asynchronous L1-gain controller design problems of DSPLSs with polytopic uncertainties are also solved. The stability and L1-gain analysis results are given in terms of linear programming (LP). The controller design results are presented in terms of bilinear programming (BP), which can be solved with the help of iterative algorithm. At last, both numerical and practical examples are provided to show the effectiveness of the results. 相似文献
15.
《Journal of The Franklin Institute》2023,360(9):6060-6080
Constraints are very common for practical control systems. For logical systems, the existing technique of pre-feedback is an effective way of treating state-dependent constraints in control when the state is measurable. However, it is inapplicable for the case when measurement information is not available. In this situation, in order for the control input to not violate the state-dependent constraint, the control at each step must be selected from the common admissible controls of all possible states. Motivated by this observation, in this study, we propose a novel technique, termed the subset transition method, for finite-time controllability and stabilization of probabilistic logical dynamic control system (PLDCS) with a state-dependent control constraint. The main idea of this method is to construct an unconstrained deterministic logical control system over the power set of the state space, called the subset transition system (SubSTS), characterizing the transitional dynamics between subsets under common admissible controls. We prove that a control sequence is admissible with respect to all states in an initial subset if and only if it does not steer the SubSTS from the initial subset to the empty set. Based on this, necessary and sufficient conditions for set controllability and set stabilizability are obtained. Examples are presented to demonstrate the application of the obtained results. 相似文献
16.
Yongge Tian 《Journal of The Franklin Institute》2009,346(6):557-10057
Suppose that AXB=C is a consistent matrix equation and partition its solution X into a 2×2 block form. In this article we give some formulas for the maximal and minimal ranks of the submatrices in a solution X to AXB=C. From these formulas, we derive necessary and sufficient conditions for the submatrices to be zero and nonsingular, respectively. As applications, we give a group of formulas for the maximal and minimal ranks of submatrices in generalized inverses of matrices and their properties. 相似文献
17.
Hossein Parastvand Airlie Chapman Octavian Bass Stefan Lachowicz 《Journal of The Franklin Institute》2021,358(7):3919-3942
This study investigates on a strong correlation between complex network (CN) controllability (characterized by the number of required driver nodes) and graph symmetry (described by automorphism groups) in undirected and unweighted networks. Based on the properties of permutation products of elementary automorphisms, novel necessary conditions for CN controllability are presented which are computationally more effective than previous method. In addition, a novel index of symmetry is proposed upon which a more meaningful understanding of symmetry impact on CN controllability can be comprehended. Based on this new index, a modification strategy is suggested aiming to satisfy CN controllability with a lower number of driver nodes. The study shows that the proposed modification approach can result in a minimal set of driver nodes with a reasonable computational complexity. Further, the critical components of complex networks, in terms of their impact on the number of required driver nodes, are identified. The results of the proposed methodologies have been verified for several synthetic and real test systems including small, medium, and large power networks. 相似文献
18.
The robust controllability problem for the continuous linear time-delay systems with structured parametric uncertainties is studied in this paper. A new sufficient algebraic criterion for the robust controllability of uncertain linear time-delay systems is established. The proposed sufficient condition can provide the explicit relationship of the bounds on system uncertainties for guaranteeing the controllability property. Three numerical examples are given to illustrate the application of the proposed sufficient algebraic criterion and to compare the results with those obtained from the approaches in the literature. 相似文献
19.
This paper investigates the event-triggered control design for state/output synchronization of switched k-valued logical control networks (SKVLCNs). Firstly, based on the algebraic form of SKVLCNs, some necessary and sufficient conditions are presented for the event-triggered state/output synchronization of SKVLCNs. Secondly, using the partitioning technique of matrix, a constructive procedure is proposed to design state feedback event-triggered controllers for the synchronization of SKVLCNs. Finally, an illustrative example is worked out to show the effectiveness of the obtained new results. 相似文献