Performance modeling of networked control systems

Networked control systems (NCS) are in existence for quite some time. The network-induced delays and packet drops; and their effect on control system's performance has been a burning topic for last one decade. Dependability in context of NCS has not got much attention. While it is an important aspect of NCS intended to be used in critical application. The paper reviews the present state of developments in NCS and presents open problems pertaining to dependability of NCS. Solutions to these problems may increase the presence of NCS by many folds and in many fields.

On the use of information quality in stochastic networked control systems

Research on mean square exponential stability of networked control systems with multi-step delay

Based on the controlled process that is linear time-invariant system, the network-induced long time delay is viewed as time-varying parameter uncertainties. The uncertainty parameters model of networked control systems with long time delay is set up. The existing conditions of asymptotic stability for networked control system with long time delay are presented by Lyapunov method and robust control theory. The design method of stabilization controller for networked control system is proposed in terms of linear matrix inequalities. In the end the simulation based on the networked control unstable system is studied. The simulation results show the proposed controller is feasible and effective.

A mathematical model of networked control systems (NCS) with dynamic controllers is presented when the network-induced random time-varying delays of NCS are bounded and the upper bound of which is longer than one sampling period. This paper discretizes the model of continuous-time systems, applies augmented state-space method to the model and builds a discrete-time jump system model governed by a finite state Markov process. And the necessary and sufficient conditions guaranteeing stability of the system are discussed. This paper applies interior-point algorithm to design stabilizing controllers, presents a method to get the feasible initial solution and replaces Newton direction which is generally used in the interior-point algorithm with conjugate gradient direction for simplifying the algorithm. And this improved algorithm stated above is applied effectively to the networked control system of a cart and inverted pendulum with long delays.

Packet loss in a networked control system (NCS) is a stochastic event that depends on the current network state, which, as an abstract and hidden variable, can not be well defined but can be perceived by the observation of the packet-loss process. We model the network in an NCS as a Markov chain and the packet losses as stochastic events whose probability depends on the Markov chain state (i.e. network state). Thus, the network state estimation is a hidden Markov model (HMM) estimation problem. To derive the HMM of the NCS under study, we propose the expectation maximization (EM) algorithm to estimate the parameters of the HMM based on the packet dropping sequence. Finally, a simulation example illustrates the effectiveness of the proposed approach.

A new model for networked control systems (NCSs) with structured uncertainties and multiple state time-delays is presented, In view of multi-input and multi-output (MIMO) NCSs with many independent sensors and actuators, a continuous time model of NCSs with distributed time-delays and uncertainties are proposed. A method of delay-estimation online is also given. Then a scheme based on LQG controller is designed to achieve desired Real-time performance. The result illustrate that the effectiveness of the proposed control design and the satisfactory performance of the system.

