Distributed Parameter Systems

Abstract-The propagation of guided waves along a metal grating lying on a grounded dielectric substrate is studied. Hitherto, investigation of the properties of such waves has been restricted to directions of propagation perpendicular to or nearly parallel to the strips of grating. Averaged boundary conditions for the fields at the grating are used here to simplify the analysis, and are expected to yield accurate results for grating periods that are sufficiently small compared to a wavelength. Comparisons made with more exact computations in the literature are shown to be good. The results have potential application for microwave
and millimeter wave waveguides, slotted microstrip antennas, and circuit elements.

This paper addresses the stabilization of nonlinear systems described by Takagi-Sugeno models affected by input actuator saturation. A parallel distributed compensation design is used for the state feedback controller. Stabilization conditions in the sense of the Lyapunov method are derived and expressed as a linear matrix inequality problem. The obtained gains depend on the actuator saturation limits. A cart-pendulum example is presented to illustrate the effectiveness of the proposed approach.

This paper presents the results of applying POD (Proper orthogonal decomposition) and predictive control techniques to the control of a non-isothermal tubular reactor. The control goal is to keep the operation of the reactor around a desired operating condition in spite of the disturbances in the feeding flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles the nonlinear PDEs (Partial Differential Equations) that model the reactor are linearized, and afterwards the resulting linear PDEs are discretized in space giving as result a high order linear model. Then a reduced order model is found by means of the POD technique which makes possible the design of an MPC controller for rejecting the disturbances that affect the tubular reactor. TuB12.2 ISBN: 978-960-89028-5-5 1046 L z 1 J T AB o 2 J T 3 J op J =T ∆,op J +T * J whereT ∆,op J is the solution of the QP problem stated in the previous step. 6) UsingT op J , simulate (3) in order to obtain the new temperature (T op ∈ℜ N ) and concentration (C op ∈ ℜ N ) profiles of the reactor in steady state. 7) If max T op J −T * J ≤ Tol then stop, else makē T * J =T op J ,C * =C op ,T * =T op and go to step 3.

Piezoelectric transduction has received great attention for vibration-to-electric energy conversion over the last five years. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure, to generate electrical energy from base excitations. Several authors have investigated modeling of cantilevered piezoelectric energy harvesters under base excitation. The existing mathematical modeling approaches range from elementary single-degree-of-freedom models to approximate distributed parameter solutions in the sense of Rayleigh-Ritz discretization as well as analytical solution attempts with certain simplifications. Recently, the authors have presented the closed-form analytical solution for a unimorph cantilever under base excitation based on the Euler-Bernoulli beam assumptions. In this paper, the analytical solution is applied to bimorph cantilever configurations with series and parallel connections of piezoceramic layers. The base excitation is assumed to be translation in the transverse direction with a superimposed small rotation. The closed-form steady state response expressions are obtained for harmonic excitations at arbitrary frequencies, which are then reduced to simple but accurate single-mode expressions for modal excitations. The electromechanical frequency response functions (FRFs) that relate the voltage output and vibration response to translational and rotational base accelerations are identified from the multi-mode and single-mode solutions. Experimental validation of the single-mode coupled voltage output and vibration response expressions is presented for a bimorph cantilever with a tip mass. It is observed that the closed-form single-mode FRFs obtained from the analytical solution can successfully predict the coupled system dynamics for a wide range of electrical load resistance. The performance of the bimorph device is analyzed extensively for the short circuit and open circuit resonance frequency excitations and the accuracy of the model is shown in all cases.

This paper presents a solution to the boundary stabilization of a symmetric composite laminated plate in free transverse vibration. The symmetric composite laminated plate dynamics is presented by a linear fourth order partial differential equation (PDE). A linear control law is constructed to stabilize the plate. The control force consists of feedback of the velocity at the boundary of the plate. The novelty of this article is that it is possible to stabilize asymptotically a free transversely vibrating symmetric composite laminated plate with simply supported boundary condition via boundary control without resorting to truncation of the model.

We address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system. The criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system [3], [121. The key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different ' number of sensors. The discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation.

Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler–Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are ...

A collocation method is adopted as a numerical framework to develop approximate inertial manifolds (AIMs) in the case of partial differential problems (e.g. reaction/diffusion models) containing non-polynomial nonlinearities. The spatial discretization, based on the collocation approach, is the starting point for the alternative construction of AIMs by means of a renormalization/ decimation approach naturally derived from the incremental unknown method developed by Temam in a finite difference framework.

This work focuses on the evaluation of some of the advanced recursive state estimation techniques applied to packed bed reactors. Tubular, packed or fixed bed reactors are typically modeled as infinite dimensional partial differential equations, also called Distributed Parameter Systems (DPS). Discretization methods such as orthogonal collocation or any other polynomial approximation can be used to convert these DPS into a set of Ordinary Differential Equations (ODE) or Differential Algebraic Equations (DAE), that are more suitable for application of the estimation algorithms. Here we demonstrate the superior performance of the Ensemble Kalman Filter over its other variants (EKF and UKF) for a tubular reactor model. This work also includes the evaluation of the constrained forms of these algorithms for the same tubular reactor model and the results show that the Constrained EnKF which is a nondeterministic approach is able to estimate the states accurately and is less susceptible to numerical errors unlike the Constrained UKF and Constrained EKF which encounter the problem of the covariance matrix becoming negative definite.

In this paper we address the problem of synthesizing controllers that have to be implemented distributively and have structure. The effect of sub-controller to subcontroller communication noise on stability and performance is considered. Using an observer based controller parameterization, we provide suitable stabilizing sub-controller architectures that directly take into account the effect of communication noise on performance. In particular, the overall performance optimization can be cast as a convex problem in the Youla-Kucera parameter Q. Similar results hold for banded controller structures, i.e., when there is also a delay in the subsystem to subsystem communication.

This study is concerned with the reliable controller design for networked control systems (NCS) against both probabilistic sensors faults and actuators faults. The faults of each sensor or actuator occur randomly and their failure rates are governed by two sets of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of every sensor or actuator, new type of distribution-based NCS fault model is proposed. Based on the new built model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of NCS are obtained by using Lyapunov functional method. The main contribution of the proposed fault model and methods lies with its practicality and generalisation, which contains many realistic problems in the NCS, such as probabilistic sensors or actuators failures, partial degradation, data distortion, packet dropout, network-induced delay and so on. Moreover, some existing models in the open literatures are deemed as special cases of the proposed fault model. To illustrate the implementation procedure, a vertical take-off and landing (VTOL) aircraft system is given to show the effectiveness and application of the proposed method.

The idea of vibration-to-electric energy conversion for powering small electronic components by using the ambient vibration energy has been investigated by researchers from different disciplines in the last decade. Among the possible transduction mechanisms, piezoelectric transduction has received the most attention for converting ambient vibrations to useful electrical energy. In the last five years, there have been a considerable number of publications using various models for the electromechanical behavior of piezoelectric energy harvester beams. The models used in the literature range from elementary single-degree-of-freedom (SDOF) models to approximate distributed parameter models as well as analytical distributed parameter solution attempts. Because of the diverse nature of researchers working in energy harvesting (including electrical, mechanical and materials engineers), several oversimplified and incorrect physical assumptions have been propagated in the literature. Issues of the correct formulation for piezoelectric coupling, correct physical modeling, use of low fidelity models, incorrect base motion modeling, and the use of static expressions in a fundamentally dynamic problem are discussed and clarified here. These common indiscretions, which have been repeated in the existing piezoelectric energy harvesting literature, are addressed and clarified with improved models, and examples are provided. This paper aims to provide corrections and necessary clarifications for researchers from different engineering disciplines interested in electromechanical modeling of piezoelectric energy harvesters.

This paper presents a new solution for the semiactive suspension control problem. First, a quarter vehicle model equipped with a semi-active damper is reformulated in the LPV framework using the nonlinear static semi-active damper model. This formulation allows to turn the control problem with dissipativity constraint into that with input saturation. Then the damper force saturation is taken into account in an original LPV fashion. This leads to the definition of a new LPV model with two parameters which is handled in a polytopic way. The H∞ control design for polytopic systems is then applied. The interest of the provided methodology is emphasized by simulations on a nonlinear vehicle model.

