Maximum Allowable Transmission Interval Research Articles

Reverse average dwell time constraints enable arbitrary maximum allowable transmission intervals

When designing networked control systems (NCS), stability guarantees are typically derived based on the maximum possible time between successive transmissions. A bound on this time is called the maximum allowable transmission interval (MATI). In order to minimize network usage, one is often interested in the maximum value of the MATI for which stability can still be guaranteed for the NCS. However, in many practical scenarios, the worst case transmission behavior occurs only seldom, rendering an analysis based solely on the MATI unnecessarily conservative. It was recently shown in the literature that considering information about the average allowable transmission interval in the form of a reverse average dwell time (RADT) can be used to increase the maximum value of the MATI for which stability can be guaranteed. Using the same assumptions, we show that stability guarantees can even be obtained for any arbitrary given value of the MATI as long as the RADT is small enough.

Optimal Transmission Power and Controller Design for Networked Control Systems Under State-Dependent Markovian Channels

This article considers a codesign problem for industrial networked control systems to ensure both stability and efficiency properties of such systems. This problem is particularly challenging due to the fact that wireless communications in industrial environments are not only subject to shadow fading, but also stochastically correlated with their surrounding environments. This article first introduces a novel state-dependent Markov channel (SD-MC) model that explicitly captures the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">state-dependent features</i> of industrial wireless communication systems by defining the proposed model’s transition probabilities as a function of both environments’ states and transmission power. Under the SD-MC model, sufficient conditions on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Maximum Allowable Transmission Interval</i> are presented to ensure both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">asymptotic stability in expectation</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">almost sure asymptotic stability</i> properties of a nonlinear control system with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">state-dependent fading channels</i> . Based on these stability conditions, the codesign problem is then formulated as a constrained polynomial optimization problem (CPOP), which can be efficiently solved using semidefinite programming methods for the case of a two-state SD-MC model. The solutions to such a CPOP represent optimal control and power strategies that optimize the average expected joint costs in an infinite time horizon while respecting the stability constraints. For a general SD-MC model, this article further shows that suboptimal solutions can be obtained from linear programming formulations of the considered CPOP. Simulation results are given to illustrate the efficacy of the proposed codesign scheme.

Scheduling of over-actuated networked control systems

We investigate the scenario where an over-actuated plant is controlled over a network. We concentrate on the effect of two network-induced phenomena: varying transmission intervals and scheduling, in the sense that only one of the actuators receives new data at each transmission instant. We present an emulation-based solution for the controller design, i.e., the controller is first designed to stabilize the origin of the plant ignoring the network and second, the packet-based network is taken into account and conditions on the maximum allowable transmission interval (MATI) and the scheduling protocol are given to preserve the stability of the closed-loop system. Our results are tailored to over-actuated plants leading to significant improvements compared to applying off-the-shelf results available in the literature. In particular, a new model is derived and new conditions on the scheduling protocol are given, which lead to a two-measure stability property for the networked control system. We illustrate how new classes of scheduling protocols can be derived by exploiting over-actuation, which leads to larger MATI bounds compared to applying existing results, as shown on a numerical example.

A Simple Approach to Increase the Maximum Allowable Transmission Interval

When designing Networked Control Systems (NCS), the maximum allowable transmission interval (MATI) is an important quantity, as it provides the admissible time between two transmission instants. An efficient procedure to compute a bound on the MATI such that stability can be guaranteed for general nonlinear NCS is the emulation of a continuous-time controller. In this paper, we present a simple but efficient modification to the well-established emulation-based approach from Carnevale et al. (2007) to derive a bound on the MATI. Whilst only minor technical changes are required, the proposed modification can lead to significant improvements for the MATI bound as compared to Carnevale et al. (2007). We revisit two numerical examples from literature and demonstrate that the improvement may amount to more than 100%.

Network‐based robust performance analysis for uncertain systems interconnected over an undirected graph

SummaryThis article aims at providing tractable conditions of robust performance (RP) analysis for interconnected uncertain system with networked communication, which is composed of heterogeneous uncertain subsystems connected over an undirected graph. Each subsystem communicates with its neighbors through local packet‐based communication network asynchronously and independently. First, the interconnected uncertain system with networked communication is modeled as a hybrid system. Then sufficient conditions in terms of linear matrix inequalities (LMIs), which are related to the interconnection structure and the maximum allowable transmission interval (MATI) of each local network, are derived such that the interconnected uncertain system is robustly asymptotically stable and achieves the desired RP. These conditions only depend on the parameters of individual subsystem and local network. Finally, an example of power system is given to demonstrate the applicability and effectiveness of our results.

