Adaptive Identification of SIS Models

Effective containment of spreading processes such as epidemics requires accurate knowledge of several key parameters that govern their dynamics. In this work, we first show that the problem of identifying the underlying parameters of epidemiological spreading processes is often ill-conditioned and lacks the persistence of excitation required for the convergence of adaptive learning schemes. To tackle this challenge, we leverage a relaxed property called initial excitation combined with a recursive least squares algorithm to design an online adaptive identifier to learn the parameters of the susceptible-infected-susceptible (SIS) epidemic model from the knowledge of its states. We prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. We illustrate the convergence of the error of the estimated epidemic parameters via several numerical case studies and compare it with results obtained using conventional approaches

Adaptive Linear System Identification over Simulated Wireless Environment

Wireless technologies have become one of the basic industrial pillars, whereas system identification represents an important tool in many practical engineering circumstances and thus sooner or later both wireless technologies and system identification should be linked together in sense of having an identifier that is able to reliably identify a system over wireless links. It is well known that wireless links are considered as unreliable medium and therefore the loss of the system observations across them is unavoidable. The system observations represent the main element in the identification process since the identifier relies only on these observations in order to identify the underlying function of the system as they are the only information available to tell about the system dynamics, for this reason vast amount of literature in the context of system identification is written about the way the excitation signal is chosen to force the system to show its dynamic and also about the way the sampling process is carried out to obtain informative observations in order to construct a satisfactory model for the system. This shows that the random loss of these observations (which are vital and core element of identification process) might deter the system modeling process. Experience shows that well sampled observations over regular intervals during observations loss could not guarantee a satisfactory model for the system. This thesis looks into the concepts of system identification and the behavior of the identifier components when placing wireless links between the system and the identifier. The thesis investigates the possibility of performing system identification over wireless network for both on-line and off-line system identification approaches. This research work studies the effects of observations loss on the performance of the learning algorithms and it focuses only on first order autoregressive with exogenous input (ARX) model structure adopted on linear network. The work looks thoroughly on three forms of instantaneous learning algorithms which are: first order algorithms (e.g. least mean square (LMS)), second order algorithms (e.g. recursive least squares (RLS)) and finally high order or sliding window (SW) algorithms (e.g. moving average (MA))

Cooperative Adaptive Control for Cloud-Based Robotics

This paper studies collaboration through the cloud in the context of cooperative adaptive control for robot manipulators. We first consider the case of multiple robots manipulating a common object through synchronous centralized update laws to identify unknown inertial parameters. Through this development, we introduce a notion of Collective Sufficient Richness, wherein parameter convergence can be enabled through teamwork in the group. The introduction of this property and the analysis of stable adaptive controllers that benefit from it constitute the main new contributions of this work. Building on this original example, we then consider decentralized update laws, time-varying network topologies, and the influence of communication delays on this process. Perhaps surprisingly, these nonidealized networked conditions inherit the same benefits of convergence being determined through collective effects for the group. Simple simulations of a planar manipulator identifying an unknown load are provided to illustrate the central idea and benefits of Collective Sufficient Richness.Comment: ICRA 201

Adaptive Observers for MIMO Discrete-Time LTI Systems

In this paper, an adaptive observer is proposed for multi-input multi-output (MIMO) discrete-time linear time-invariant (LTI) systems. Unlike existing MIMO adaptive observer designs, the proposed approach is applicable to LTI systems in their general form. Further, the proposed method uses recursive least square (RLS) with covariance resetting for adaptation that is shown to guarantee that the estimates are bounded, irrespective of any excitation condition, even in the presence of a vanishing perturbation term in the error used for updation in RLS. Detailed analysis for convergence and boundedness has been provided along with simulation results for illustrating the performance of the developed theory.Comment: 6 pages, 5 figure

Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal Processin