This paper develops linear quadratic robust control theory for a class of spatially invariant distributed control systems that appear in areas of economics such as New Economic Geography, management of ecological systems, optimal harvesting of spatially mobile species, and the like. Since this class of problems has an infinite dimensional state and control space it would appear analytically intractable. We show that by Fourier transforming the problem, the solution decomposes into a countable number of finite state space robust control problems each of which can be solved by standard methods. We use this convenient property to characterize "hot spots" which are points in the transformed space that correspond to "breakdown" points in conventional finite dimensional robust control, or where instabilities appear or where the value function loses concavity. We apply our methods to a spatial extension of a well known optimal fishing model.

This paper proves the bouudeduess of boundary and distributed damped strings and Euler-Bernoulli beams under combined distributed and boundary inputs. Distributed viscous or Kelvin-Voigt damping or a translational boundary damper stabilize strings and beams. Pointwise bounded re sponse is proven using the energy multiplier method. Without disturbances, the method proves strong exponential stability.

A version of the input-to-output stability (IOS) small gain theorem is derived for interconnections where the subsystems communicate asynchronously over multiple channels, and the communication is subject to multiple time-varying possibly unbounded communication delays. It is shown that a "multi-channel" version of the small gain condition guarantees the stability of the interconnection of IOS subsystems under certain mild assumptions imposed on communication process. The fulfillment of these assumptions does not depend on characteristics of the communication channels, but can always be guaranteed by implementation of certain features of the underlying communication protocol. This result is applicable to a wide range of dynamical systems whose parts communicate over networks, such as Internet-based teleoperators.

This study aims at improving the control of a heat exchanger, described by a partial differential equation, by optimizing a linear proportional–integral fuzzy controller. The design of the controller is based on the use of a finite-dimensional approximate model, of high order, derived by spatially lumping the infinite-dimensional model of the heat exchanger. The design procedure consists to optimize the scaling factors of the linear fuzzy controller, by solving an unconstrained optimization problem issued from the simplification of a formulated constrained optimization where the objective function is an integral error measure, and the constraints are the relationships between fuzzy and conventional PID gains. The formulated unconstrained optimization problem is then solved using jointly the Matlab Optimization Toolbox and Simulink. Through simulation, the performances of the heat exchanger are evaluated, and the obtained results show that the fuzzy controller produces improved control performance with respect to the conventional controller.

We consider a problem of stabilization of the linearized Schrödinger equation using boundary actuation and measurements. We propose two different control designs. First, a simple proportional collocated boundary controller is shown to exponentially stabilize the system. However, the decay rate of the closed-loop system cannot be prescribed. The second, full-state feedback boundary control design, achieves an arbitrary decay rate. We formally view the Schrödinger equation as a heat equation in complex variables and apply the backstepping method recently developed for boundary control of reaction-advection-diffusion equations. The resulting controller is then supplied with the backstepping observer to obtain an output-feedback compensator. The designs are illustrated with simulations.

In this paper, the nonsimilarity boundary-layer flows of second-order fluid over a flat sheet with arbitrary stretching velocity are studied. The boundary-layer equations describing the steady laminar flow of an incompressible viscoelastic fluid past a semiinfinite stretching flat sheet are transformed into a partial differential equation with variable coefficients. An analytic technique for highly nonlinear problems, namely, the homotopy analysis method, is applied to give convergent analytical approximations, which agree well with the numerical results given by the Keller box method. Furthermore, the effects of physical parameters on some important physical quantities, such as the local skin-friction coefficient and the boundary-layer thickness, are investigated in detail. Mathematically, this analytic approach is rather general in principle and can be applied to solve different types of nonlinear partial differential equations with variable coefficients in physics.

