Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

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.

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

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.

Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

We consider a problem of robust performance analysis of linear discrete time varying systems on a bounded time interval. The system is represented in the state-space form. It is driven by a random input disturbance with imprecisely known probability distribution; this distributional uncertainty is described in terms of entropy. The worst-case performance of the system is quantified by its a-anisotropic norm. Computing the anisotropic norm is reduced to solving a set of difference Riccati and Lyapunov equations and a special form equation.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

QoC Elastic Scheduling for Real-Time Control Systems

The elastic task model, a significant development in scheduling of real-time control tasks, provides a mechanism for flexible workload management in uncertain environments. It tells how to adjust the control periods to fulfill the workload constraints. However, it is not directly linked to the quality-of-control (QoC) management, the ultimate goal of a control system. As a result, it does not tell how to make the best use of the system resources to maximize the QoC improvement. To fill in this gap, a new feedback scheduling framework, which we refer to as QoC elastic scheduling, is developed in this paper for real-time process control systems. It addresses the QoC directly through embedding both the QoC management and workload adaptation into a constrained optimization problem. The resulting solution for period adjustment is in a closed-form expressed in QoC measurements, enabling closed-loop feedback of the QoC to the task scheduler. Whenever the QoC elastic scheduler is activated, it improves the QoC the most while still meeting the system constraints. Examples are given to demonstrate the effectiveness of the QoC elastic scheduling.

LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

A transport protocol for real-time applications in wireless networked control systems

A Networked Control System (NCS) is a feedback-driven control system wherein the control loops are closed through a real-time network. Control and feedback signals in an NCS are exchanged among the system’s components in the form of information packets via the network. Nowadays, wireless technologies such as IEEE802.11 are being introduced to modern NCSs as they offer better scalability, larger bandwidth and lower costs. However, this type of network is not designed for NCSs because it introduces a large amount of dropped data, and unpredictable and long transmission latencies due to the characteristics of wireless channels, which are not acceptable for real-time control systems. Real-time control is a class of time-critical application which requires lossless data transmission, small and deterministic delays and jitter. For a real-time control system, network-introduced problems may degrade the system’s performance significantly or even cause system instability. It is therefore important to develop solutions to satisfy real-time requirements in terms of delays, jitter and data losses, and guarantee high levels of performance for time-critical communications in Wireless Networked Control Systems (WNCSs). To improve or even guarantee real-time performance in wireless control systems, this thesis presents several network layout strategies and a new transport layer protocol. Firstly, real-time performances in regard to data transmission delays and reliability of IEEE 802.11b-based UDP/IP NCSs are evaluated through simulations. After analysis of the simulation results, some network layout strategies are presented to achieve relatively small and deterministic network-introduced latencies and reduce data loss rates. These are effective in providing better network performance without performance degradation of other services. After the investigation into the layout strategies, the thesis presents a new transport protocol which is more effcient than UDP and TCP for guaranteeing reliable and time-critical communications in WNCSs. From the networking perspective, introducing appropriate communication schemes, modifying existing network protocols and devising new protocols, have been the most effective and popular ways to improve or even guarantee real-time performance to a certain extent. Most previously proposed schemes and protocols were designed for real-time multimedia communication and they are not suitable for real-time control systems. Therefore, devising a new network protocol that is able to satisfy real-time requirements in WNCSs is the main objective of this research project. The Conditional Retransmission Enabled Transport Protocol (CRETP) is a new network protocol presented in this thesis. Retransmitting unacknowledged data packets is effective in compensating for data losses. However, every data packet in realtime control systems has a deadline and data is assumed invalid or even harmful when its deadline expires. CRETP performs data retransmission only in the case that data is still valid, which guarantees data timeliness and saves memory and network resources. A trade-off between delivery reliability, transmission latency and network resources can be achieved by the conditional retransmission mechanism. Evaluation of protocol performance was conducted through extensive simulations. Comparative studies between CRETP, UDP and TCP were also performed. These results showed that CRETP significantly: 1). improved reliability of communication, 2). guaranteed validity of received data, 3). reduced transmission latency to an acceptable value, and 4). made delays relatively deterministic and predictable. Furthermore, CRETP achieved the best overall performance in comparative studies which makes it the most suitable transport protocol among the three for real-time communications in a WNCS.

A conditional retransmission enabled transport protocol for real-time networked control systems

Real-time networked control systems (NCSs) over data networks are being increasingly implemented on a massive scale in industrial applications. Along with this trend, wireless network technologies have been promoted for modern wireless NCSs (WNCSs). However, popular wireless network standards such as IEEE 802.11/15/16 are not designed for real-time communications. Key issues in real-time applications include limited transmission reliability and poor transmission delay performance. Considering the unique features of real-time control systems, this paper develops a conditional retransmission enabled transport protocol (CRETP) to improve the delay performance of the transmission control protocol (TCP) and also the reliability performance of the user datagram protocol (UDP) and its variants. Key features of the CRETP include a connectionless mechanism with acknowledgement (ACK), conditional retransmission and detection of ineffective data packets on the receiver side.

A reliable real-time transport protocol for networked control systems over wireless networks

Deploying wireless networks in networked control systems (NCSs) has become more and more popular during the last few years. As a typical type of real-time control systems, an NCS is sensitive to long and nondeterministic time delay and packet losses. However, the nature of the wireless channel has the potential to degrade the performance of NCS networks in many aspects, particularly in time delay and packet losses. Transport layer protocols could play an important role in providing both reliable and fast transmission service to fulfill NCS’s real-time transmission requirements. Unfortunately, none of the existing transport protocols, including the Transport Control Protocol (TCP) and the User Datagram Protocol (UDP), was designed for real-time control applications. Moreover, periodic data and sporadic data are two types of real-time data traffic with different priorities in an NCS. Due to the lack of support for prioritized transmission service, the real-time performance for periodic and sporadic data in an NCS network is often degraded significantly, particularly under congested network conditions. To address these problems, a new transport layer protocol called Reliable Real-Time Transport Protocol (RRTTP) is proposed in this thesis. As a UDP-based protocol, RRTTP inherits UDP’s simplicity and fast transmission features. To improve the reliability, a retransmission and an acknowledgement mechanism are designed in RRTTP to compensate for packet losses. They are able to avoid unnecessary retransmission of the out-of-date packets in NCSs, and collisions are unlikely to happen, and small transmission delay can be achieved. Moreover, a prioritized transmission mechanism is also designed in RRTTP to improve the real-time performance of NCS networks under congested traffic conditions. Furthermore, the proposed RRTTP is implemented in the Network Simulator 2 for comprehensive simulations. The simulation results demonstrate that RRTTP outperforms TCP and UDP in terms of real-time transmissions in an NCS over wireless networks.