Dragan Nesic

Input-output stability properties of networked control systems

Results on input-output L/sub p/ stability of networked control systems (NCS) are presented for a large class of network scheduling protocols. It is shown that static protocols and a recently considered dynamical protocol called try-once-discard belong to this class. Our results provide a unifying framework for generating new scheduling protocols that preserve L/sub p/ stability properties of the system if a design parameter is chosen sufficiently small. The most general version of our results can be used to treat NCS with data packet dropouts. The model of NCS and, in particular, of the scheduling protocol that we use appears to be novel and we believe that it will be useful in further study of these systems. The proof technique we use is based on the small gain theorem and it lends itself to an easy interpretation. We prove that our results are guaranteed to be better than existing results in the literature and we illustrate this via an example of a batch reactor.

Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations

Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.

Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

On non-local stability properties of extremum seeking control

In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.

A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models

A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.

Input-to-state stability of networked control systems

A new class of Lyapunov uniformly globally asymptotically stable (UGAS) protocols in networked control systems (NCS) is considered. It is shown that if the controller is designed without taking into account the network so that it yields input-to-state stability (ISS) with respect to external disturbances (not necessarily with respect to the error that will come from the network implementation), then the same controller will achieve semi-global practical ISS for the NCS when implemented via the network with a Lyapunov UGAS protocol. Moreover, the ISS gain is preserved. The adjustable parameter with respect to which semi-global practical ISS is achieved is the maximal allowable transfer interval (MATI) between transmission times.

Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems

Abstract We provide an explicit KL stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the KL estimate for the corresponding discrete-time system and a K function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [1] or extend some results in [4] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.

A Unified Framework for Design and Analysis of Networked and Quantized Control Systems

We generalize and unify a range of recent results in quantized control systems (QCS) and networked control systems (NCS) literature and provide a unified framework for controller design for control systems with quantization and time scheduling via an emulation-like approach. A crucial step in our proofs is finding an appropriate Lyapunov function for the quantization/time-scheduling protocol which verifies its uniform global exponential stability (UGES). We construct Lyapunov functions for several representative protocols that are commonly found in the literature, as well as some new protocols not considered previously. Our approach is flexible and amenable to further extensions which are briefly discussed.

Stability of Wireless and Wireline Networked Control Systems

This paper provides a general framework for analyzing the stability of general nonlinear networked control systems (NCS) with disturbances in the setting of stability. Our presentation provides sharper results for both gain and maximum allowable transfer interval (MATI) than previously obtainable and details the property of uniformly persistently exciting scheduling protocols. This class of protocols was shown to lead to stability for high enough transmission rates and were a natural property to demand, especially in the design of wireless scheduling protocols. The property is used directly in a novel proof technique based on the notions of vector comparison and (quasi)-monotone systems. We explore these results through analytical comparisons to those in the literature, as well as through simulations and numerical comparisons that verify that the uniform persistence of excitation property of protocols is, in some sense, the ldquofinestrdquo property that can be extracted from wireless scheduling protocols.

Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems

The purpose of this note is to apply recent results on stabilization of networked control systems to obtain an explicit formula for the maximum allowable sampling period (MASP) that guarantees stability of a nonlinear sampled-data system with an emulated controller. Such formulas are of great value to control practitioners.