Mauro Boccadoro

Optimal Control of Switching Surfaces in Hybrid Dynamical Systems

This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The systems mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics.

Supply Chain Management by H-Infinity Control

In this paper, a H infin control technique is proposed for the management of a supply chain (SC) model linearized about nominal operating conditions. The performance considered is a weighted H infin norm comprising the inventory and the orders placed by each site, hence controlling the bullwhip effect together with local management costs. It is shown how the optimization of local costs at each site is related to the performance of the whole chain and a decentralized control methodology is proposed based on this relation.

Constrained and quantized Kalman filtering for an RFID robot localization problem

In this paper a global localization problem of a robot moving in a known environment is considered. The environment is equipped with a relatively sparse set of passive RFID (Radio Frequency IDentification) tags. The robot can detect the presence of the tags when traveling in their proximity and combines this information with the one given by other sensors (e.g. odometry). The RFID measurements are characterized by a highly non Gaussian noise: for this reason in the literature Particle Filter (PF) methods have often been used to fuse these data with the measurements coming from other sensors. In this paper a different approach is pursued, based on the observation that RFID readings can be considered as noisy quantized measurements of the pose of the robot or as noisy dynamic constraints on the pose itself. This allows to exploit the rich literature on Kalman quantized filtering or Kalman constrained estimation, to realize reliable methods with a satisfactory performance which require a computational time significantly lower with respect to the one needed by a PF. Simulative and experimental results will be reported to illustrate the proposed methods.

Optimal control of switching surfaces

This paper studies the problem of optimal switching surface design for hybrid systems. In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters. The formula reflects the hybrid nature of the system in that it is based on a costate variable having a discrete element and a continuous element. A numerical example with a gradient descent algorithm suggests the potential viability of the formula in optimization.

H-infinity control of a Supply Chain model

A Hinfin control approach has been developed in this paper for a simple supply chain model, linearized about typical operative conditions, and fed with an exogenous and unknown demand. The considered approach has been compared with other emerging control techniques in terms of a performance index defined on the inventory levels in the supply chain, showing a good performance when the exogenous demand presents significant low frequency components. Robustness issues, regarding the knowledge of the production and transport delays in the chain, are considered in the paper, and a properly modified Hinfin technique is proposed to deal with uncertain and/or time varying delays

Optimal control of two symmetric competing queues with finite capacity and non negligible setup times

In this paper we study optimal scheduling for a two part-type, symmetric manufacturing systems subject to non negligible setup times, and characterized by finite buffer capacity. The solution method relies on 1) restricting the possible control policies to those which respect some general necessary conditions of optimality, and on 2) the exploitation of such properties to introduce a two-dimensional sampled version of the original system. The symmetric assumptions allows to map the two-dimensional sampled model onto an equivalent scalar one. By means of such a scalar sampled model we give the analytical solution of the optimal control problem addressed.

The p53 network and its control via MDM2 inhibitors: insights from a dynamic model

The p53 gene plays a critical role in the cells response to DNA damage. In this paper we propose a new dynamic model of p53 activation in response to a particular type of damage (double strand brakes), known to be the most important kind of lesion through which ionizing radiation induces cancer and hereditary diseases. Then we try to sum up the main features of this network resulting from experimental observations and use the model to show the correlation that exists between the periodic behavior of this system and its healthy operation. Finally, we apply the model to study the mechanism of action of a particular class of drugs which offer a new interesting research perspective to cancer therapy

Optimal mode-switching for hybrid systems with unknown initial state

Abstract This paper concerns an optimal control problem defined on a class of switched mode hybrid dynamical systems. Such systems change modes whenever the state intersects certain surfaces that are defined in the state space. These switching surfaces are parameterized by a finite dimensional vector called the switching parameter. The optimization problem we consider is to minimize a given cost-functional with respect to the switching parameter under the assumption that the initial state of the system is not completely known. Instead, we assume that the initial state can be anywhere in a given set. We will approach this problem by minimizing the worst possible cost over the given set of initial states using results from minimax optimization. The results are then applied in order to solve a navigation problem in mobile robotics.

Optimal control of switching surfaces in hybrid dynamic systems

Abstract This paper studies the problem of optimal switching surface design for hybrid systems. In particular, a formula is derived for computing the gradient of a given integral performance cost with respect to the switching surface parameters. The novelty of the work lies both in the problem formulation itself, and in the introduction of a discrete event variational system for propagating the perturbations across switching surfaces.

Obstacle avoidance for mobile robots using switching surface optimization

Abstract This paper studies the problem of letting an autonomous mobile robot negotiate obstacles in an optimal manner. In particular, a multi-modal control problem is addressed, where different modes of operation control the robot at different locations in the state space. The specification of the optimal discrete event dynamics is pursued through the design of optimal, parametrized switching surfaces, using results on switching surface optimization.