On the controllability of switching linear systems

This note presents a necessary and sufficient condition for small time controllability of a linear switching system (that is, a collection of linear time-invariant control systems, where a trajectory is any concatenation of trajectories of the individual systems). This result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone.     

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.     

Constructing checking sequences for distributed testing

The objective of testing is to determine whether an implementation under test conforms to its specification. In distributed test architectures involving multiple remote testers, this objective can be complicated by the fact that testers may encounter coordination problems relating to controllability (synchronization) and observability during the application of tests. Based on a finite state machine (FSM) specification of the externally observable behaviour of a distributed system and a distinguishing sequence, this paper proposes a method for constructing a checking sequence where there is no potential controllability or observability problems, and where the use of external coordination message exchanges among testers is minimized. The proposed method does not assume a reliable reset feature in the implementations of the given FSM to be tested by the resulting checking sequence. phone: 613-562-5800(Extn)6684 Received May 2004 Revised March 2005 Accepted April 2005 by J. Derrick, M. Harman and R. M. Herons     

Communication and control co-design for networked control systems

This paper discusses the stabilization of a networked control system (NCS) in which sensors and actuators of a plant exchange information with a remote controller via a shared communication medium. Access to that medium is governed by a pair of periodic communication sequences. Under the model utilized here, the controller and plant handle communication disruptions by “ignoring” (in a sense to be made precise) sensors and actuators that are not actively communicating. This choice has the effect of significantly reducing the complexity of selecting control/communication policies. It is shown that, for discrete-time NCS, the reachability and observability of the plant can be preserved if the communication sequences are chosen properly. We propose a method for exponentially stabilizing a NCS by first identifying a pair of communication sequences that preserve reachability and observability and then designing an observer-based feedback controller based on those sequences.     

Supervisory control of timed discrete event systems under partial observation based on activity models and eligible time bounds

To avoid the state–space explosion by including tick events in timed discrete event systems (DESs) under partial observation, a notion of eligible time bounds is introduced and based on the notion, controllability and observability conditions of languages are presented. In particular, this paper shows that these controllability and observability conditions are necessary and sufficient for the existence of a supervisor to achieve the given language specification.     

Uniform controllability of semidiscrete approximations of parabolic control systems

Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the present paper, under the main assumptions that the discretized semigroup is uniformly analytic, and that the control operator is mildly unbounded, we prove that the semidiscrete approximation models are uniformly controllable. Moreover, we provide a computationally efficient way to compute the approximation controls. An example of application is implemented for the one- and two-dimensional heat equation with Neumann boundary control.     

A modified normality condition for decentralized supervisory control of discrete event systems

In this paper, we study nonblocking decentralized supervisory control of discrete event systems. We introduce a modified normality condition defined in terms of a modified natural projection map. The modified normality condition is weaker than the original one and stronger than the co-observability condition. Moreover, it is preserved under union. Given a marked language specification, there exists a nonblocking decentralized supervisor for the supremal sublanguage which satisfies L_m(G)-closure, controllability, and modified normality. Such a decentralized supervisor is more permissive than the one which achieves the supremal L_m(G)-closed, controllable, and normal sublanguage.     

Infinite horizon backward stochastic differential equation and exponential convergence index assignment of stochastic control systems

This paper studies exponential convergence index assignment of stochastic control systems from the viewpoint of backward stochastic differential equation. Like deterministic control systems, it is shown that the exact controllability of an open-loop stochastic system is equivalent to the possibility of assigning an arbitrary exponential convergence index to the solution of the closed-loop stochastic system, formed by means of suitable linear feedback of the states. As an application, a sufficient and necessary condition for the existence and uniqueness of the solution of a class of infinite horizon forward-backward stochastic differential equations is provided.     

The average-case identifiability and controllability of large scale systems

Needs for increased product quality, reduced pollution, and reduced energy and material consumption are driving enhanced process integration. This increases the number of manipulated and measured variables required by the control system to achieve its objectives. This paper addresses the question of whether processes tend to become increasingly more difficult to identify and control as the process dimension increases. Tools and results of multivariable statistics are used to show that, under a variety of assumed distributions on the elements, square processes of higher dimension tend to be more difficult to identify and control, whereas the expected controllability and identifiability of nonsquare processes depends on the relative numbers of measured and manipulated variables. These results suggest that the procedure of simplifying the control problem so that only a square process is considered is a poor practice for large scale systems.     

Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator

A second-order hyperbolic system with collocated sensor/actuator is considered. The semigroup generation is shown for the closed-loop system under the feedback of a generic unbounded observation operator. The equivalence between the exponential stability of the closed-loop system and exact controllability of the open-loop system is established in the general framework of well-posed linear systems. Finally, the conditions are weakened for the diagonal semigroups with finite dimensional inputs. Example of beam equation is presented to display the application.