The paper considers financial derivatives and option pricing models which are described with the use of diffusiontype partial differential equations (e.g. Black-Scholes models). Using this approach a new filtering method for distributed parameter systems is developed, for estimating option prices variations without knowledge of initial conditions. The proposed filtering method is the so-called Derivative-free nonlinear Kalman Filter and is based on a decomposition of the nonlinear partial-differential equation of the financial system into a set of ordinary differential equations with respect to time. Next, each one of the local models associated with the ordinary differential equations is written in the linear canonical form through a transformation which is based on differential flatness theory. This transformation provides a model of the nonlinear dynamics of the option pricing model for which state estimation is possible by applying the standard Kalman Filter recursion. Based on the obtained state estimate, validation of the Black-Scholes PDE model can be performed and the existence of inconsistent parameters in the Black-Scholes PDE model can be concluded.

In this study, an innovative solution is developed for vibration suppression of the high-rise building. The infinite dimensional system model has been presented for describing high-rise building structures which have a large inertial load with the help of the Hamilton’s principle. On the basis of this system model and with the use of the Lyapunov’s direct method, a boundary controller is proposed and the closed-loop system is uniformly bounded in the time domain. Finally, by using the Smart Structure laboratory platform which is produced by Quancer, we conduct a set of experiments and find that the designed method is resultful.

Increased availability of electronics at much lower costs have helped to create a new breed of control system components; so called "smart" components, which can perform control responsibilities in the actuator and sensor components as well as in the controller. "Smart" components can communicate bi-directionally in networked control systems. Our results show that an "ideal" system with bidirectional communications is equivalent to a single loop control system in terms of performance. However, performance improvements are possible in "non-ideal" cases. Using bi-directional communications can also improve the control system design process since it facilitates the configuration and re-configuration. Building cost effective modular control systems using bi-directional controls appears increasingly attractive.

When network induced delays are considered in the event-triggered control literature, they are typically delays from the plant to the controller and a tight bound on the admissible delays is usually imposed based on the analysis of inter-event time. In [19], a dynamic output feedback based event-triggered control scheme is introduced for stabilization of input feed-forward output feedback passive (IF-OFP) networked control systems (NCSs), which is a more general case compared with the passive and the output feedback passive (OFP) systems studied in [18]. Based on the results shown in [19], we propose a dynamic output feedback based eventtriggered control set-up for NCSs which allows us to consider network induced delays both from the plant to the controller and from the controller to the plant. We show that based on the proposed set-up, finite-gain L2 stability can be achieved in the presence of arbitrary constant network induced delays or time-varying delays with bounded jitters.

The start-up and the shutdown of tubular fixed-bed reactors can be improved by an explicit trajectory design and active control. By using the inflow concentration as a control the outflow concentration can be changed in arbitrary finite time. Explicit series expansions of the control inputs are calculated using the distributed parameter system model. It is shown that these promising techniques are not restricted to the single-input case, but can easily be extended to certain multivariable models. The control laws derived are new in the scalar case

Abstract. The domination is an original way for systems classification, based on input and output operators. In this paper, we consider first a class of controlled discrete distributed parameter systems (DPS). We extend the domination concept to these systems. By duality, we consider a classification for discrete observed systems, based on output operators. We give various characterizations and the main properties in the general case, and then by means of the choice of actuators and sensors.

A nonlinear optimal control approach based on an infinite-dimensional model is presented which determines the optimal opening of a regulator gate at the upstream end in the case of a single reach hydraulic system, in order to minimize the waste water and the variation of the water depth. The effectiveness of the control algorithm is demonstrated by a simulation example. The simulation results show good improvements in reducing the variation of water depth compared to the uncontrolled case. The Saint-Venant equations and their adjoint equations have been solved numerically by using a nonlinear implicit integration scheme (the Preissmann scheme). Our main contribution in this paper is the solution of an open-channel control problem which includes a distributed parameter model, with nonlinearities, friction, canal slope, an adjustable regulator gate and a pumping station, via variational calculus.

