Panos J. Antsaklis

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

Control and Communication Challenges in Networked Real-Time Systems

A current survey of the emerging field of networked control systems is provided. The aim is to introduce the fundamental issues involved in designing successful networked control systems, to provide a snapshot assessment of the current state of research in the field, to suggest useful future research directions, and to provide a broad perspective on recent fundamental results. Reflecting the goals of the Special Issue itself, this paper surveys relevant work from the areas of systems and control, signal processing, detection and estimation, data fusion, and distributed systems. We discuss appropriate network architectures, topics such as coding for robustly stable control in the presence of time-varying channel capacity, channels with fixed versus adaptively variable data width, issues in data rate problems in nonlinear feedback problems, and problems in routing for stability and performance. In surveying current research on networked control systems, we find that recent theoretical advances and target applications are intimately intertwined. The common goal of papers in the Special Issue which follows is to describe key aspects of this relationship. We also aim to provide a bridge between networked control systems and closely related contemporary work dealing with sensor networks and wireless communication protocols

Brief On the model-based control of networked systems

In this paper the control of linear plants, where the sensor is connected to a linear controller/actuator via a network is addressed. Both, state and output feedback, are considered and results are derived for both continuous and discrete plants. A key idea is that knowledge of the plant dynamics is used to reduce the usage of the network. Necessary and sufficient conditions for stability are derived as simple eigenvalue tests of a well-structured test matrix, constructed in terms of the update time h, and the parameters of the plant and of its model. These tests are extended to include network delay as well.

Stability of model-based networked control systems with time-varying transmission times

In model-based networked control systems (MB-NCSs), an explicit model of the plant is used to produce an estimate of the plant state behavior between transmission times. In this paper, the stability of MB-NCSs is studied when the controller/actuator is updated with the sensor information at nonconstant time intervals. Networked control systems with transmission times that are varying either within a time interval or are driven by a stochastic process with identically independently distributed and Markov-chain driven transmission times are studied. Sufficient conditions for Lyapunov stability are derived. For stochastically modeled transmission times almost sure stability and mean-square sufficient conditions for stability are introduced.

Optimal control of switched systems based on parameterization of the switching instants

This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a prespecified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. In order to search for the optimal switching instants, the derivatives of the optimal cost with respect to the switching instants need to be known. The most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state, costate, stationarity equations, the boundary and continuity conditions, along with their differentiations. This method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed. An extension of the method is also applied to problems with internally forced switching. Examples are shown to illustrate the results in the paper.

Neural networks for control systems

A description is given of 11 papers from the April 1990 special issue on neural networks in control systems of IEEE Control Systems Magazine. The emphasis was on presenting as varied and current a picture as possible of the use of neural networks in control. The papers described cover: the design of associative memories using feedback neural networks; a method to use neural networks to control highly nonlinear systems; the modeling of nonlinear chemical systems using neural networks; the identification of dynamical systems; the comparison of conventional adaptive controllers and neural-network-based controllers; a method to provide adaptive control for nonlinear systems; neural networks and back-propagation; the back-propagation algorithm; the use of trained neural networks to regulate the pitch attitude of an underwater telerobot; the control of mobile robots; and the issues involved in integrating neural networks and knowledge-based systems.

Supervisory Control of Discrete Event Systems Using Petri Nets

From the Publisher: Supervisory Control of Discrete Event Systems Using Petri Nets presents a novel approach for the supervisory control of discrete event systems using Petri nets. The concepts of supervisory control and discrete event systems are explained, and the background material on general Petri net theory necessary for using the books control techniques is provided. A large number of examples are used to illustrate the concepts and techniques presented in the text, and there are plenty of references for those interested in additional study or more information on a particular topic. Supervisory Control of Discrete Event Systems Using Petri Nets is intended for graduate students, advanced undergraduates, and practicing engineers who are interested in the control problems of manufacturing, communication and computer networks, chemical process plants, and other high level control applications.

Stability of the pseudo-inverse method for reconfigurable control systems

Abstract One of the key reconfigurable control methods, the pseudo-inverse method (PIM), is analysed and new insight is obtained which provides the theoretical basis for this practical approach. The main shortcoming of this method, the lack of stability guarantees, is pointed out and a new approach is proposed in which recent results on the stability robustness of linear systems are used to provide stability constraints for the solutions of the PIM. When the original PIM solution results in an unstable closed-loop system, the control redesign problem is treated as a constraint minimization problem. For single-input systems, a closed-form solution is presented; for multi-input systems, a near-optimal solution is found which maintains the stability of the closed-loop system.

Design of a wireless assisted pedestrian dead reckoning system - the NavMote experience

In this paper, we combine inertial sensing and sensor network technology to create a pedestrian dead reckoning system. The core of the system is a lightweight sensor-and-wireless-embedded device called NavMote that is carried by a pedestrian. The NavMote gathers information about pedestrian motion from an integrated magnetic compass and accelerometers. When the NavMote comes within range of a sensor network (composed of NetMotes), it downloads the compressed data to the network. The network relays the data via a RelayMote to an information center where the data are processed into an estimate of the pedestrian trajectory based on a dead reckoning algorithm. System details including the NavMote hardware/software, sensor network middleware services, and the dead reckoning algorithm are provided. In particular, simple but effective step detection and step length estimation methods are implemented in order to reduce computation, memory, and communication requirements on the Motes. Static and dynamic calibrations of the compass data are crucial to compensate the heading errors. The dead reckoning performance is further enhanced by wireless telemetry and map matching. Extensive testing results show that satisfactory tracking performance with relatively long operational time is achieved. The paper also serves as a brief survey on pedestrian navigation systems, sensors, and techniques.

Supervisory control of hybrid systems

In this paper, the supervisory control of hybrid systems is introduced and discussed at length. Such control systems typically arise in the computer control of continuous processes, for example, in manufacturing and chemical processes, in transportation systems, and in communication networks. A functional architecture of hybrid control systems consisting of a continuous plant, a discrete-event controller, and an interface is used to introduce and describe analysis and synthesis concepts and approaches. Our approach highlights the interaction between the continuous and discrete dynamics, which is the cornerstone of any hybrid system study. Discrete abstractions are used to approximate the continuous plant. Properties of the discrete abstractions to be appropriate representations of the continuous plant are presented, and important concepts such as determinism and controllability are discussed. Supervisory control design methodologies are presented to satisfy control specifications described by formal languages. Several examples are used throughout the paper to illustrate our approach.