Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network.It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network.For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed.In an event-triggered system, when an error signal exceeds a specified time-varying threshold, it indicates the occurrence of a typical event.The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed.Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs.A simulation example is finally used to verify that the effectiveness of such a control strategy can enhance the system performance.

Exponential stabilization of distributed parameter switched systems under dwell time constraints

The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results.

Improved control of distributed parameter systems using wireless sensor and actuator networks:An observer-based method

In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method.Firstly,a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter systems.The mobile agents,each of which is affixed with a controller and an actuator,can provide the observer-based control for the target systems.By using Lyapunov stability arguments,the stability for the estimation error system and distributed parameter control system is proved,meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance.A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches.

Improved control for distributed parameter systems with time-dependent spatial domains utilizing mobile sensor-actuator networks

A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.

Optimal switching policy for performance enhancement of distributed parameter systems based on event-driven control

This paper aims to improve the performance of a class of distributed parameter systems for the optimal switching of actuators and controllers based on event-driven control. It is assumed that in the available multiple actuators, only one actuator can receive the control signal and be activated over an unfixed time interval, and the other actuators keep dormant. After incorporating a state observer into the event generator, the event-driven control loop and the minimum inter-event time are ultimately bounded. Based on the event-driven state feedback control, the time intervals of unfixed length can be obtained. The optimal switching policy is based on finite horizon linear quadratic optimal control at the beginning of each time subinterval. A simulation example demonstrate the effectiveness of the proposed policy.

SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS

Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.

Coverage-optimization based guidance of mobile agents for improved control of distributed parameter systems

The control problem of a class of parabolic distributed parameter systems (DPSs) is investigated by using mobile agents with capabilities of sensing and actuating. The guidance strategies of mobile agents based on coverage optimization methods are proposed to improve the control performance of the system and make the state norm of the system converge to zero faster. The coverage optimization problems are constructed based on the measurement of each agent. By solving the coverage optimization problems, the local optimal moving direction of each agent can be obtained. Then the gradient-based agent motion control laws are established. With the indicator function and the surface delta function, this method is generalized to n-dimensional space, and suitable for any sensing region with piecewise smooth boundaries. The stability and control performance of the system are analyzed. Numerical simulations show the effectiveness of the proposed methods.

A MAXIMUM PRINCIPLE FOR DISTRIBUTED PARAMETER SYSTEMS WITH MIXED PHASE-CONTROL CONSTRAINTS ANDENDPOINT CONSTRAINTS

This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.

Control synthesis of linear distributed parameter switched systems

The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwell time approach, sufficient con- ditions are derived in terms of linear operator inequalities frame- work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin- ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system＇s parameter and the boundary condition. Finally, two numerical examples are given to illustrate the proposed method.

Cyber-Physical Systems as General Distributed Parameter Systems:Three Types of Fractional Order Models and Emerging Research Opportunities

Cyber-physical systems (CPSs) are man-made complex systems coupled with natural processes that, as a whole, should be described by distributed parameter systems (DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks. © 2014 Chinese Association of Automation.

Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.

Observer for Linear Distributed-Parameter Systems with Application to Isothermal Plug-Flow Reactor

This paper presents a conception of an exponential observer for a class of linear distributed-parameter systems (DPSs), in which the dynamics are partially unknown. The given distributed-parameter observer ensures asymptotic state estimator with exponentially decay error, based on the theory of C0-semigroups in a Hilbert space. The theoretical observer developed is applied to a chemical tubular reactor, namely the isothermal Plug-Flow reactor basic dynamical model for which measurements are available at the reactor output only. The process is described by Partial differential equations with unknown initial states. For this application, performance issues are illustrated in a simulation study.

Simulation of a class of delay stochastic system with distributed parameter

Simulation of a class of delay stochastic system with distributed parameter is discussed. Difference schemes for the numerical computation of delay stochastic system are obtained. The precision of the difference scheme and the efficiency of the difference scheme in simulation of delay stochastic system with distributed parameter are analyzed. Examples are given to illustrate the application of the method.

THE STUDY ON A KIND OF CONTROL SYSTEM WITH NONLINEAR PARABOLIC DISTRIBUTED PARAMETERS

The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented, Two methods were used to investigate the basic characteristics of the system: I) transforming the system it? the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the lumped parameter system. It is found that there are two critical values for the control variable : the larger one determines whether or not the boundary would move, while the smaller one determines whether or not the boundary, would atop automatically. For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is well posed, stable, measurable and controllable.

