Michael J. McCourt

Control of cyberphysical systems using passivity and dissipativity based methods

Abstract In cyberphysical systems, where compositionality of design is an important requirement, passivity and dissipativity based design methods have shown a lot of promise. Although these concepts are classical, their application to cyberphysical systems poses new and interesting challenges. The aim of this paper is to summarize some of the on-going work in this area by the authors.

On relationships among passivity, positive realness, and dissipativity in linear systems ✩

The notions of passivity and positive realness are fundamental concepts in classical control theory, but the use of the terms has varied. For LTI systems, these two concepts capture the same essential property of dynamical systems, that is, a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment. This paper summarizes the connection between these two concepts for continuous and discrete time LTI systems. Beyond that, relationships are provided between classes of strictly passive systems and classes of positive real systems. The more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy-based results. The frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity. After surveying relevant existing results, some clarifying results are presented. These involve connections between classes of passive systems and finite-gain L2L2 stability as well as asymptotic stability. Additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results. This paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts.

Control design for switched systems using passivity indices

This paper presents a framework for control design of interconnected nonlinear switched systems using passivity and passivity indices. Background material is presented on the concept of passivity indices for continuously-varying systems. The passivity indices are then generalized to apply to switched systems to measure the level of passivity in a system. The main result of the paper shows how the indices can be compared between two systems in feedback to verify stability. It is explained how this theorem can be used as a control design tool for general nonlinear switched systems. An example is provided to demonstrate this design method. The connection between passivity indices and conic systems theory is summarized in the appendix.

Stability of interconnected switched systems using QSR dissipativity with multiple supply rates

This paper considers a notion of QSR dissipativity for discrete-time switched systems that uses multiple supply rates. The focus on switched systems is motivated by cyber physical systems (CPS) where physical dynamics interact with discrete-event or logical dynamics. The notion of QSR dissipativity used in this paper is based on previous work on QSR dissipativity for non-switched systems and decomposable dissipativity for switched systems. The notion of QSR dissipativity is well established for non-switched systems and generalizes many system results including both the passivity theorem and the small gain theorem. In decomposable dissipativity, separate supply rates are developed for each subsystem depending on whether it is currently active or inactive. This paper presents this definition of QSR dissipativity for switched systems and then uses it to prove stability for single systems and interconnected systems. Beyond stability, the dissipative property for interconnected systems is shown. This allows for large scale systems to be studied using successive dissipative assessments. When considering passive systems, these results are studied in more detail.

Passivity and stability of switched systems under quantization

Passivity theory is a well-established tool for analysis and synthesis of dynamical systems. Recently, this work has been extended to switched and hybrid systems where passivity and stability results of single systems as well as interconnected systems are derived. However, the results may no longer hold when quantization is present as is the case with digital controllers or communication channels. The contribution in this paper is to introduce a control framework under which passivity for switched and non-switched systems can be maintained. This framework centers on the use of an input-output coordinate transformation to recover the passivity property. In order to present these results, background material is provided on passive quantization and output strict passivity for switched and non-switched systems. The proposed framework is first presented for non-switched systems and then generalized to switched systems.

Stability of networked passive switched systems

In this paper the problem of controlling nonlinear switched systems over a network with time-varying delay is addressed. The solution presented is an extension of results from the control of continuously-varying passive systems over a network using the wave variable transformation. Background material is presented on passivity and the wave variable transformation. The concept of passivity for switched systems is also covered in this paper. Stability results are then shown for passive switched systems connected over a network with time-varying delay.

Human-autonomy sensor fusion for rapid object detection

Human-autonomy sensor fusion is an emerging technology with a wide range of applications, including object detection/recognition, surveillance, collaborative control, and prosthetics. For object detection, humans and computer-vision-based systems employ different strategies to locate targets, likely providing complementary information. However, little effort has been made in combining the outputs of multiple autonomous detectors and multiple human-generated responses. This paper presents a method for integrating several sources of human- and autonomy-generated information for rapid object detection tasks. Human electroencephalography (EEG) and button-press responses from rapid serial visual presentation (RSVP) experiments are fused with outputs from trained object detection algorithms. Three fusion methods-Bayesian, Dempster-Shafer, and Dynamic Dempster-Shafer-are implemented for comparison. Results demonstrate that fusion of these human classifiers with computer-vision-based detectors improves object detection accuracy over purely computer-vision-based detection (5% relative increase in mean average precision) and the best individual computer vision algorithm (28% relative increase in mean average precision). Computer vision fused with button press response and/or the XDAWN + Bayesian Linear Discriminant Analysis neural classifier provides considerable improvement, while computer vision fused with other neural classifiers provides little or no improvement. Of the three fusion methods, Dynamic Dempster-Shafer Theory (DDST) Fusion exhibits the greatest performance in this application.

Determining Passivity Using Linearization for Systems With Feedthrough Terms

In this technical note, we consider the following problem: what passivity properties for a nonlinear system can be inferred when its linearization around an equilibrium point is known to be passive. We consider both continuous-time and discrete-time systems with feedthrough terms. Our main results show that when the linearized model is simultaneously strictly passive and strictly input passive, the nonlinear system is passive as well within a neighborhood of the equilibrium point around which the linearization is done.

Information fusion in human-robot collaboration using neural network representation

In this paper, an algorithm for hard and soft data fusion is developed for tracking moving objects using hard data from sensors on autonomous agents and soft data from human observations. Two main challenges are identified and addressed in this paper: 1. how to model the human observation, 2. how to estimate state using soft data and fuse it with the state estimates from the sensors on autonomous agents (e.g., a camera sensor). A novel approach is developed to model perceived human observations to the real physical states using artificial neural networks (ANN). A particle filter (PF) is used to estimate a moving targets state based on range and bearing observation data from a human observer and an EKF is used to estimate the target state using on-board camera sensor. The range measurement is represented using Kumaraswamys double bounded distribution. The state estimates computed based on a model of human observation learned by an ANN are fused with the state estimates from the on-board sensors using a fast covariance intersection (CI) algorithm. The CI algorithm yields consistent fused estimates in the absence of unknown correlations between state estimates obtained using human measurements and robot sensor measurements. The performance of the developed algorithms is validated on a target tracking simulation platform.

Model-based event-triggered control of nonlinear dissipative systems

The Model-Based Networked Control System (MB-NCS) framework can be used to improve performance in applications where communication rates are limited. This framework has been studied for linear systems with state feedback, but little has been done for the nonlinear case or for the output feedback case. This paper approaches the problem of networking discrete-time nonlinear systems in the MB-NCS framework by using dissipativity theory and output feedback measurements. By combining the MB-NCS approach and aperiodic event-triggered updates, the NCS may operate open loop for long time intervals. Additionally, this paper considers model uncertainties and non-vanishing input disturbances as these factors can be destabilizing in the absence of continuous feedback. While these issues can be mitigated, traditional notions of stability are simply not achievable. The main contribution of this paper is a boundedness result on the system output with a constructive bound. The bound is guaranteed despite the presence of aperiodic updates, model uncertainties, and input disturbances.