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

Stabilizing predictive control with persistence of excitation for constrained linear systems

A new adaptive predictive controller for constrained linear systems is presented. The main feature of the proposed controller is the partition of the input in two components. The first part is used to persistently excite the system, in order to guarantee accurate and convergent parameter estimates in a deterministic framework. An MPC-inspired receding horizon optimization problem is developed to achieve the required excitation in a manner that is optimal for the plant. The remaining control action is employed by a conventional tube MPC controller to regulate the plant in the presence of parametric uncertainty and the excitation generated for estimation purposes. Constraint satisfaction, robust exponential stability, and convergence of the estimates are guaranteed under design conditions mildly more demanding than that of standard MPC implementations

Robustness analysis of a Maximum Correntropy framework for linear regression

In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based correntropy estimators as special cases. An analysis of the robustness properties is then provided. The analysis includes a quantitative characterization of the informativity degree of the regression which is appropriate for studying the stability of the estimator. Using this tool, a sufficient condition is expressed under which the parametric estimation error is shown to be bounded. Explicit expression of the bound is given and discussion on its numerical computation is supplied. For illustration purpose, two special cases are numerically studied.Comment: 10 pages, 5 figures, To appear in Automatic

Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems

We study the problem of adaptive control in partially observable linear dynamical systems. We propose a novel algorithm, adaptive control online learning algorithm (AdaptOn), which efficiently explores the environment, estimates the system dynamics episodically and exploits these estimates to design effective controllers to minimize the cumulative costs. Through interaction with the environment, AdaptOn deploys online convex optimization to optimize the controller while simultaneously learning the system dynamics to improve the accuracy of controller updates. We show that when the cost functions are strongly convex, after T times step of agent-environment interaction, AdaptOn achieves regret upper bound of polylog(T). To the best of our knowledge, AdaptOn is the first algorithm which achieves polylog(T) regret in adaptive control of unknown partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control