Asymptotic behaviour and boundedness of linear systems with time varying coefficients

Motivated by developments in spacecraft dynamics, the asymptotic behaviour and boundedness of solution of a special class of time varying systems in which each term appears as the sum of a constant and a time varying part, are analysed in this paper. It is not possible to apply standard textbook results to such systems, which are originally in second order. Some of the existing results are reformulated. Four theorems which explore the relations between the asymptotic behaviour/boundedness of the constant coefficient system, obtained by equating the time varying terms to zero, to the corresponding behaviour of the time varying system, are developed. The results show the behaviour of the two systems to be intimately related, provided the solutions of the constant coefficient system approach zero are bounded for large values of time, and the time varying terms are suitably restrained. Two problems are tackled using these theorems.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Load Profiling in Distributed Real-Time Systems

Load balancing is often used to ensure that nodes in a distributed systems are equally loaded. In this paper, we show that for real-time systems, load balancing is not desirable. In particular, we propose a new load-profiling strategy that allows the nodes of a distributed system to be unequally loaded. Using load profiling, the system attempts to distribute the load amongst its nodes so as to maximize the chances of finding a node that would satisfy the computational needs of incoming real-time tasks. To that end, we describe and evaluate a distributed load-profiling protocol for dynamically scheduling time-constrained tasks in a loosely-coupled distributed environment. When a task is submitted to a node, the scheduling software tries to schedule the task locally so as to meet its deadline. If that is not feasible, it tries to locate another node where this could be done with a high probability of success, while attempting to maintain an overall load profile for the system. Nodes in the system inform each other about their state using a combination of multicasting and gossiping. The performance of the proposed protocol is evaluated via simulation, and is contrasted to other dynamic scheduling protocols for real-time distributed systems. Based on our findings, we argue that keeping a diverse availability profile and using passive bidding (through gossiping) are both advantageous to distributed scheduling for real-time systems.

H-infinity control design for time-delay linear systems: a rational transfer function based approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

H2 and/or H∞-norm model reduction of uncertain discrete-time systems

This paper addresses the problem of model reduction for uncertain discrete-time systems with convex bounded (polytope type) uncertainty. A reduced order precisely known model is obtained in such a way that the H2 and/or the H∞ guaranteed norm of the error between the original (uncertain) system and the reduced one is minimized. The optimization problems are formulated in terms of coupled (non-convex) LMIs - Linear Matrix Inequalities, being solved through iterative algorithms. Examples illustrate the results.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Discrete-time sliding mode control of input-delay systems applied on a power generation system

This paper presents two discrete sliding mode control (SMC) design. The first one is a discrete-time SMC design that doesn't take into account the time-delay. The second one is a discrete-time SMC design, which takes in consideration the time-delay. The proposed techniques aim at the accomplishment simplicity and robustness for an uncertainty class. Simulations results are shown and the effectiveness of the used techniques is analyzed. © 2006 IEEE.

H ∞ state feedback control of discrete-time Markov jump linear systems through linear matrix inequalities

This paper addresses the H ∞ state-feedback control design problem of discretetime Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This results allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than one available in the current literature. An example is solved for illustration and comparisons. © 2011 IFAC.

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system. (C) 2012 Elsevier Ltd. All rights reserved.

Communication Middleware for Distributed Hard Real-Time Systems in Java

Distributed real-time embedded systems are becoming increasingly important to society. More demands will be made on them and greater reliance will be placed on the delivery of their services. A relevant subset of them is high-integrity or hard real-time systems, where failure can cause loss of life, environmental harm, or significant financial loss. Additionally, the evolution of communication networks and paradigms as well as the necessity of demanding processing power and fault tolerance, motivated the interconnection between electronic devices; many of the communications have the possibility of transferring data at a high speed. The concept of distributed systems emerged as systems where different parts are executed on several nodes that interact with each other via a communication network. Java’s popularity, facilities and platform independence have made it an interesting language for the real-time and embedded community. This was the motivation for the development of RTSJ (Real-Time Specification for Java), which is a language extension intended to allow the development of real-time systems. The use of Java in the development of high-integrity systems requires strict development and testing techniques. However, RTJS includes a number of language features that are forbidden in such systems. In the context of the HIJA project, the HRTJ (Hard Real-Time Java) profile was developed to define a robust subset of the language that is amenable to static analysis for high-integrity system certification. Currently, a specification under the Java community process (JSR- 302) is being developed. Its purpose is to define those capabilities needed to create safety critical applications with Java technology called Safety Critical Java (SCJ). However, neither RTSJ nor its profiles provide facilities to develop distributed realtime applications. This is an important issue, as most of the current and future systems will be distributed. The Distributed RTSJ (DRTSJ) Expert Group was created under the Java community process (JSR-50) in order to define appropriate abstractions to overcome this problem. Currently there is no formal specification. The aim of this thesis is to develop a communication middleware that is suitable for the development of distributed hard real-time systems in Java, based on the integration between the RMI (Remote Method Invocation) model and the HRTJ profile. It has been designed and implemented keeping in mind the main requirements such as the predictability and reliability in the timing behavior and the resource usage. iThe design starts with the definition of a computational model which identifies among other things: the communication model, most appropriate underlying network protocols, the analysis model, and a subset of Java for hard real-time systems. In the design, the remote references are the basic means for building distributed applications which are associated with all non-functional parameters and resources needed to implement synchronous or asynchronous remote invocations with real-time attributes. The proposed middleware separates the resource allocation from the execution itself by defining two phases and a specific threading mechanism that guarantees a suitable timing behavior. It also includes mechanisms to monitor the functional and the timing behavior. It provides independence from network protocol defining a network interface and modules. The JRMP protocol was modified to include two phases, non-functional parameters, and message size optimizations. Although serialization is one of the fundamental operations to ensure proper data transmission, current implementations are not suitable for hard real-time systems and there are no alternatives. This thesis proposes a predictable serialization that introduces a new compiler to generate optimized code according to the computational model. The proposed solution has the advantage of allowing us to schedule the communications and to adjust the memory usage at compilation time. In order to validate the design and the implementation a demanding validation process was carried out with emphasis in the functional behavior, the memory usage, the processor usage (the end-to-end response time and the response time in each functional block) and the network usage (real consumption according to the calculated consumption). The results obtained in an industrial application developed by Thales Avionics (a Flight Management System) and in exhaustive tests show that the design and the prototype are reliable for industrial applications with strict timing requirements. Los sistemas empotrados y distribuidos de tiempo real son cada vez más importantes para la sociedad. Su demanda aumenta y cada vez más dependemos de los servicios que proporcionan. Los sistemas de alta integridad constituyen un subconjunto de gran importancia. Se caracterizan por que un fallo en su funcionamiento puede causar pérdida de vidas humanas, daños en el medio ambiente o cuantiosas pérdidas económicas. La necesidad de satisfacer requisitos temporales estrictos, hace más complejo su desarrollo. Mientras que los sistemas empotrados se sigan expandiendo en nuestra sociedad, es necesario garantizar un coste de desarrollo ajustado mediante el uso técnicas adecuadas en su diseño, mantenimiento y certificación. En concreto, se requiere una tecnología flexible e independiente del hardware. La evolución de las redes y paradigmas de comunicación, así como la necesidad de mayor potencia de cómputo y de tolerancia a fallos, ha motivado la interconexión de dispositivos electrónicos. Los mecanismos de comunicación permiten la transferencia de datos con alta velocidad de transmisión. En este contexto, el concepto de sistema distribuido ha emergido como sistemas donde sus componentes se ejecutan en varios nodos en paralelo y que interactúan entre ellos mediante redes de comunicaciones. Un concepto interesante son los sistemas de tiempo real neutrales respecto a la plataforma de ejecución. Se caracterizan por la falta de conocimiento de esta plataforma durante su diseño. Esta propiedad es relevante, por que conviene que se ejecuten en la mayor variedad de arquitecturas, tienen una vida media mayor de diez anos y el lugar ˜ donde se ejecutan puede variar. El lenguaje de programación Java es una buena base para el desarrollo de este tipo de sistemas. Por este motivo se ha creado RTSJ (Real-Time Specification for Java), que es una extensión del lenguaje para permitir el desarrollo de sistemas de tiempo real. Sin embargo, RTSJ no proporciona facilidades para el desarrollo de aplicaciones distribuidas de tiempo real. Es una limitación importante dado que la mayoría de los actuales y futuros sistemas serán distribuidos. El grupo DRTSJ (DistributedRTSJ) fue creado bajo el proceso de la comunidad de Java (JSR-50) con el fin de definir las abstracciones que aborden dicha limitación, pero en la actualidad aun no existe una especificacion formal. El objetivo de esta tesis es desarrollar un middleware de comunicaciones para el desarrollo de sistemas distribuidos de tiempo real en Java, basado en la integración entre el modelo de RMI (Remote Method Invocation) y el perfil HRTJ. Ha sido diseñado e implementado teniendo en cuenta los requisitos principales, como la predecibilidad y la confiabilidad del comportamiento temporal y el uso de recursos. El diseño parte de la definición de un modelo computacional el cual identifica entre otras cosas: el modelo de comunicaciones, los protocolos de red subyacentes más adecuados, el modelo de análisis, y un subconjunto de Java para sistemas de tiempo real crítico. En el diseño, las referencias remotas son el medio básico para construcción de aplicaciones distribuidas las cuales son asociadas a todos los parámetros no funcionales y los recursos necesarios para la ejecución de invocaciones remotas síncronas o asíncronas con atributos de tiempo real. El middleware propuesto separa la asignación de recursos de la propia ejecución definiendo dos fases y un mecanismo de hebras especifico que garantiza un comportamiento temporal adecuado. Además se ha incluido mecanismos para supervisar el comportamiento funcional y temporal. Se ha buscado independencia del protocolo de red definiendo una interfaz de red y módulos específicos. También se ha modificado el protocolo JRMP para incluir diferentes fases, parámetros no funcionales y optimizaciones de los tamaños de los mensajes. Aunque la serialización es una de las operaciones fundamentales para asegurar la adecuada transmisión de datos, las actuales implementaciones no son adecuadas para sistemas críticos y no hay alternativas. Este trabajo propone una serialización predecible que ha implicado el desarrollo de un nuevo compilador para la generación de código optimizado acorde al modelo computacional. La solución propuesta tiene la ventaja que en tiempo de compilación nos permite planificar las comunicaciones y ajustar el uso de memoria. Con el objetivo de validar el diseño e implementación se ha llevado a cabo un exigente proceso de validación con énfasis en: el comportamiento funcional, el uso de memoria, el uso del procesador (tiempo de respuesta de extremo a extremo y en cada uno de los bloques funcionales) y el uso de la red (consumo real conforme al estimado). Los buenos resultados obtenidos en una aplicación industrial desarrollada por Thales Avionics (un sistema de gestión de vuelo) y en las pruebas exhaustivas han demostrado que el diseño y el prototipo son fiables para aplicaciones industriales con estrictos requisitos temporales.