ABSTRACT In this work, a model predictive control (MPC) synthesis is proposed to regulate, in the presence of naturally present state and input constraints, the thickness of falling film in the vertical tube, modelled by the Kuramoto-Sivashinsky (K-S) equation. The infinite-dimensional state space representation is developed and an exact transformation modifies the boundary control problem into the distributed control problem. The appropriate analysis of K-S spectral operator reveals dissipative structure of the linearized operator which benefits from the applicability of spectral decomposition for the control purpose. The model predictive control synthesis utilizes the finite dimensional representation of the K-S PDE state in the formulation of the optimization functional, while the infinite dimensional K-S PDE state constraints are appropriately defined and cast in a form of constrained quadratic optimization. The simulation study evaluates the performance of proposed methods which achieves both stabilization of the thin film thickness and obeys inputs and states constraints.

T he dynamic optimization (DO) of complex distributed parameter systems (DPSs), like e.g., reaction-diffusion processes, is a challenging task. Most of the existing numerical approaches imply a large computational effort, therefore precluding its application to demanding applications like real time DO or model predictive control. This work, based on the control vector parameterization (CVP) approach, describes two ways to enhance the efficiency of the resulting nonlinear programming (NLP) problem solution. On the one hand, the convergence properties of the NLP solver are enhanced through the use of exact gradients and projected Hessians (H.p). On the other hand, simulation efficiency is improved through the use of reduced order descriptions of the DPSs. The capabilities and possibilities of these two enhancements are illustrated with a number of complex distributed case studies.

In this paper, we design a modal controller for conservative ßexible systems that uses distributed sensing. A spatial Þlter design based on the eigenfunctions coupled with a velocity observer prevents spillover instabilities in the closed-loop system. The proposed control is proven to stabilize a discrete set of controlled modes without destabilizing the remaining, residual modes. We then apply the theory to a single ßexible link robot arm and experimentally demonstrate the feasibility of the proposed control strategy. The experiments use high speed video feedback with image processing to determine the spatial beam curve. The controller quickly damps the Þrst modal response without causing instability in the remaining modes.

This paper presents some approaches on the new applications in fault estimation, detection and diagnosis emerged from three powerful concepts: theory of distributed parameter systems, applied to large and complex physical processes, artificial intelligence, with its tool adaptive-network-based fuzzy inference and the intelligent wireless ad-hoc sensor networks. Sensor networks have large and successful applications in the real world. They may be placed in the areas of distributed parameter systems, to be seen as a "distributed measuring sensor" for the physical variables. Using sensor networks multivariable estimation techniques may be applied in distributed parameter systems. Fault detection and diagnosis in distributed parameter systems become more easily and more performing using these concepts. The paper presents some applications in fault detection and diagnosis based on the adaptive-network-based fuzzy inference, allows treatment of large and complex systems with man...

This paper investigates the closed-loop properties of the differential coding scheme known as Delta-Modulation (∆-M ) when used in feedback loops within the context of linear systems controlled through some communication network. We propose a new modified scheme of the original form of the ∆-M algorithm which improves the closed-loop properties. Semiglobal stability with convergence to a finite ball is proved in this framework, where the domain of attraction may be arbitrarily enlarged by tuning a quantization factor ∆, in tradeoff with the precision at steady state. In a further step, parameter ∆ is made adaptive, by defining an adaptation law exclusively in terms of information available at both the transmitter and receiver. With this approach, global asymptotic Stability of the Networked Controlled System is achieved for a class of unstable plants.

This note addresses observer design for second-order distributed parameter systems in R 2 . Particularly, second-order distributed parameter systems without distributed damping are studied. Based on finite number of measurements, exponentially stable observer is designed. The existence, uniqueness and stability of solutions of the observers are based on semigroup theory.

In this paper, the identification and control of open-flow canals using linear parameter varying (LPV) models is proposed. A single reach open-flow canal has been modeled with an LPV first-order plus delay model relating upstream and downstream flows. The parameters of such model depend on the operating point and have been estimated using a parameter estimation algorithm for LPV models. The control is based on a gain-scheduling PI controller with a delayscheduling Smith Predictor. Finally, the proposed LPV model, identification and control algorithms have been applied to a simulated open-canal: the Lunax gallery located at Gascogne (France).