Driven by recent telecommunication demand, shared communication channels are more abundant today than ever before. These shared wired/wireless networks for communication are being exploited more and more in control systems to connect sensors, controllers and actuators resulting in so-called networked control systems (NCSs). NCSs replace the more traditional control systems where dedicated point-to-point (wired) connections are being used. The advantages of using NCS technology are inexpensive and easily modifiable communication links which allow control algorithms to be easily implemented in situations where dedicated connections are not possible (either economically or physically). However, the drawback is that the control system is susceptible to undesirable (possibly destabilizing) side-effects such as time-varying transmission intervals, time-varying delays, packet dropouts, quantization and a shared communication medium. These network-induced effects undermine fundamental assumptions on which traditional control theory is built and, therefore, it is essential to develop new techniques and tools that can be used to analyze and/or design control systems which communicate via a shared network. This thesis advances NCS analysis and design methodologies by contributing new theoretical developments, new software tools and new experimental validation results. The first new theoretical development is in the area of analyzing robust stability properties with respect to network-induced effects. A sum of squares (SOS) approach for a class of nonlinear NCSs incorporating bounded time-varying delays, bounded time-varying transmission intervals and a shared communication medium is developed. Mathematical models that describe these nonlinear NCSs are cast into suitable hybrid system formulations. Based on these hybrid system formulations, (families of) Lyapunov functions are constructed using SOS techniques. Amongst other benefits, it is shown that this technique improves the guaranteed robustness margins compared to existing work. The second new theoretical development concerns the design of networkaware decentralized controllers guaranteeing robust stability properties with respect to network-induced effects. We develop one of the first approaches based on semidefinite programming techniques to synthesize stabilizing decentralized observer-based output-feedback controllers for linear plants where the controllers, sensors and actuators are connected via a shared communication network subject to time-varying transmission intervals and delays. To effectively deal with the shared communication medium, a switched observer structure is adopted that switches based on the transmitted measured outputs and a switched controller structure is also adopted that switches based on the transmitted control inputs at each transmission time. By taking a discrete-time switched linear system perspective on modeling these decentralized NCSs, we are able to derive a general model that captures all these networked and decentralized control aspects. We provide linear matrix inequality (LMI)-based synthesis conditions which, if satisfied, provide stabilizing observer-based controllers that are both decentralized and robust to network effects. Regarding new software tools, the first prototype of a toolbox is developed to automate (robust) stability analysis (and controller design) for NCSs. Specifically, it is shown that the toolbox can be employed to efficiently verify if a linear time-invariant (LTI) plant and an LTI controller interconnected with a shared network are robust to certain network imperfections. The main intention of the toolbox is to make the available theory readily accessible to and applicable for the general control community. Additionally, the chosen software structure enables the incorporation of custom models or custom stability/performance analysis conditions in an easy manner, thereby allowing the control community to contribute and to further develop the toolbox. Finally, an experimental case study involving a wirelessly controlled inverted pendulum/cart system is investigated. In particular, the communication network itself is analyzed such that the network-induced effects can be characterized in terms of bounds on the transmission intervals and transmission delays. Based on these bounds, the prototype toolbox is applied to analyze the robustness regions for different performance specifications, which aid in tuning the controller to achieve more closed-loop robustness with respect to the network-induced effects. This leads to a validation of the developed theory in an experimental setting. In addition to the validation of the developed theory, many new insights into the network behavior are obtained and explained, thereby raising new interesting questions for future research on NCSs.

Periodic event-triggered control for networked control systems based on non-monotonic Lyapunov functions

A new approach to exponential stabilization for a class of nonlinear networked systems with stochastic delays is given in this paper. By using the fuzzy T-S method, a new model of nonlinear networked control systems with is derived. The networked induced delays are assumed to have some stochastic characteristics. A stochastic variable satisfying Bernoulli distribution is introduced with the probability of the delays taking value in different interval. With the Lyapunov stability theorem, a exponential stabilization condition and a state feedback controller design method are obtained. And all the conditions are expressed in terms of LMI. Finally, a numerical example is given to demonstrate the validity of the results.

This paper concerns the problem of the model, stability and controller design for networked control system (NCS) with time-varying delay and dropped out packet. For the NCS with time-varying delay and data packet dropout, four new control methods of dynamical state feedback control, dynamical state feedback proportional-integral (PI) control, state feedback proportional-derivative (PD) control and dynamical state feedback PD control are presented. The NCS with time-varying delay and data packet dropout based on the four control methods is modeled as an asynchronous dynamical system (ADS) constrained by event rates. Furthermore, based on the ADS theory, principle of Lyapunov stability and method of linear matrix inequality, both the semi-negative definite matrix conditions of exponential stability and the controller design for NCS are given. Finally, numerical example illustrates the feasibility of the results.

International audience

A new method for modeling and analysis of networked control systems with time delay using hidden Markov models is presented. The optimal estimator of system state for networked control systems without full state information is given when the networked induced time delay is governed by an underlying Markov chain. The design of stochastic optimal controllers of networked control systems with output feedback is also presented. The result of simulation verified the efficiency and correction of the proposed methods.

Modeling and analysis of networked control systems using stochastic hybrid systems

We study stabilization problems for networked control systems (NCSs) with asymmetric information. In this NCSs model, the remote controller can receive packet-dropout states of the plant, and the available information for the embedded controller are observations of states and packet-dropout states sent from the remote controller. It is shown that the system is bounded in the mean-square sense if and only if there exist the solutions to the two coupled algebraic Riccati equations and the packet-dropout probability satisfies certain condition.