Antonio Vicino

Optimal estimation theory for dynamic systems with set membership uncertainty: an overview

In many problems such as linear and nonlinear regressions, parameter and state estimation of dynamic systems, state-space and time series prediction, interpolation, smoothing and functions approximation, one has to evaluate some unknown variable using available data. The data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables. Typically, the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory. An interesting alternative approach, referred to as set membership or unknown but bounded (UBB) error description, has been investigated since the late 1960s. In this approach, uncertainty is described by an additive noise which is known only to have given integral (typically l2 of l1) or componentwise (l∞) bounds. In this paper we review the main results of this theory, with special attention to the most recent advances obtained in the case of componentwise bounds.

A bounded-error approach to piecewise affine system identification

This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.

Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems

Positive Forms.- Positivity Gap.- Robustness with Time-varying Uncertainty.- Robustness with Time-invariant Uncertainty.- Robustness with Bounded-rate Time-varying Uncertainty.- Distance Problems with Applications to Robust Control.

The automatic control telelab: a user-friendly interface for distance learning

In this paper, a remote laboratory of automatic control is presented. The main target of this laboratory is to allow students to easily interact with a set of physical processes through the Internet. The student will be able to run experiments, change control parameters, and analyze the results remotely. The automatic control telelab (ACT) allows the user to design his/her own controller by means of the MATLAB/Simulink environment, and to test it on the actual plant through a user-friendly interface. An additional feature of ACT is its architecture, allowing for an easy integration of new processes for control experiments. The ACT is reachable at http://www.dii.unisi.it//spl sim/control/act.

Solving quadratic distance problems: an LMI-based approach

The computation of the minimum distance of a point to a surface in a finite-dimensional space is a key issue in several system analysis and control problems. The paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality (LMI) techniques. Exploiting a suitable representation of homogeneous forms, a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one-parameter family of LMI optimization problems. Several properties of the proposed technique are discussed. In particular, tightness of the lower bound is investigated, providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori. Extensive numerical simulations are reported showing promising performances of the proposed method.

Sequential approximation of feasible parameter sets for identification with set membership uncertainty

In this paper the problem of approximating the feasible parameter set for identification of a system in a set membership setting is considered. The system model is linear in the unknown parameters. A recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented, and an efficient algorithm is proposed. Its computational complexity is similar to that of the commonly used ellipsoidal approximation schemes. Numerical results are also reported on some simulation experiments conducted to assess the performance of the proposed algorithm.

The automatic control telelab

A remote laboratory for automatic control is presented. The main aim of this laboratory is to allow students to easily interact with a set of physical processes through the Internet. The student can run experiments, change control parameters, and analyze the results remotely. The automatic control telelab (ACT) allows the user to choose a predefined controller or synthesize a new controller through the Matlab/Simulink environment, and to test it on actual plant through a user friendly interface. An additional feature of ACT is its architecture, allowing for an easy integration of processes for control experiments.

Brief paper: Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions

This paper deals with robust stability analysis of linear state space systems affected by time-varying uncertainties with bounded variation rate. A new class of parameter-dependent Lyapunov functions is introduced, whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms. This class of Lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time-invariant perturbations. The main result of the paper is a sufficient condition to determine the sought Lyapunov function, which amounts to solving an LMI feasibility problem, derived via a suitable parameterization of polynomial homogeneous forms. Moreover, lower bounds on the maximum variation rate for which robust stability of the system is preserved, are shown to be computable in terms of generalized eigenvalue problems. Numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature.

Load Scheduling for Household Energy Consumption Optimization

This paper concerns the problem of optimally scheduling a set of appliances at the end-user premises. In the context of electricity smart grids, the electric energy fee varies over time and the user may receive a reward from an energy aggregator if he/she modifies his/her consumption profile during certain time intervals. The problem is to schedule the operation of the appliances taking into account overall costs, climatic comfort level and timeliness. We devise a MILP model and a heuristic algorithm accounting for a typical household user. Several numerical simulation results are reported, showing that the problem can be efficiently solved in real-life instances.

Mobile robot SLAM for line-based environment representation

This paper presents an algorithm for solving the simultaneous localization and map building (SLAM) problem, a key issue for autonomous navigation in unknown environments. The considered scenario is that of a mobile robot using range scans, provided by a 2D laser rangefinder, to update a map of the environment and simultaneously estimate its position and orientation within the map. The environment representation is based on linear features whose parameters are extracted from range scans, while the corresponding covariance matrices are computed from the statistical properties of the raw data. Simultaneous update of robot pose and linear feature estimates is performed via extended Kalman filtering. Experimental tests performed within a real-world indoor environment demonstrate the effectiveness of the proposed SLAM technique.