Robust Adaptive Cooperative Control for Formation-Tracking Problem in a Network of Non-Affine Nonlinear Agents

In this chapter, a decentralized cooperative control protocol is proposed with application to any network of agents with non-affine nonlinear multi-input-multi-output (MIMO) dynamics. Here, the main purpose of cooperative control protocol is to track a time-variant reference trajectory while maintaining a desired formation. The reference trajectory is defined to a leader, which has at least one information connection with one of the agents in the network. The design procedure includes a robust adaptive law for estimating the unknown nonlinear terms of each agent’s dynamics in a model-free format, that is, without the use of any regressors. Moreover, an observer is designed to have an approximation on the values of control parameters for the leader at the agents without connection to the leader. The entire design procedure is analysed successfully for the stability using Lyapunov stability theorem. Finally, the simulation results for the application of the proposed method on a network of nonholonomic wheeled mobile robots (WMR) are presented. Desirable leader-following tracking and geometric formation control performance have been successfully demonstrated through simulated group of wheeled mobile robots

Noise and delays in adaptive interacting oscillatory systems

Rodriguez J. Noise and delays in adaptive interacting oscillatory systems. Bielefeld: Universitätsbibliothek; 2013.In this thesis, we explore the global behavior of complex systems composed of interacting local dynamical systems, each set on a vertex of a network which characterizes the mutual interactions. We consider heterogeneous arrangements, meaning that for each vertex the local dynamics can be different. To better match potential applications we allow mutual interactions to be time delayed and subject to noise sources affecting either the orbits of the local dynamics and/or the connectivity of the network. Within this very general dynamical context, we construct and focus on interactions enabling a certain level of adaptation between the local dynamical systems. By propagation of information via the coupling network, the local parameters are adaptively tuned and ultimately reach a set of consensual values. This is explicitly and analytically carried out for frequency- and radius-adapting HOPF oscillators. We then consider adapting the time scale and the shape of periodic signals. We also study how adaptive mechanisms can be implemented in heterogeneous networks formed by a couple of subnetworks, the first one with adaptive capability and the second one without. The first subnetwork defines interactions between phase oscillators with adaptive frequency capability, the other subnetwork connects damped vibrating systems without adaptation. Next, noise sources are introduced into the dynamics via stochastic switchings of the network connections. This extra time-dependence in the network opens the possibility for parametric resonance and destabilization of a consensual oscillatory state, found for purely static networks. Finally, we introduce external noise environments which corrupt the orbits of the local systems. For ''All-to-All'' network topology, we analytically derive the effects of Gaussian and non-Gaussian noise sources and unveil noise induced emergent oscillating patterns of the relevant order parameter that characterizes this dynamics. Although in this thesis the emphasis is made on deriving analytical results, we systematically supplement our findings with extensive numerical simulations. They not only corroborate and illustrate our theoretical assertions but provide additional insights where analytical results could not be found

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Virtual Reality Games for Motor Rehabilitation

This paper presents a fuzzy logic based method to track user satisfaction without the need for devices to monitor users physiological conditions. User satisfaction is the key to any product’s acceptance; computer applications and video games provide a unique opportunity to provide a tailored environment for each user to better suit their needs. We have implemented a non-adaptive fuzzy logic model of emotion, based on the emotional component of the Fuzzy Logic Adaptive Model of Emotion (FLAME) proposed by El-Nasr, to estimate player emotion in UnrealTournament 2004. In this paper we describe the implementation of this system and present the results of one of several play tests. Our research contradicts the current literature that suggests physiological measurements are needed. We show that it is possible to use a software only method to estimate user emotion