Stabilization of hereditary distributed parameter control systems

In this paper, we study the asymptotic stabilization of semilinear distributed parameter control systems with delay. Assuming that the semigroup of operators associated with the uncontrolled and undelayed equation is compact we prove that a well known rank condition, which implies the feedback stabilization for lumped systems, can be extended to this type of systems.     

Robust control and tuning problem for distributed parameter systems

In this paper robust multivariable controllers for parabolic distributed parameter systems will be discussed. The purpose of a robust controller is to achieve output regulation, disturbance rejection and insensitivity against some perturbations in the system's and controller's parameters. The robust controller consists of two parts: the unstable servo-compensator and the stabilizing compensator. The servo-compensator will be fixed on the basis of the spectrum of the reference and disturbance signals. The purpose of the stabilizing compensator is to stabilize the extended unstable system that consists of the stable plant and the servo-compensator. In this paper it is proved that the stabilizing compensator can be decomposed into a scalar gain and a matrix gain. A simple sufficient condition for finding stabilizing matrix gains will be given and a straightforward way to compute the gains will be presented. The proposed method is practical in the sense that the dimension of the controller is finite and small, output feedback is used and tuning the controller can be done with the information that can be measured from the stable plant with input-output measurements. To the authors’ knowledge, the main results are new even for finite-dimensional systems.     

Stabilization of polynomially parametrized families of linear systems. The single-input case

Given a continuous-time family of finite-dimensional single-input linear systems, parametrized polynomially, such that each of the systems in the family is controllable, there exists a polynomially parametrized control law making each of the systems in the family stable.     

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.     

Analysis and synthesis of switched linear control systems

Switched linear systems have a long history of interest in the control community, and have attracted considerable attention recently because they are not only practically relevant, but also tangible with the rich results in the linear system theory. Rapid progress in the field has generated many new ideas and powerful tools. This paper provides a concise and timely survey on analysis and synthesis of switched linear control systems, and presents the basic concepts and main properties of switched linear systems in a systematic manner. The fundamental topics include (i) controllability and observability, (ii) system structural decomposition, (iii) feedback controller design for stabilization, and (iv) optimal control.     

Verification of distributed control systems in intelligent manufacturing

This paper presents an application of formal methods for validation of flexible manufacturing systems controlled by distributed controllers. A software tool verification environment for distributed applications (VEDA) is developed for modeling and verification of distributed control systems. The tool provides an integrated environment for formal, model-based verification of the execution control of function blocks following the new international standard IEC61499. The modeling is performed in a closed-loop way using manually developed models of plants and automatically generated models of controllers.     

Observer-based event-triggered containment control of multi-agent systems with time delay

This paper studies the containment control of general linear multi-agent systems with or without time delay. The observer-based event-triggered control schemes will be considered. For the conventional distributed containment control protocol, we will not update the relative state continuously, i.e. the relative state will be updated by some events which happen intermittently. A completely decentralised event trigger will be designed for leader–follower systems. Under the proposed protocol, if we design some appropriate feedback gain matrices, all followers will asymptotically converge to the convex hull spanned by the dynamic leaders. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

Stabilization of Markovian jump linear system over networks with random communication delay

This paper is concerned with the stabilization problem for a networked control system with Markovian characterization. We consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a Markov chain. The resulting closed-loop system is modeled as a Markovian jump linear system with two jumping parameters, and a necessary and sufficient condition on the existence of stabilizing controllers is established. An iterative linear matrix inequality (LMI) approach is employed to calculate a mode-dependent solution. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.     

Stabilization of linear discrete-time systems with actuator saturation

This paper investigates the stabilization problem of linear discrete-time systems with actuator saturation. A simple method recently developed for analyzing the elemental perturbation bound of robust pole-assignment is extended to obtain the stabilization condition. The state feedback controller is designed to satisfy the requirement of stability under the nonlinear saturation. An example is given to demonstrate the use of the proposed approach.     

Stabilization of linear systems over networks with bounded packet loss

This paper is concerned with the stabilization problem of networked control systems where the main focus is the packet-loss issue. Two types of packet-loss processes are considered. One is the arbitrary packet-loss process, the other is the Markovian packet-loss process. The stability conditions of networked control systems with both arbitrary and Markovian packet losses are established via a packet-loss dependent Lyapunov approach. The corresponding stabilizing controller design techniques are also given based upon the stability conditions. These results are also extended to the unit time delay case. Finally, the numerical example and simulations have demonstrated the usefulness of the developed theory.     