DISOPE distributed model predictive control of cascade systems with network communication

A novel distributed model predictive control scheme based on dynamic integrated system optimization and parameter estimation （DISOPE） was proposed for nonlinear cascade systems under network environment. Under the distributed control structure, online optimization of the cascade system was composed of several cascaded agents that can cooperate and exchange information via network communication. By iterating on modified distributed linear optimal control problems on the basis of estimating parameters at every iteration the correct optimal control action of the nonlinear model predictive control problem of the cascade system could be obtained, assuming that the algorithm was convergent. This approach avoids solving the complex nonlinear optimization problem and significantly reduces the computational burden. The simulation results of the fossil fuel power unit are illustrated to verify the effectiveness and practicability of the proposed algorithm.

Backstepping-Based Distributed Abnormality Detection for Nolinear Parabolic Distributed Prameter Systems

In this paper, we proposed a model-based abnormality detection scheme for a class of nonlinear parabolic distributed parameter systems (DPSs). The proposed methodology consists of the design of an observer and an abnormality detection filter (ADF) based on the backstepping technique and a limited number of in-domain measurements plus one boundary measurement. By taking the difference between the measured and estimated outputs from observer, a residual signal is generated for fault detection. For the detection purpose, the residual is evaluated in a lumped manner and we propose an explicit expression for the time-varying threshold. The convergence properties of the PDE observer and the residual are analyzed by Lyapunov stability theory. Eventually, the proposed abnormality detection scheme is demonstrated on a nonlinear DPS.

Distributed Secondary Control and Optimal Power Sharing in Microgrids

We address the control problem of microgrids and present a fully distributed control system which consists of primary controller, secondary controller, and optimal active power sharing controller. Different from the existing control structure in microgrids, all these controllers are implemented as local controllers at each distributed generator. Thus, the requirement for a central controller is obviated. The performance analysis of the proposed control systems is provided, and the finite-time convergence properties for distributed secondary frequency and voltage controllers are achieved. Moreover, the distributed control system possesses the optimal active power sharing property. In the end, a microgrid test system is investigated to validate the effectiveness of the proposed control strategies. © 2014 Chinese Association of Automation.

Data-driven Detection and Identification of Line Parameters with PMU and Unsynchronized SCADA Measurements in Distribution Grids

Line parameters play an important role in the control and management of distribution systems.Currently,phasor measurement unit(PMU)systems and supervisory control and data acquisition(SCADA)systems coexist in distribution systems.Unfortunately,SCADA and PMU measurements usually do not match each other,resulting in inaccurate detection and identification of line parameters based on measurements.To solve this problem,a data-driven method is proposed.SCADA measurements are taken as samples and PMU measurements as the population.A probability parameter identification index(PPII)is derived to detect the whole line parameter based on the probability density function(PDF)parameters of the measurements.For parameter identification,a power-loss PDF with the PMU time stamps and a power-loss chronological PDF are derived via kernel density estimation(KDE)and a conditional PDF.Then,the power-loss samples with the PMU time stamps and chronological correlations are generated by the two PDFs of the power loss via the Metropolis-Hastings(MH)algorithm.Finally,using the power-loss samples and PMU current measurements,the line parameters are identified using the total least squares(TLS)algorithm.Hardware simulations demonstrate the effectiveness of the proposed method for distribution network line parameter detection and identification.

DEGENERATE SEMI-GROUP METHODS FOR THE EXPONENTIAL STABILITY OF THE FIRST ORDER SINGULAR DISTRIBUTED PARAMETER SYSTEMS

Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.

Performance Improvement of Distributed Systems by Autotuning of the Configuration Parameters

The performance of distributed computing systems is partially dependent on configuration parameters recorded in configuration files. Evolutionary strategies, with their ability to have a global view of the structural information, have been shown to effectively improve performance. However, most of these methods consume too much measurement time. This paper introduces an ordinal optimization based strategy combined with a back propagation neural network for autotuning of the configuration parameters. The strat- egy was first proposed in the automation community for complex manufacturing system optimization and is customized here for improving distributed system performance. The method is compared with the covariance matrix algorithm. Tests using a real distributed system with three-tier servers show that the strategy reduces the testing time by 40% on average at a reasonable performance cost.