Robust and fault-tolerant supervisory control of discrete event systems with partial observation and model uncertainty

This paper proposes the notions of faults and failures in discrete event systems (DESs) with partial observation. They are associated with controllability and an observability property. The proposed notions are used to address the notion of tolerable fault event sequences which represents fault-tolerant behaviour of systems as a desired specification. A robust and fault-tolerant supervisor is a controller which is robust to model uncertainty and guarantees fault-tolerant behaviour of a system. In this paper we present necessary and sufficient conditions for the existence of a robust and fault-tolerant supervisor. The developed conditions capture the concepts of controllability and observability which are cores in the control of DESs with partial observation     

On the design of linear time-invariant systems by-periodic output feedback Part II. Output feedback controllability†

In this paper it is shown that complete controllability and complete observability are necessary and sufficient conditions for the complete controllability of linear time-invariant systems by discrete output feedback. In the case where the desired final state is the origin, the resultant, output feedback gain is periodic and the transfer is accomplished in at most vd periods, where vd is the discrete-time index of observability. In the more general case where the desired final state is non-zero, the transfer is accomplished using at most vd output measurements.     

New necessary and sufficient conditions for local controllability and local observability of 2-D separable denominator systems

New necessary and sufficient conditions for local controllability and observability of 2-D separable denominator systems (SDS's) are presented on the basis of the reduced-dimensional decomposition of 2-D SDS's. It is proved that local controllability of a 2-D SDS is equivalent to controllability of two 1-D systems which are a special decomposition pair of the 2-D SDS. Furthermore, local observability of a 2-D SDS is equivalent to a full rank condition of the coefficient matrices of the 2-D SDS in addition to observability of two 1-D systems which are another special decomposition pair of the 2-D SDS. Thus, these new conditions which use only 1-D controllability matrices, 1-D observability matrices, and coefficient matrices of the 2-D SDS are much simpler than any previous conditions which use complex 2-D controllability and observability matrices.     

Controllability and observability for time‐varying switched impulsive controlled systems

This 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.     

Controllability and Observability of Parallel Magnetic Suspension Systems

The controllability and observability of parallel magnetic suspension systems are investigated analytically. A parallel magnetic suspension system has multiple floators and electromagnets driven by a single amplifier. In this paper, the multiplicity is set to an arbitrary counting number n. Parallel systems are classified into four types based on the output of the power amplifier and the connection of the coils. This paper treats three of them: current‐controlled with series‐connected coils; voltage‐controlled with series‐connected coils; and voltage‐controlled with parallel‐connected coils. The conditions of controllability and observability of each system are clarified. The feasibility of parallel magnetic suspension is demonstrated by simulations and experiments.     

网络控制系统的能控性和能观性

给出了网络控制系统的定义，并基于线性时不变系统的被控对象，建立了传感器为时钟驱动，控制器和作动器为事件驱动时长时滞网络控制系统的数学模型，对网络控制系统的均值能控、均方能控、均值能观及均方能观作了定义，得到了网络控制系统能控的充分或必要条件及能观的充要条件．     

On controllability and observability of time delay systems

This paper deals with controllability and observability properties of time delay systems in the state spaceR^{n} times L^{p}. In particular, we prove the equivalence of spectral controllability and approximate null-controllability. Moreover, it is shown that the necessary, condition for approximateF-controllability-obtained recently by Manitius-is also sufficient, and a verifiable and matrix type criterion forF-controllability is derived for systems with commensurate delays. Finally, we introduce the dual observability notion of approximate controllability and prove that the control system Σ is exactly null-controllable if and only if the transposed delay system Σ^Tis continuously finally observable.     

The robustness of controllability and observability for discrete linear time-varying systems with norm-bounded uncertainty

Controllability and observability of discrete linear time-varying systems with norm-bounded parameter uncertainties are analyzed in this note. Like in the continuous case, we propose the sufficient conditions, which ensure controllability and observability of the uncertain system. The proposed conditions allow the evaluation of controllability and observability of the uncertain system without knowledge of specific values of uncertainties.     