Generalized control systems,boundary control systems,and delayed control systems

We investigate the relationships between the three classes of systems mentioned in the title: we show that systems with delays in control are a special instance of boundary control systems, and a boundary control system produces a generalized control system when projected onto its (unstable) eigenspaces. We use this observation to investigate the action of feedback on the dynamical behavior of systems with boundary controls. In particular, the well-known fact that spectral controllability is necessary and sufficient for a system with delays in control to be stabilizable is derived from a general rather than from anad hoc method. This paper was written according to the programs of the GNAFA-CNR group, with the financial support of the Italian “Ministero della Pubblica Istruzione.”     

Predictive control for a class of distributed delay systems using Chebyshev polynomials

In this paper, the model predictive control (MPC) is developed for linear time-varying systems with distributed time delay in state. The Chebyshev operational matrices of product, integration and delay are utilized to transform the solution of distributed delay differential equation to the solution of algebraic equations. The Chebyshev functions are also applied to derive approximate solution of finite horizon optimal control problem involved in MPC. The proposed method is simple and computationally advantageous. Illustrative example demonstrates the validity and applicability of the technique.     

Stabilization of positive linear systems

We consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant. The existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane. This allows to transform the problem to the stabilization problem of compartmental systems, which is known and for which a solution has been proposed already. We provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback. A class of stabilizing feedbacks is given explicitly.     

A PI-controller for distributed delay systems

A finite dimensional control theory is developed for the design of a proportional plus integral control law for tracking step command inputs in general autonomous time-lag systems with distributed heredity in state, control and output variables. With respect to an ordinary differential equation describing the delay system unstable modes, an auxiliary tracking problem is posed. This auxiliary problem derives its importance from the fact that its solution directly yields a solution to the original tracking problem. This point of contact with a finite dimensional system permits the application of well-tested ordinary systems tracking theory to the tracking problem in time-lag systems.     

PI stabilization of first-order systems with time delay

This paper considers the problem of stabilizing a first-order plant with dead time using a PI controller. Using a version of the Hermite–Biehler Theorem applicable to quasipolynomials, a complete and constructive characterization of all stabilizing PI gain values is obtained.     

Asymptotic methods in the optimal control of distributed systems

A short review of the various problems which arise in connection with the use of asymptotic methods in the optimal control of distributed systems is presented. We consider the cases when the asymptotic analysis comes from the state equation, or from the cost function, or both and also when the state equation is defined in perturbed domains.     

Stabilization of continuous-time switched nonlinear systems

The paper considers three problems for continuous-time nonlinear switched systems. The first result of this paper is a open-loop stabilization strategy based on dwell time computation. The second considers a state switching strategy for global stabilization. The strategy is of closed loop nature (trajectory dependent) and is designed from the solution of what we call nonlinear Lyapunov–Metzler inequalities from which the stability condition is expressed. Finally, results on the stabilization of nonlinear time varying polytopic systems are provided.     

Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays

In this paper, we consider delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed delays. Although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained, almost no stability condition for fuzzy systems with distributed delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed delays. Here we employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of fuzzy systems with discrete and distributed delays. We introduce some free weighting matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative stability conditions. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we give two examples to illustrate our results. Delay-dependent stability conditions obtained here are shown to guarantee a wide stability region.     

Intelligent distributed and supervised flow control methodology for production systems

This paper deals with the development of an intelligent distributed and supervised control approach for high-volume production systems, in which the flow of parts can be approximated by a continuous (fluid) model. The proposed approach is based on the decomposition of the production system into elementary modules in order to reduce the control design computational complexity. In this context, a two levels control structure is proposed. At the local level, a surplus-based principle is adopted to regulate the production flow for each module according to the distributed structure. The proposed control methodology decides how to adjust the production rate in order to avoid system overloading and eliminate machine starvation or blocking. In this context, the local control law is synthesized by using the Takagi–Sugeno fuzzy systems. At the high level, a supervisory controller is designed to improve the overall system performances. A supervisor provides an additive component for each local controller when the overall system performances deviate from their acceptable domains (degraded mode). This is done by combining both local and global information into a unified formalism by using aggregation operators and according to fuzzy interval representation of the desired objectives. Finally, the feasibility of the proposed methodology is validated with simulation examples.