### 2017

Piga, Dario; Benavoli, Alessio

A unified framework for deterministic and probabilistic D-stability analysis of uncertain polynomial matrices Journal Article

In: Automatic Control, IEEE Transactions on, vol. 62, no. 10, pp. 5437-5444, 2017.

Abstract | Links | BibTeX | Tags: Control

@article{benavoli2016c,

title = {A unified framework for deterministic and probabilistic D-stability analysis of uncertain polynomial matrices},

author = {Piga, Dario and Benavoli, Alessio},

url = {http://arxiv.org/abs/1604.02031},

doi = {10.1109/TAC.2017.2699281},

year = {2017},

date = {2017-10-01},

journal = {Automatic Control, IEEE Transactions on},

volume = {62},

number = {10},

pages = {5437-5444},

abstract = { Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability analysis is an NP-hard problem and many polynomial-time algorithms providing either sufficient or necessary conditions for an uncertain matrix to be robustly D-stable have been developed in the past decades. Despite the vast literature on the subject, most of the contributions consider specific families of uncertain matrices, mainly with interval or polytopic uncertainty. In this work, we present a novel approach providing sufficient conditions to verify if a family of matrices, whose entries depend polynomially on some uncertain parameters, is robustly D-stable. The only assumption on the stability region D is that its complement is a semialgebraic set described by polynomial constraints, which comprises the main important cases in stability analysis. Furthermore, the D-stability analysis problem is formulated in a probabilistic framework. In this context, the uncertain parameters characterizing the considered family of matrices are described by a set of non a priori specified probability measures. Only the support and some of the moments (e.g., expected values) are assumed to be known and, among all possible probability measures, we seek the one which provides the minimum probability of D-stability. The robust and the probabilistic D-stability analysis problems are formulated in a unified framework, and relaxations based on the theory of moments are used to solve the D-stability analysis problem through convex optimization. Application to robustness and probabilistic analysis of dynamical systems is discussed. },

keywords = {Control},

pubstate = {published},

tppubtype = {article}

}

Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability analysis is an NP-hard problem and many polynomial-time algorithms providing either sufficient or necessary conditions for an uncertain matrix to be robustly D-stable have been developed in the past decades. Despite the vast literature on the subject, most of the contributions consider specific families of uncertain matrices, mainly with interval or polytopic uncertainty. In this work, we present a novel approach providing sufficient conditions to verify if a family of matrices, whose entries depend polynomially on some uncertain parameters, is robustly D-stable. The only assumption on the stability region D is that its complement is a semialgebraic set described by polynomial constraints, which comprises the main important cases in stability analysis. Furthermore, the D-stability analysis problem is formulated in a probabilistic framework. In this context, the uncertain parameters characterizing the considered family of matrices are described by a set of non a priori specified probability measures. Only the support and some of the moments (e.g., expected values) are assumed to be known and, among all possible probability measures, we seek the one which provides the minimum probability of D-stability. The robust and the probabilistic D-stability analysis problems are formulated in a unified framework, and relaxations based on the theory of moments are used to solve the D-stability analysis problem through convex optimization. Application to robustness and probabilistic analysis of dynamical systems is discussed.

Balleri, Alessio; Farina, Alfonso; Benavoli, Alessio

Coordination of optimal guidance law and adaptive radiated waveform for interception and rendezvous problems Journal Article

In: IET Radar, Sonar & Navigation, vol. 11, no. 7, pp. 1132 - 1139, 2017, ISSN: 1751-8784.

Abstract | Links | BibTeX | Tags: Control

@article{benavoli2017a,

title = {Coordination of optimal guidance law and adaptive radiated waveform for interception and rendezvous problems},

author = { Balleri, Alessio and Farina, Alfonso and Benavoli, Alessio},

url = {http://digital-library.theiet.org/content/journals/10.1049/iet-rsn.2016.0547},

doi = {10.1049/iet-rsn.2016.0547},

issn = {1751-8784},

year = {2017},

date = {2017-07-01},

journal = {IET Radar, Sonar & Navigation},

volume = {11},

number = {7},

pages = {1132 - 1139},

publisher = {Institution of Engineering and Technology},

abstract = {We present an algorithm that allows an interceptor aircraft equipped with an airborne radar to meet another air target (the intercepted) by developing a guidance law and automatically adapting and optimising the transmitted waveform on a pulse to pulse basis. The algorithm uses a Kalman filter to predict the relative position and speed of the interceptor with respect to the target. The transmitted waveform is automatically selected based on its ambiguity function and accuracy properties along the approaching path. For each pulse, the interceptor predicts its position and velocity with respect to the target, takes a measurement of range and radial velocity and, with the Kalman filter, refines the relative range and range rate estimates. These are fed into a Linear Quadratic Gaussian (LQG) controller that ensures the interceptor reaches the target automatically and successfully with minimum error and with the minimum guidance energy consumption. },

keywords = {Control},

pubstate = {published},

tppubtype = {article}

}

We present an algorithm that allows an interceptor aircraft equipped with an airborne radar to meet another air target (the intercepted) by developing a guidance law and automatically adapting and optimising the transmitted waveform on a pulse to pulse basis. The algorithm uses a Kalman filter to predict the relative position and speed of the interceptor with respect to the target. The transmitted waveform is automatically selected based on its ambiguity function and accuracy properties along the approaching path. For each pulse, the interceptor predicts its position and velocity with respect to the target, takes a measurement of range and radial velocity and, with the Kalman filter, refines the relative range and range rate estimates. These are fed into a Linear Quadratic Gaussian (LQG) controller that ensures the interceptor reaches the target automatically and successfully with minimum error and with the minimum guidance energy consumption.