Mohamed El Mongi Ben Gaid

Optimal integrated control and scheduling of networked control systems with communication constraints: application to a car suspension system

This brief addresses the problem of the optimal control and scheduling of networked control systems over limited bandwidth deterministic networks. Multivariable linear systems subject to communication constraints are modeled in the mixed logical dynamical (MLD) framework. The translation of the MLD model into the mixed integer quadratic programming (MIQP) formulation is described. This formulation allows the solving of the optimal control and scheduling problem using efficient branch and bound algorithms. Advantages and drawbacks of online and offline scheduling algorithms are discussed. Based on this discussion, a computationally efficient online scheduling algorithm, which can be seen as a compromise, is presented and its performance is evaluated. Finally, this algorithm, called optimal pointer placement (OPP) scheduling algorithm, is applied to the control and scheduling of a car suspension system.

MODEL PREDICTIVE CONTROL OF SYSTEMS WITH COMMUNICATION CONSTRAINTS

Abstract This paper addresses the problem of the on-line scheduling of a limited communication resource in order to optimize the control performance. A multivariable linear system with communication constraints is modeled in the Mixed Logical Dynamical (MLD) framework. The system is controlled using a Model Predictive Controller (MPC), which computes, at each sampling period, the appropriate control values and network allocation. The performance of the controlled system is evaluated using a Linear-Quadratic cost function. At each step, the MPC needs to solve an optimization problem, including logic constraints. The translation of this problem into the Mixed Integer Quadratic Programming (MIQP) formulation is described. Finally, using a numerical example, the relationship between the state variables of the plant and the resultant allocation of the communication resource is investigated.

Efficient utilization of bus idle times in CAN-based networked control systems

Abstract This paper presents a novel approach to networked control systems (NCS) analysis and design that provides increased control performance for a set of control loops that exchange control data over the Controller Area Network (CAN). This is achieved by enabling the following functionality for each control loop: first, standard periodic messaging is guaranteed to ensure stability, and second, non-periodic additional messaging is added whenever the bus is idle in such a way that the aggregated control performance for all control loops is improved. The proposed approach, named Maximum Difference (MD) policy, is computable in a distributed manner, and is practically feasible (computationally efficient and CAN-implementable). We theoretically prove that the MD policy behaves better than static strategies. Simulation results complement the theoretical derivations and show that the MD policy outperforms static, random and Largest Error First policies.

Discussion on: "A Control Based Solution for Integrated Dynamic Capacity Assignment, Congestion Control and Scheduling in Wireless Networks''

This paper is a contribution in the emerging domain of control, computing and networking co-design. More specifically it presents a closed-loop control design to guarantee the Quality of Service (QoS) for a set of wireless-based networked nodes. The proposed design jointly handles several sub-objectives, i.e. dynamic capacity assignment, congestion control and scheduling packets on links, to maximize a cost function as the overall objective. As usual, control design involves several steps such as the formalization of the control objective, the choice of a suitable abstraction (model) of the system, the identification of the available and significant output signals that can be used for control purpose (sensors and probes) and the selection of the actuators able to modify the system’s state. Note that when the plant is made of computing devices, sensors and actuators are software probes and functions which can be implemented at a moderate cost. However making such control system effective needs to keep the control complexity and associated communication induced overheads low compared with a statically tuned system, as the control related budget is a part of the overall computing and networking cost. Indeed control theoretic approaches are traditionally based on models of the addressed plant. A model (often a set of differential or difference equations) is first chosen. Then, an identification phase is undertaken in order to experimentally determine the model parameters. Control design is performed based on the identified model, and using well known control design methodologies. For example, in control approaches for computing systems, e.g. [5], queuing processes modeling introduces dynamics in the computing system model. Existing modeling frameworks has been reused to model computing and networking devices, e.g. linear models and fluid modeling. Beyond linear models, non-linear models has been successively used to better handle and control undesirable phenomena like trashing [7]. However, conversely with the traditional targets of control systems, e.g. mechanics or electrical systems involving complex dynamics, computing systems such as stacks of tasks to be executed or messages to be transmitted often have a static (or a simple dynamic) behavior. Thus modeling w.r.t. dynamic aspects can be kept elementary, as in this paper where the control laws (for congestion avoidance and for air interface assignment) are build step by step to satisfy the involved quality of service requirements. Understanding the dynamics of the addressed phenomena (if any) is disregarded in this paper. The proposed approach only relies on the knowledge of plant inputs and outputs, and on well known constraints (and cost functions) which are related to the QoS satisfaction. Therefore it might be seen as a model free control approach. The main contribution is to handle jointly two different problems using a hierarchical and coordinated control structure. The proposed approach may be seen as a heuristic to this difficult QoS formalization and solving problem. The communication load

Discussion on: “Stabilization of Networked Control System with Time Delays and Data-packet Losses”

The paper by Kun Ji and Won-Jong Kim studies theproblem of the control of dynamic systems calledNetworked Control Systems (NCS) where sensors,actuators and controllers are interconnected over acommunication network. It mainly focuses on theapplicationofthetheoreticalresultsobtainedby[1]onthe ball-maglev system test bed. It may be viewed as asimple teaching benchmark, which gives us someinteresting insight concerning the handling of dis-tributed information and decision making using NCS.The authors consider different models of com-munication constraints one has to face in NCS suchas stochastic network-induced bounded delays, data-packet losses and out-of-order data-packet transmis-sion. Although these models correspond mostly to softreal-time networks, the raised problem is very inter-estingandhasattractedtheattentionoftheresearchersin control community.We prefer to open the discussion without limitingit to point-to-point control applications. There aremanyapplicationsthatcorrespondtothisarchitecturesuch as remote-control of embedded systems withlimited processing power and dedicated communica-tion channel. We may consider that the network andprocessor nodes are shared by different applicationsand that the chosen architecture acts as a part of theproblem solution.The NCS architecture chosen for study is a verysimple one consisting of three nodes. The sensor andactuator nodes are located at the plant side of NCS,and the controller node communicates with themthrough a TCP/IP network. The time-driven model ischosen to describe the sensor and actuator activities,whereas an event-driven model is applied to the con-troller node. These temporal models associated to eachnode, which are part of information communicationmodels associated to the overall distributed system,determine the flexibility and delay-compensation pro-perties of the prediction algorithm. The basic ideais that the controller node sends the current controlu(k) as well as an array of predicted control inputsð^uðk þ 1jkÞ, ...,u^ðk þ pjkÞÞ to the actuators. In thesituation were the actuators do not receive the controlinput u(k