There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations

/pdf/consensus-and-cooperation-in-networked-multi-agent-systems-5ame7z72ny.pdf

Consensus and Cooperation in Networked Multi-Agent Systems

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

System Identification I

Dynamics of structures

http://www.egr.msu.edu/~xbtan/Papers/Journal/2004/Automatica04_MagnetoHys.pdf

Modeling and control of hysteresis in magnetostrictive actuators

In this paper, a physics-based model is proposed for a biomimetic robotic fish propelled by an ionic polymer-metal composite (IPMC) actuator. Inspired by the biological fin structure, a passive plastic fin is further attached to the IPMC beam. The model incorporates both IPMC actuation dynamics and the hydrodynamics, and predicts the steady-state cruising speed of the robot under a given periodic actuation voltage. The interactions between the plastic fin and the IPMC actuator are also captured in the model. Experimental results have shown that the proposed model is able to predict the motion of robotic fish for different tail dimensions. Since most of the model parameters are expressed in terms of fundamental physical properties and geometric dimensions, the model is expected to be instrumental in optimal design of the robotic fish.

Modeling of Biomimetic Robotic Fish Propelled by An Ionic Polymer–Metal Composite Caudal Fin

Hysteresis hinders the effective use of smart materials in sensors and actuators. This paper addresses recursive identification and adaptive inverse control of hysteresis in smart material actuators, where hysteresis is modeled by a Preisach operator with a piecewise uniform density function. Two classes of identification schemes are proposed and compared, one based on the hysteresis output, the other based on the time-difference of the output. Conditions for parameter convergence are presented in terms of the input to the Preisach operator. An adaptive inverse control scheme is developed by updating the Preisach operator (and thus its inverse) with the output-based identification method. The asymptotic tracking property of this scheme is established, and for periodic reference trajectories, the parameter convergence behavior is characterized. Practical issues in the implementation of the adaptive identification and inverse control methods are also investigated. Simulation and experimental results based on a magnetostrictive actuator are provided to illustrate the proposed approach.

/pdf/adaptive-identification-and-control-of-hysteresis-in-smart-333sfpjxag.pdf

Adaptive identification and control of hysteresis in smart materials

Ionic polymer-metal composite (IPMC) actuators have promising applications in biomimetic robotics, biomedical devices, and micro/nanomanipulation. In this paper, a physics- based model is developed for IPMC actuators, which is amenable to model reduction and control design. The model is represented as an infinite-dimensional transfer function relating the bending displacement to the applied voltage. It is obtained by exactly solving the governing partial differential equation in the Laplace domain for the actuation dynamics, where the effect of the distributed surface resistance is incorporated. The model is expressed in terms of fundamental material parameters and actuator dimensions, and is thus, geometrically scalable. To illustrate the utility of the model in controller design, an Hinfin controller is designed based on the reduced model and applied to tracking control. Experimental results are presented to validate the proposed model and its effectiveness in real-time control design.

A Control-Oriented and Physics-Based Model for Ionic Polymer--Metal Composite Actuators

Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Holder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.

Xiaobo Tan

Papers

Modeling and control of hysteresis in magnetostrictive actuators

Modeling of Biomimetic Robotic Fish Propelled by An Ionic Polymer–Metal Composite Caudal Fin

Adaptive identification and control of hysteresis in smart materials

A Control-Oriented and Physics-Based Model for Ionic Polymer--Metal Composite Actuators

Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators