Gianni Bianchini

Passivity Analysis and Passification of Discrete-Time Hybrid Systems

For discrete-time hybrid systems in piecewise affine or piece-wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stability of interconnected heterogeneous dynamical systems.

Optimal H2 controllers for spatially invariant systems with delayed communication requirements

Abstract We consider the problem of optimal H 2 design of semi-decentralized controllers for a special class of spatially distributed systems. This class includes spatially invariant and distributed discrete-time systems with an inherent temporal delay in the interaction of neighboring sites. We consider the problem of optimal design of distributed controllers that have the same information passing delay structure as the plant. We show how for stable plants, the YJBK parameterization of such stabilizing controllers yields a convex parameterization for this class. We then show how the optimal H 2 problem can be solved.

Optimal decentralized controllers for spatially invariant systems

We consider the problem of optimal H/sub 2/ design of semi-decentralized controllers for a special class of spatially distributed systems. This class includes spatially invariant and distributed discrete-time systems with an inherent temporal delay in the interaction of neighbouring sites. Such a structure arises naturally from spatio-temporal discretizations of many physical systems described by partial differential equations. We consider the problem of optimal design of distributed controllers that have the same information passing delay structure as the plant. We show how the YJBK parametrization of such stabilizing controllers yields a convex parametrization for this class. We then show how the optimal H/sub 2/ problem can be solved exactly.

Passivity analysis and passification of discrete-time hybrid systems

Abstract This paper proposes several (sufficient) criteria based on the numerical solution of systems of linear matrix inequalities (LMIs) for proving the passivity of discrete-time hybrid systems in piecewise affine form, and for the synthesis of switched linear control laws that enforce passivity.

Enhancing the Performance of Passive Teleoperation Systems via Cutaneous Feedback

We introduce a novel method to improve the performance of passive teleoperation systems with force reflection. It consists of integrating kinesthetic haptic feedback provided by common grounded haptic interfaces with cutaneous haptic feedback. The proposed approach can be used on top of any time-domain control technique that ensures a stable interaction by scaling down kinesthetic feedback when this is required to satisfy stability conditions (e.g., passivity) at the expense of transparency. Performance is recovered by providing a suitable amount of cutaneous force through custom wearable cutaneous devices. The viability of the proposed approach is demonstrated through an experiment of perceived stiffness and an experiment of teleoperated needle insertion in soft tissue.

Improving transparency in passive teleoperation by combining cutaneous and kinesthetic force feedback

A novel idea for improving transparency of teleoperation systems with force feedback is presented. This approach is based on the idea of sensory subtraction presented in [12], and consists of providing the operator with independently controlled kinesthetic and cutaneous feedback to improve the realism of haptic rendering of the remote environment (i.e., transparency), while preserving stability. More specifically, cutaneous force feedback is employed to recover transparency when a lack of kinesthetic feedback has to be enforced to keep the teleoperation loop stable. The viability of this approach is demonstrated with two experiments of teleoperated needle insertion. Results showed improved performance with respect to common control techniques not employing the proposed cutaneous compensation.

Model estimation of photovoltaic power generation using partial information

In this paper we propose a method for the estimation of the parameters of the well-known PVUSA model of a photovoltaic plant, to be used for generation forecasting purposes. We address this problem in a scenario where measurements of meteorological variables (i.e. solar irradiance and temperature) at the plant site are not available. The proposed approach efficiently exploits only power generation measurements and theoretical clear-sky irradiance, and is characterized by very low computational effort. Experimental validation is also presented. The proposed procedure is currently being deployed at several DSO control centres in Italy.

Passivity analysis of discrete-time hybrid systems using piecewise polynomial storage functions

This paper proposes some sufficient criteria based on the computation of polynomial and piecewise polynomial storage functions for checking passivity of discrete-time hybrid systems in piecewise affine or piecewise polynomial form. The computation of such storage functions is performed by means of convex optimization techniques via the sum of squares decomposition of multivariate polynomials.

Convex relaxations for L2-gain analysis of piecewise affine/polynomial systems

This paper proposes some sufficient conditions based on the computation of polynomial and piecewise polynomial storage functions for -gain analysis of discrete-time piecewise affine or piecewise polynomial systems. The computation of such storage functions is performed by means of convex optimisation techniques via the sum-of-squares decomposition of multivariate polynomials.

Passivity-based Analysis and Design of Multi-Contact Haptic Systems via LMIs

Stability is a key feature in haptic interaction with virtual environments, since unwanted oscillations can impair realism and, most importantly, may be potentially harmful for the human operator. The issue of stability in this context has been addressed by several authors since the early 90’s (Minsky et al. (1990)) and involves quite a few aspects, since the systems at hand are complex and some of their components, namely the human operators, are difficult to model. Stability has been considered from multiple viewpoints, and passivity has often been exploited in this context, since it provides a powerful tool for analyzing etherogeneous interconnected systems (Lozano et al. (2000)). The fundamental paper Colgate & Schenkel (1997) and more recent works such as Stramigioli et al. (2005) provide different approaches to the characterization of passivity in sampled-data systems and in particular in haptics. In Miller (2000); Miller et al. (1999; 2000; 2004) a discrete-time passivity framework is proposed to deal with stability analysis and controller (virtual coupling) design also in the presence of non-passive virtual environments, and in particular Miller et al. (2000) addresses the presence of nonlinearities. In Naghshtabrizi & Hespanha (2006), an H∞-type approach to the design of virtual couplings ensuring passivity and transparency is proposed. Most of the above contributions are mainly focused on the case of a single human operator interacting with a one-degree of freedom virtual environment, although also multivariable systems can be addressed to some extent. In this chapter, we deal specifically with stability analysis and controller design for haptic systems involving several devices and human operators that interact with a common virtual environment through multiple points of contact. Multi-contact interaction is an important issue in virtual reality and haptics (Barbagli et al. (2005a)). Researchers from the computer haptics community, the branch of the haptic science closer to traditional robotics (Salisbury et al. (2004)), have investigated several aspects in this scenario such as friction modeling (Barbagli et al. (2004); Melder & Harwin (2003)) and interaction with deformable objects (Barbagli et al. (2005b)), but mostly neglected stability issues. Our approach is related to the framework of Miller (2000); Miller et al. (1999; 2000; 2004) but exploits some features that are peculiar to multi-contact systems. Indeed, in a multi-contact scenario, several structural constraints arise due to the number, type and (physical or virtual) location of the devices that are coupled through the virtual environment. Moreover, virtual coupling implementation may be subject to structure constraints as well. As a matter of fact, it is often the case that the device and virtual coupling must be lumped together. More 8