Concerning controllability and observability of linear sequential machines

The concept of output–controllability for linear sequential machines over a GF(p) is studied and conditions for k output-controllability are given. Then the concept of k observability is introduced which is the dual of the k state–controllability concept. discussed by Cohn. The duality of controllability and observability is revealed and several examples are studied which illustrate the theoretical results.     

The robustness of controllability and observability of linear time-varying systems

Fixed point methods from nonlinear analysis are used to establish conditions under which the uniform complete controllability, of linear time-varying systems is preserved under nonlinear perturbations in the state dynamics and the zero-input uniform complete observability of linear time-varying systems is preserved under nonlinear perturbation in the state dynamics and output read-out map. Robustness of partial controllability., observability, and a specific kind of nonzero input observability are also proven.     

Robustness of controllability and observability of continuouslinear time-varying systems with parameter perturbations

The controllability and the observability of continuous linear time-varying systems with norm-bounded parameter perturbations are analyzed. The sufficient conditions which ensure the controllability of the perturbed system are presented by using the derived state transition matrix relationship between the nominal system and the perturbed system. The proposed sufficient conditions allow the evaluation of controllability under the norm-bounded parameter perturbations. The robustness of the observability is also studied for continuous linear time varying systems with norm-bounded parameter perturbations, and the corresponding sufficient conditions are provided     

Band criteria and recursive tests of complete controllability and observability of linear algebraic-differentiable systems

New criteria are introduced of complex controllability and observability of controllable linear stationary algebraic-differentiable systems with many inputs and outputs, which reduce to the calculation of the rank of special band matrices. Recursive tests are set up, which permit reducing computational expenses in the verification for the fulfillment of the conditions of complete controllability and observability of algebraic-differentiable systems of a large dimension.     

Controllability and observability of linear time varying singularsystems

Controllability and observability of analytically solvable linear time varying singular systems are considered. Our analysis includes the possible impulsive zero-input response. Based on the definitions of controllability and observability naturally extended from the ones adopted in the time-invariant setting, sufficient and necessary conditions for these two properties are derived. Furthermore, according to the specific definitions of these concepts used here, the authors show that the dual relationship between controllability and observability does not hold     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

Necessary and sufficient conditions for the controllability andobservability of a class of linear, time-invariant systems with intervalplants

We establish necessary and sufficient conditions for the controllability of single-input/multi-output linear time-invariant systems with interval plants and for the observability of multi-input/single-output linear time-invariant systems with interval plants. In arriving at our results, we determine allowable plant uncertainty bounds for controllability and observability. Two specific examples are considered to demonstrate the applicability of our results     

Controllability and observability of switched multi-agent systems

This paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.     

On the structure of energy functions of singularly perturbed bilinear systems

Two balanced model reduction schemes for bilinear systems have been proposed in the literature. The first schema is based on the algebraic controllability and observability matrices Gramians. The second is based on the notion of the controllability and observability energy functions already introduced for nonlinear systems. The aim of this paper is to present some interesting structures of the energy functions and algebraic Gramians of bilinear singularly perturbed systems. These results permit to avoid the ill conditioning and the high dimensionality in the computation of the energy functions of bilinear singularly perturbed systems. In the second part of the paper, closed‐loop balancing is considered and similar development leads to the so‐called past and future energy functions. Copyright © 2005 John Wiley & Sons, Ltd.     

The Controllability,Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.      

Controllability and observability of an n‐link robot with multiple active links

This paper considers an n‐link planar robot moving in the vertical plane with multiple active links. The controllability and observability of the robot around the upright equilibrium point, which are important for the existence of an output‐feedback controller, are investigated in detail. Specific properties of the mechanical parameters are extracted to demonstrate that when there are adjacent active links, the robot is strongly structurally controllable and observable around the upright equilibrium point. When the active links are not adjacent to each other, a necessary and sufficient condition is established to ensure the linear controllability and observability. Finally, the theoretical results are illustrated via several practical examples. Copyright © 2017 John Wiley & Sons, Ltd.