Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

L'abstract è presente nell'allegato / the abstract is in the attachmen

A unified framework for solving a general class of conditional and robust set-membership estimation problems

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic Control (2014

On the performance of nonlinear dynamical systems under parameter perturbation

AbstractWe present a method for analysing the deviation in transient behaviour between two parameterised families of nonlinear ODEs, as initial conditions and parameters are varied within compact sets over which stability is guaranteed. This deviation is taken to be the integral over time of a user-specified, positive definite function of the difference between the trajectories, for instance the L2 norm. We use sum-of-squares programming to obtain two polynomials, which take as inputs the (possibly differing) initial conditions and parameters of the two families of ODEs, and output upper and lower bounds to this transient deviation. Equality can be achieved using symbolic methods in a special case involving Linear Time Invariant Parameter Dependent systems. We demonstrate the utility of the proposed methods in the problems of model discrimination, and location of worst case parameter perturbation for a single parameterised family of ODE models

Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables

This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input, measurement, and process noise (error in variable setting). Certificates of state-feedback superstability or quadratic stability of all plants in a consistency set are provided by solving a feasibility program formed by polynomial nonnegativity constraints. Under mild compactness and data-collection assumptions, SOS tightenings in rising degree will converge to recover the true superstabilizing controller, with slight conservatism introduced for quadratic stabilizability. The performance of this SOS method is improved through the application of a theorem of alternatives while retaining tightness, in which the unknown noise variables are eliminated from the consistency set description. This SOS feasibility method is extended to provide worst-case-optimal robust controllers under H2 control costs. The consistency set description may be broadened to include cases where the data and process are affected by a combination of L-infinity bounded measurement, process, and input noise. Further generalizations include varying noise sets, non-uniform sampling, and switched systems stabilization.Comment: 27 pages, 1 figure, 9 table

Region of attraction analysis with Integral Quadratic Constraints

A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Contro