Functional analysis of a real-time protocol for networked control systems

Traditional real-time control systems are tightly integrated into the industrial processes they govern. Now, however, there is increasing interest in networked control systems. These provide greater flexibility and cost savings by allowing real-time controllers to interact with industrial processes over existing communications networks. New data packet queuing protocols are currently being developed to enable precise real-time control over a network with variable propagation delays. We show how one such protocol was formally modelled using timed automata, and how model checking was used to reveal subtle aspects of the control system's dynamic behaviour.

Towards platform-independent real-time systems

Real-time software systems are rarely developed once and left to run. They are subject to changes of requirements as the applications they support expand, and they commonly outlive the platforms they were designed to run on. A successful real-time system is duplicated and adapted to a variety of applications - it becomes a product line. Current methods for real-time software development are commonly based on low-level programming languages and involve considerable duplication of effort when a similar system is to be developed or the hardware platform changes. To provide more dependable, flexible and maintainable real-time systems at a lower cost what is needed is a platform-independent approach to real-time systems development. The development process is composed of two phases: a platform-independent phase, that defines the desired system behaviour and develops a platform-independent design and implementation, and a platform-dependent phase that maps the implementation onto the target platform. The last phase should be highly automated. For critical systems, assessing dependability is crucial. The partitioning into platform dependent and independent phases has to support verification of system properties through both phases.

The design of robust protocols for distributed real-time systems

Modern distributed control systems comprise of a set of processors which are interconnected using a suitable communication network. For use in real-time control environments, such systems must be deterministic and generate specified responses within critical timing constraints. Also, they should be sufficiently robust to survive predictable events such as communication or processor faults. This thesis considers the problem of coordinating and synchronizing a distributed real-time control system under normal and abnormal conditions. Distributed control systems need to periodically coordinate the actions of several autonomous sites. Often the type of coordination required is the all or nothing property of an atomic action. Atomic commit protocols have been used to achieve this atomicity in distributed database systems which are not subject to deadlines. This thesis addresses the problem of applying time constraints to atomic commit protocols so that decisions can be made within a deadline. A modified protocol is proposed which is suitable for real-time applications. The thesis also addresses the problem of ensuring that atomicity is provided even if processor or communication failures occur. Previous work has considered the design of atomic commit protocols for use in non time critical distributed database systems. However, in a distributed real-time control system a fault must not allow stringent timing constraints to be violated. This thesis proposes commit protocols using synchronous communications which can be made resilient to a single processor or communication failure and still satisfy deadlines. Previous formal models used to design commit protocols have had adequate state coverability but have omitted timing properties. They also assumed that sites communicated asynchronously and omitted the communications from the model. Timed Petri nets are used in this thesis to specify and design the proposed protocols which are analysed for consistency and timeliness. Also the communication system is mcxielled within the Petri net specifications so that communication failures can be included in the analysis. Analysis of the Timed Petri net and the associated reachability tree is used to show the proposed protocols always terminate consistently and satisfy timing constraints. Finally the applications of this work are described. Two different types of applications are considered, real-time databases and real-time control systems. It is shown that it may be advantageous to use synchronous communications in distributed database systems, especially if predictable response times are required. Emphasis is given to the application of the developed commit protocols to real-time control systems. Using the same analysis techniques as those used for the design of the protocols it can be shown that the overall system performs as expected both functionally and temporally.