In this paper we present a decentralized control strategy for the connectivity maintenance for groups of mobile robots performing some desired task. Exploiting a completely decentralized estimation strategy for the algebraic connectivity of the graph, we prove the connectivity maintenance property in the general case, i.e. in presence of a generic (bounded) additional control term. Then, we address two specific decentralized control applications: rendezvous and formation control. We analytically prove that our control strategy ensures the global connectivity maintenance, while preserving the convergence properties of the rendezvous and formation controllers respectively. Simulations and experimental results are presented as well, in order to show the effectiveness of the proposed control law.

This paper is concerned with the parameter estimation and asymptotic stabilization of a one-dimensional wave equation that is subject to general harmonic disturbances at the controlled end and suffers from instability at the other end. First, we design an adaptive observer in terms of measured position and velocity. We then adopt the backstepping method for infinite-dimensional systems to design the observer-based output feedback law. It is shown that the resulting closed-loop system is asymptotically stable and that the estimates of the parameters converge to the unknown parameters.

The theory of consensus dynamics is widely employed to study various linear behaviors in networked control systems. Moreover, nonlinear phenomena have been observed in animal groups, power networks and in other networked systems. These observations inspire the development in this paper of three novel approaches to define distributed nonlinear dynamical interactions. The resulting dynamical systems are akin to higher-order nonlinear consensus systems. Over connected undirected graphs, the resulting dynamical systems exhibit various interesting behaviors that we rigorously characterize.

The energy efficiency (EE) maximization in multi-carrier code division multiple access (MC-CDMA) 1 cooperative wireless networks is a NP-hard optimization problem of great interest for future networks systems as well as wireless sensor networks. This paper presents a game theoretic approach for EE maximization in MC-CDMA wireless cooperative networks considering receiver single-user or multi-user design, as well as distributed implementation approach in order to solve the EE design problem. Moreover, the iterative water-filling algorithm (IWFA) and the Verhulst distributed power control algorithm (V-DPCA) are employed to solve the inner loop of the proposed EE maximization algorithm. A study over the quasi-concavity of the utility function is presented while numerical results are offered to corroborate the mathematical model, as well as to verify the better performance of the IWFA over the V-DPCA. Indeed, the superiority of the IWFA over V-DPCA in terms of both EE and SE is evident. This may be explained through the fact that the IWFA optimizes the power allocation of each user through all sub-carriers at the same time, while Verhulst-based DPCA performs the power control on each sub-channel considering all users.

Abstract: The classical Lagrangian and Hamiltonian formulation of an electrical transmis-sion line is reviewed and extended to allow for varying boundary conditions. This extension is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems formulation. However, the framework is limited to a line that is terminated on both ends by independent voltage sources. Additionally, the inclusion of the usual line resistance and shunt conductance via a Rayleigh dissipation functional is nontrivial. To overcome these problems, a family of alternative Lagrangian functionals is proposed. The method is inspired by a (not so well-known) concept from network theory called ‘the traditor’.

This article focuses on output feedback control of distributed parameter systems with limited number of sensors employing adaptive proper orthogonal decomposition (APOD) methodology. The controller design issue is addressed by combining a robust state controller with a dynamic observer of the system states to reduce sensor requirements. The use of APOD methodology allows the development of locally accurate low-dimensional reduced order dynamic models (ROMs) for controller synthesis thus resulting in a computationally-efficient alternative to using large-dimensional models with global validity. The derived ROMs are subsequently employed for the design of dynamic observers and controllers. The proposed methods are successfully used to achieve the desired control objective of stabilizing the Kuramoto-Sivashinksy equation (KSE) at a desired state spatial profile. Financial support from the National Science Foundation, CAREER Award # CBET 06-44519 is gratefully acknowledged.

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), 2 and , optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.

Networked Control Systems (NCSs) are often associated with problems like random data losses which might lead to system instability. This paper proposes a method based on the use of variable controller gains to achieve maximum parametric robustness of the plant controlled over a network. Stability using variable controller gains under data loss conditions is analyzed using a suitable Linear Matrix Inequality (LMI) formulation. Also, a Particle Swarm Optimization (PSO) based technique is used to maximize parametric robustness of the plant.