Stability analysis for networked control systems with sampling, transmission protocols and input delays

In this paper, the stability problem is investigated for networked control systems. Input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols are considered. A unified framework based on the hybrid systems with memory is proposed to model the whole networked control system. Hybrid systems with memory are used to model hybrid systems affected by delays and permit multiple jumps at a jumping instant. The stability analysis depends on the Lyapunov–Krasovskii functional approaches for hybrid systems with memory and the proposed stability theorem does not need strict decrease of the Lyapunov–Krasovskii functional during jumps. Based on the developed stability theorems, stability conditions for networked control systems are established. An explicit formula is given to compute the maximal allowable transmission interval. In the special case that the networked control system contains linear dynamics, an explicit Lyapunov functional is constructed and stability conditions in terms of linear matrix inequalities (LMI) are proposed. Finally, an example of a chemical batch reactor is given to illustrate the effectiveness of the proposed results.

An Average Allowable Transmission Interval Condition for the Stability of Networked Control Systems

A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with Lyapunov-based analysis techniques for hybrid systems. In virtually all papers that use this framework, bounds in terms of the maximal allowable transmission interval (MATI) are provided to guarantee stability, and performance properties of the NCS. However, having only such a MATI condition is rather restrictive, and unrealistic in practice due to various network effects such as packet losses, leading to conservative bounds. In this article, we therefore consider an alternative condition on the communication instants to better capture the time-varying properties of the transmission intervals. In particular, we propose, in addition to the existence of a MATI, to also impose a bound on the average allowable transmission interval, expressed in terms of a reverse average dwell-time condition on the transmission intervals. We demonstrate by means of a novel Lyapunov-based analysis that stability of the NCS can still be guaranteed under this different condition on the transmission intervals, which can, in addition, lead to a significant improvement of the MATI. The strengths of these new results will be illustrated on a numerical example.

Integral Input-to-State Stability of Networked Control Systems

We investigate integral input-to-state stability (iISS) of nonlinear networked control systems (NCSs). The controller is designed by emulation, i.e., it is constructed to ensure iISS for the closed-loop system in the absence of the network. Afterward, the latter is taken into account and explicit conditions are provided on the scheduling protocol and the maximum allowable transmission interval to preserve iISS for the NCS. The results are applied to two case studies: bilinear systems and neutrally stable linear systems under saturated feedback, where the conditions are formulated as linear matrix inequalities. The effectiveness of the results is further illustrated via a numerical example.

Observer Design for Nonlinear Networked Control Systems With Persistently Exciting Protocols

We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a network, and we provide sufficient conditions on the latter to preserve the stability property of the observer. In particular, we provide a bound on the maximum allowable transmission interval (MATI) that guarantees an input-to-state stability (ISS) property for the corresponding estimation error system. The stability analysis is trajectory-based, utilizes small-gain arguments, and exploits a persistently exciting property of the scheduling protocols. This property is key in our analysis and allows us to obtain significantly larger MATI bounds in comparison to the ones found in the literature. Our results hold for a general class of NCSs; however, we show that these results are also applicable to NCSs implemented over a specific physical network called WirelessHART (WH). The latter is mainly characterized by its multihop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We show that our results can be further improved by taking into account the intrinsic structure of the WH–NCS model. That is, we explicitly exploit the model structure in our analysis to obtain an even tighter MATI bound that guarantees the same ISS property for the estimation error system. Finally, to illustrate our results, we present analysis and numerical simulations for a class of Lipschitz nonlinear systems and high-gain observers.

Formula omitted] stability of networked control systems implemented on WirelessHART

This paper provides results on input–output Lp stability of networked control systems (NCSs) implemented over WirelessHART (WH). WH is a communication protocol widely used in process instrumentation. It is mainly characterised by its multi-hop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We propose a non-linear hybrid model of WH–NCSs that is able to capture these network functionalities, and that it is more general than existing models in the literature. Particularly, the multi-hop nature of the network is translated into an interesting mathematical structure in our model. We then follow the emulation approach to stabilise the NCS. We first assume that we know a stabilising controller for the plant without the network. We subsequently show that, under reasonable assumptions on the scheduling protocol, stability is preserved when the controller is implemented over the network with sufficiently frequent data transmission. Specifically, we provide bounds on the maximum allowable transmission interval (MATI) under which all protocols that satisfy the property of being persistently exciting (PE) lead to Lp stable WH–NCSs. These bounds exploit the mathematical structure of our WH–NCS model, improving the existing bounds in the literature. Additionally, we explain how to schedule transmissions over the hops to satisfy the PE property. In particular, we show how simultaneous transmissions over different frequency channels can be exploited to further enlarge the MATI bound.

