Miguel Barão

Nonlinear control of HIV-1 infection with a singular perturbation model

Abstract Using a singular perturbation approximation, a nonlinear state-space model of HIV-1 infection, having as state variables the number of healthy and infected CD4+T cells and the number of virion particles, is simplified and used to design a control law. The control law comprises an inner block that performs feedback linearizing of the virus dynamics and an outer block implementing an LQ regulator that drives the number of virion particles to a number below the specification. A sensitivity analysis of the resulting law is performed with respect to the model parameter to the infection rate, showing that the controlled system remains stable in the presence of significant changes of this parameter with respect to the nominal value.

An efficient Kullback-Leibler optimization algorithm for probabilistic control design

This paper addresses the problem of iterative optimization of the Kullback-Leibler (KL) divergence on discrete (finite) probability spaces. Traditionally, the problem is formulated in the constrained optimization framework and is tackled by gradient like methods. Here, it is shown that performing the KL optimization in a Riemannian space equipped with the Fisher metric provides three major advantages over the standard methods: 1. The Fisher metric turns the original constrained optimization into an unconstrained optimization problem; 2. The optimization using a Fisher metric behaves asymptotically as a Newton method and shows very fast convergence near the optimum; 3. The Fisher metric is an intrinsic property of the space of probability distributions and allows a formally correct interpretation of a (natural) gradient as the steepest-descent method. Simulation results are presented.

Nonlinear and Adaptive Control of a HIV-1 Infection Model

Abstract This paper presents algorithms for nonlinear and adaptive control of the viral load in a HIV-1 infection model. The model considered is a reduced complexity nonlinear state-space model with two state variables, representing the plasma concentration of un-infected and infected CD4+ T-cells of the human immune system. The viral load is assumed to be proportional to the concentration of infected cells. First, a change of variables that exactly linearizes this system is obtained. For the resulting linear system the manipulated variable is obtained by state feedback. To compensate for uncertainty in the infection parameter of the model an adaptation mechanism based on a Control Lyapunov Function is designed. Since the dependency on parameters is not linear, an approximation is made using a first order Taylor expansion.

An Improved EM-method for the Estimation of Transition Probabilities in Multiple Model Switching Systems

Abstract This paper concerns the joint multiple model system identification and its switching model. The problem is formulated in a probabilistic framework, where multiple vector fields are estimated from data, and a Markov switching model is identified. An Expectation-Maximization method is employed for the identification task. The present paper focus mainly the Markov identification and more specifically the M-step of the EM method. For this purpose a natural gradient algorithm is employed.

Probabilistic Control Design using an Information Geometric Framework

Abstract This paper is motivated by the problem of controlling a single system using a large number of independent simple systems that act together with the same goal, but without synchronization or communication between them. The technique used here follows the probabilistic control formulation developed by Karný. Iterative algorithms are developed, using an information geometric viewpoint, to perform the optimization over discrete probability distributions. The probability mass functions are parametrized either as mixtures or exponential distributions, for which a natural gradient method is applied.

Efficient Optimization Algorithm for Space-Variant Mixture of Vector Fields

This paper presents a methodology for trajectory classification of human activities. The presented framework uses a mixture of non parametric space-variant vector fields to describe pedestrian’s trajectories. An advantage of the proposed method is that the vector fields are not constant and depend on the pedestrian’s localization. This means that the switching motion among vector fields may occur at any image location and should be accurately estimated. In this paper, the model is equipped with a novel methodology to estimate the switching probabilities among motion regimes. More specifically, we propose an iterative optimization of switching probabilities based on the natural gradient vector, with respect to the Fisher information metric. This approach follows an information geometric framework and contrasts with more traditional approaches of constrained optimization in which Euclidean gradient based methods are used combined with probability simplex constraints. We testify the performance superiority of the proposed approach in the classification of pedestrian’s trajectories in synthetic and real data sets concerning far-field surveillance scenarios.

An algorithm for cooperative probabilistic control design

This paper deals with the decentralized closed loop control in a pure probabilistic framework. In this framework, a system is a controlled Markov chain whose transition probabilities depend on the actions of the agents. The agents are also described in a probabilistic way. The objective is to drive the system so that the joint state and agents actions are close to a set of given target probability distributions. The Kullback-Leibler divergence is used as a performance measure. The resulting algorithm uses dynamic programming interleaved with an iterative process that computes the behavior of each agent.

Alignment of velocity fields for video surveillance

Velocity fields play an important role in surveillance since they describe typical motion behaviors of video objects (e.g., pedestrians) in the scene. This paper presents an algorithm for the alignment of velocity fields acquired by different cameras, at different time intervals, from different viewpoints. Velocity fields are aligned using a warping function which maps corresponding points and vectors in both fields. The warping parameters are estimated by minimizing a non-linear least squares energy. Experimental tests show that the proposed model is able to compensate significant misalignments, including translation, rotation and scaling.

Information Geometric Algorithm for Estimating Switching Probabilities in Space-Varying HMM

This paper proposes an iterative natural gradient algorithm to perform the optimization of switching probabilities in a space-varying hidden Markov model, in the context of human activity recognition in long-range surveillance. The proposed method is a version of the gradient method, developed under an information geometric viewpoint, where the usual Euclidean metric is replaced by a Riemannian metric on the space of transition probabilities. It is shown that the change in metric provides advantages over more traditional approaches, namely: it turns the original constrained optimization into an unconstrained optimization problem; the optimization behaves asymptotically as a Newton method and yields faster convergence than other methods for the same computational complexity; and the natural gradient vector is an actual contravariant vector on the space of probability distributions for which an interpretation as the steepest descent direction is formally correct. Experiments on synthetic and real-world problems, focused on human activity recognition in long-range surveillance settings, show that the proposed methodology compares favorably with the state-of-the-art algorithms developed for the same purpose.

Optimizing mixtures of dependency trees with application to distributed probabilistic control

One of the problems in distributed control is that of establishing a communication network topology between the intervening controllers that best suits the closed loop performance of the whole system. In this paper, a particular view of this problem is analyzed where the optimal actuation is described probabilistically and assumed to be jointly specified. The main problem is that of finding a topology having pairwise communication links that best approaches a joint distribution of actions at each time instant. The proposed algorithm uses properties of the natural gradient in the manifold of categorical distributions to find a mixture of dependency trees under certain network topology constraints.