Payam Naghshtabrizi

A Survey of Recent Results in Networked Control Systems

Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

Exponential stability of impulsive systems with application to uncertain sampled-data systems

We establish exponential stability of nonlinear time-varying impulsive systems by employing Lyapunov functions with discontinuity at the impulse times. Our stability conditions have the property that when specialized to linear impulsive systems, the stability tests can be formulated as Linear Matrix Inequalities (LMIs). Then we consider LTI uncertain sampled-data systems in which there are two sources of uncertainty: the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable. We model such systems as linear impulsive systems and we apply our theorem to the analysis and state-feedback stabilization. We find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed. The control design LMIs also provide controller gains that can be used to stabilize the process. We also consider sampled-data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals.

Designing an observer-based controller for a network control system

We propose a numerical procedure to design a linear output-feedback controller for a remote linear plant in which the loop is closed through a network. The controller stabilizes the plant in the presence of delay, sampling, and dropout effects in the measurement and actuation channels. We consider two types of control units: anticipative and non-anticipative. In both cases the closed-loop system with delay, sampling and packet dropout effects can be modeled as a delay differential equation. Our method of designing the controller is based on the Lyapunov-Krasovskii theorem and a linear cone complementarity algorithm. Numerical examples show that our method is significantly better than the existing ones.

On the robust stability and stabilization of sampled-data systems: A hybrid system approach

We consider the stability analysis and state-feedback stabilization of LTI uncertain sampled-data systems. There are two sources of uncertainty: the plants parameters can be uncertain and the sampling intervals can be unknown and variable. We model the sampled-data system as a hybrid system and we employ a Lyapunov function with discontinuities to establish the stability of the system. Our stability and stabilization results are presented as linear matrix inequalities (LMIs). By solving these LMIs, one can find a positive constant which determines an upper bound on the sampling intervals such that the stability of the closed-loop is guaranteed. The control design LMIs also provide controller gains that can be used to stabilize a given process. To reduce the conservativeness we use slack matrices; however, we require a smaller number of slack matrices than in the previous results and we show that we have done it without making the results more conservative. As a special case we consider sampled-data systems with constant sampling intervals and provide results for this class of systems that are less conservative than the ones obtained for the general case of variable sampling time

Stability of Delay Impulsive Systems with Application to Networked Control Systems

We establish asymptotic and exponential stability theorems for delay impulsive systems by employing Lyapunov functionals with discontinuities. Our conditions have the property that when specialized to linear delay impulsive systems, the stability tests can be formulated as linear matrix inequalities (LMIs). Then we consider networked control systems (NCSs) consisting of an LTI process and a static feedback controller connected through a communication network. Due to the shared and unreliable channels, sampling intervals are uncertain and variable. Moreover, samples may be dropped and experience uncertain and variable delays before arriving at the destination. We show that the resulting NCSs can be modeled by linear delay impulsive systems and we provide conditions for stability of the closed-loop in terms of LMIs. By solving these LMIs, one can find a positive constant that determines an upper bound between a sampling time and the subsequent input update time, for which stability of the closed-loop system is guaranteed.

Stability of delay impulsive systems with application to networked control systems

We establish asymptotic and exponential stability theorems for delay impulsive systems by employing Lyapunov functionals with discontinuities. Our conditions have the property that when specialized to linear delay impulsive systems, the stability tests can be formulated as Linear Matrix Inequalities (LMIs). Then we consider Networked Control Systems (NCSs) consisting of an LTI process and a static feedback controller connected through a communication network. Due to the shared and unreliable channels, sampling intervals become uncertain and variable. Moreover, samples may be dropped or experience uncertain and variable delays before arriving at the destination. We show that the resulting NCSs can be modelled by linear delay impulsive systems and we provide conditions for stability of the closed-loop system in terms of LMIs. By solving these LMIs, one can find a positive constant that determines an upper bound between each sampling time and the subsequent input update time, for which stability of the closed-loop system is guaranteed.

Analysis of distributed control systems with shared communication and computation resources

We address the analysis and implementation of a distributed control system on a network of communicating control units, resulting in a Networked Control System (NCS). We propose an approach based on three steps: control system analysis in terms of sampling times and delays, mapping of control loops to computation/communication hardware components, and scheduling analysis. This procedure is especially important for applications that place a heavy load on the available computation and communication resources and finds direct application in FlexRay control networks.

Designing transparent stabilizing haptic controllers

This paper addresses the design of controllers for haptic systems that are both stable and transparent. Stability refers to the property that the control system should not introduce oscillations felt in the haptic device by the human operator. Transparency refers to the property that the haptic system should faithfully reproduce the dynamics of the virtual environment. We propose a design methodology that converts the problem of maximizing transparency, while guaranteeing stability, into a set of matrix inequalities. Then we propose a numerical procedure to solve the matrix inequalities based on the cone complementarity algorithm. With this formulation one can also incorporate other design tasks, such as robustness to parameter variations, by introducing additional norm conditions and solving Hinfin or mixed norm problems. A numerical example is used to illustrate the design methodology

Implementation Considerations For Wireless Networked Control Systems

We show that delay impulsive systems are a natural framework to model wired and wireless NCSs with variable sampling intervals and delays as well as packet dropouts. Then, we employ discontinuous Lyapunov functionals to characterize admissible sampling intervals and delays such that exponential stability of NCS is guaranteed. These results allow us to determine requirements needed to establish exponential stability, which is the most basic Quality of Performance (QoP) required by the application layer. Then we focus on the question of whether or not the Quality of Service (QoS) provided by the wireless network suffices to fulfill the required QoP. To answer this question, we employ results from real-time scheduling and provide a set of conditions under which the desired QoP can be achieved.

Distance Until Charge prediction and fuel economy impact for Plug-in Hybrid Vehicles

For a Plug-in Hybrid-Electric Vehicle (PHEV) a close to linear battery depletion profile is near optimal in terms of fuel economy, given that the driven Distance Until Charge (DUC) is known. However the intended driven distance until charge is not always known. We propose a pattern recognition method to predict the DUC based on the key-on time and day observations and the on-board stored data in vehicle. We review the energy management strategy and we show a fuel economy improvement despite prediction errors.