Improved estimation on transmission intervals and delays for networked control systems using hybrid systems tools

The work studies the stability problem of networked control systems (NCSs) exposed to various imperfections, including scheduling protocols, transmission intervals, and delays by using hybrid systems tools. First of all, the above-mentioned NCSs are converted into hybrid control systems. Then under a weaker assumption, the authors construct a novel Lyapunov function to derive a less conservative sufficient condition for the uniform global asymptotic stability of the systems. Furthermore, they derive useful upper bounds for the maximum allowable transmission interval and maximum allowable delay, which significantly improve the existing results. Finally, some examples are presented to illustrate the effectiveness of the proposed theorem.

Co-design of safe and efficient networked control systems in factory automation with state-dependent wireless fading channels

In factory automation, heterogeneous manufacturing processes need to be coordinated over wireless networks to achieve safety and efficiency. Wireless networks, however, are inherently unreliable due to shadow fading induced by the physical motion of the machinery. To assure both safety and efficiency, this paper proposes a state-dependent channel model that captures the interaction between the physical and communication systems. By adopting this channel model, sufficient conditions on the maximum allowable transmission interval are derived to ensure stochastic safety for a nonlinear physical system controlled over a state-dependent wireless fading channel. Under these sufficient conditions, the safety and efficiency co-design problem is formulated as a constrained cooperative game, whose equilibria represent optimal control and transmission power policies that minimize a discounted joint-cost in an infinite horizon. It is shown that the equilibria of the constrained game are solutions to a non-convex generalized geometric program, which are approximated by solving two convex programs. The optimality gap is quantified as a function of the size of the approximation region in convex programs, and asymptotically converges to zero by adopting a branch-bound algorithm. Simulation results of a networked robotic arm and a forklift truck are presented to verify the proposed co-design method.

Emulation-based output regulation of linear networked control systems subject to scheduling and uncertain transmission intervals

We investigate output regulation for linear networked control systems using the emulation approach. We consider a regulator solving the problem for linear systems in the absence of the network, by following the Francis-Wonham framework. Next, the network is taken into consideration, in particular the induced time-varying inter-transmission intervals and scheduling constraints, and we model the overall system dynamics as a hybrid system. We show that only practical regulation can be achieved in general since the steady-state control input steering the output to zero cannot be generated in the networked context (in general). Explicit upper bounds on the output asymptotic gain and on the maximum allowable transmission interval guaranteeing boundedness of the closed-loop trajectories are provided, which are shown to be related.

Stability analysis of networked linear control systems with direct-feedthrough terms

We consider networked control systems (NCSs) composed of a linear plant and a linear controller interconnected by packet-based communication channels with communication constraints. We are interested in the setup where direct-feedthrough terms are present in the plant and/or in the controller, a case that is largely ignored in the literature due to its inherent complexity and counterintuitive results in the analysis despite its relevance for important classes of controllers including Proportional–Integral (PI) regulators. This setup calls for a novel stability analysis, for which we take a renewed look at the concept of uniformly globally exponentially stable (UGES) scheduling protocols that turned out to be instrumental in earlier approaches. We provide a generalization of the UGES property, called (DP,DC)-UGES with DP∕DC being the direct-feedthrough matrices of the plant/controller, respectively, and we present generic conditions on these direct-feedthrough terms DP∕DC such that the classical UGES property of scheduling protocols implies (DP,DC)-UGES. This allows us to derive conditions leading to a maximally allowable transmission interval (MATI) such that stability of the overall NCS is guaranteed. In addition, it is shown that it is possible to get more tailored results for the well-known sampled-data (SD), round-robin (RR), and try-once-discard (TOD) protocols leading to less conservative conditions on the direct-feedthrough terms than the generic ones. We also introduce new (DP,DC)-UGES scheduling protocols, designed to handle the direct-feedthrough terms in a more effective way than existing protocols. Our results are illustrated using the example of a batch reactor.

Tracking Control of a Class of Cyber-Physical Systems via a FlexRay Communication Network.

Due to properties of flexibility, adaptiveness, error tolerance, and time-determinism performance, the FlexRay communication protocol has been widely used to investigate robot systems and new generation of automobiles. In this paper, with the FlexRay communication protocol, the tracking problem of a class of cyber-physical systems are investigated by developing a general hybrid model, in which an emulation controller is utilized. Based on the proposed hybrid model, some sufficient conditions are established to guarantee the convergence of tracking errors. Then, the maximum allowable transmission interval (MATI) of the static/dynamic segment is obtained with a more general formula than the ones in some the previous works. The obtained MATI over the FlexRay communication network can be adjusted via the appropriate length of the static/dynamic segment, which reflects the flexibility of FlexRay. Finally, the results are verified by considering the tracking problem of a single-link robot arm system as well as the stabilization of a batch reactor system.

Singularly Perturbed Networked Control Systems

We study networked control systems (NCSs) where the controller is given by a state-feedback law and the plant is modeled by a dynamical system evolving on two time-scales, representing a characterization by some slow and fast dynamics. When using the stability analysis frameworks for NCSs from the literature, this time-scale separation is ignored and, as a result, the slow dynamics are in general updated at the same rate as the fast dynamics, leading to many redundant transmissions of the slow dynamics. Therefore, we assume in this paper that the slow dynamics and fast dynamics can be transmitted separately over the network, allowing us to use techniques inspired by singular perturbation methods in the stability analysis. That is, we show by means of a Lyapunov-based proof how to obtain conditions on the transmission rates (expressed in maximal allowable transmission intervals (MATIs)) for the slow and fast dynamics separately such that stability of the NCS is guaranteed, based only on approximated models of the slow and the fast dynamics.

Network-Aware Design of State-Feedback Controllers for Linear Wireless Networked Control Systems

We study the problem of stabilizing the origin of a plant, modeled as a discrete-time linear system, for which the communication with the controller is ensured by a wireless network. The transmissions over the wireless channel are characterized by the so-called stochastic allowable transmission intervals (SATI), that is a stochastic version of the maximum allowable transmission interval (MATI). Instead of deterministic transmissions, SATI gives stability conditions in terms of the cumulative probability of successful transmission over N steps. We argue that SATI is well-suited for wireless networked control systems to cope both with the stochastic nature of the communications and the design of energy-efficient communication strategies. Our objective is to synthesize a stabilizing state-feedback controller and SATI parameters simultaneously. We model the overall closed-loop system as a Markov jump linear system and we first provide linear conditions for the stability of the wireless networked control systems in a mean-square sense. We then provide linear matrix inequalities conditions for the design of state-feedback controllers to ensure stability of the closed-loop system. These conditions can be used to obtain both the controller and the SATI. A numerical example is presented to illustrate our results.

Stability and Performance Analysis of Spatially Invariant Systems with Networked Communication

In this paper, tractable stability and performance conditions are presented for systems consisting of an infinite number of spatially invariant, i.e., identical subsystems that are described by (non)linear differential equations and interconnected (partly) through packet-based communication networks. These networks transmit packets asynchronously and independently of each other and are equipped with scheduling protocols that determine which actuator, sensor, or controller node is allowed access to the network. The overall system is modeled as an infinite interconnection of spatially invariant hybrid subsystems. To underline the relevance of this framework, it is shown how two well-known and natural system configurations can be captured in this hybrid modeling framework. Moreover, for the resulting overall infinite-dimensional hybrid system, a proper solution concept is introduced, which is necessary as many standard concepts do not apply as Zeno behavior is inevitable for the systems under study. Based on the proposed hybrid modeling framework, conditions leading to a maximally allowable transmission interval (MATI) for all of the individual communication networks are derived such that uniform global asymptotic stability (UGAS) or $\mathcal {L}_{p}$ -stability of the overall system is guaranteed. Interestingly, by exploiting the interconnection structure, the conditions guaranteeing UGAS or $\mathcal {L}_{p}$ -stability can be stated locally in the sense that they only involve the (local) dynamics of one subsystem in the interconnection and local conditions on the scheduling protocol. Finally, it is shown that in the linear case the derived conditions can even be stated in terms of “local” LMIs, making them amenable for computational verification.

Computing Minimal and Maximal Allowable Transmission Intervals for Networked Control Systems Using the Hybrid Systems Approach

A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with hybrid systems analysis techniques. In the rich literature regarding this framework, bounds on the maximally allowable transmission interval (MATI) are provided to guarantee stability properties of the NCS, while the minimal allowable transmission interval (MIATI) is always taken to be (essentially) zero. In this letter, we show for the first time how knowledge of the MIATI can also be exploited in the hybrid systems/emulation-based framework leading to (guaranteed) higher values for the MATI, while still obtaining stability of the NCS.

Observer design for networked control systems with FlexRay

We design state observers for nonlinear networked control systems (NCS) implemented over FlexRay. FlexRay is a communication protocol used in the automotive industry, which has the feature to switch between two scheduling rules during its communication cycles. These switches induce technical difficulties when modeling, designing and analyzing observers for such systems compared to standard NCS. We present a solution based on the emulation approach. Given an observer in the absence of communication constraints, we implement it over the network and we provide sufficient conditions on the latter, to preserve the stability property of the observer. In particular, we provide explicit bounds on the maximal allowable transmission intervals, which adapt to the lengths of the segment associated to each scheduling rule. We assume that the plant dynamics and measurements are affected by noise and we guarantee an input-to-state stability property for the corresponding estimation error system. The overall system is modeled as a hybrid system and the analysis relies on the use of a novel hybrid Lyapunov function.