Fulvio Forni

Fulvio Forni, Rodolphe Sepulchre

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves.

Fulvio Forni, Rodolphe Sepulchre

High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be studied through linear dissipation inequalities and an interconnection theory that closely mimics the classical analysis of stability by means of dissipativity theory. In this approach, stability is seen as the limiting situation where the dominant behavior is 0-dimensional. The generalization opens novel tractable avenues to study multistability through 1-dominance and limit cycle oscillations through 2-dominance.

Fulvio Forni, Rodolphe Sepulchre

We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace and positive definite in a complementary subspace. The classical theory assumes p = 0 and provides an inter- connection theory for stability analysis, i.e. convergence to a zero dimensional attractor. The generalized theory is shown to provide an interconnection theory for p-dominance analysis, i.e. convergence to a p-dimensional dominant subspace. In turn, this property is the differential characterization of a generalized contraction property for nonlinear systems. The proposed generalization opens a novel avenue for the analysis of interconnected systems with low-dimensional attractors.

Fulvio Forni, Raphael M. Jungers, Rodolphe Sepulchre

The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (or, equivalently, a projective norm). We motivate and investigate the potential of path-positivity and we propose an algorithm for the automatic verification of positivity.

Alberto Padoan, Fulvio Forni, Rodolphe Sepulchre

The paper introduces notions of robustness margins geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and in engineering, a theory of robustness for behaviors away from equilibria is lacking. The proposed framework addresses this need in the framework of p-dominance theory, which aims at generalizing stability theory for the analysis of systems with low-dimensional attractors. Dominance margins are introduced as natural generalisations of stability margins in the context of p-dominance analysis. In analogy with stability margins, dominance margins are shown to admit simple interpretations in terms of familiar frequency domain tools and to provide quantitative measures of robustness for multistable and oscillatory behaviors in Lure systems. The theory is illustrated by means of an elementary mechanical example.

Felix A. Miranda-Villatoro, Fulvio Forni, Rodolphe Sepulchre

The paper extends the concepts of dominance and p-dissipativity to the non-smooth family of linear complementarity systems. Dominance generalizes incremental stability whereas p-dissipativity generalizes incremental passivity. The generalization aims at an interconnection theory for the design and analysis of switching and oscillatory systems. The approach is illustrated by a detailed study of classical electrical circuits that switch and oscillate.

Felix A. Miranda-Villatoro, Fulvio Forni, Rodolphe Sepulchre

The concept of passivity is central to analyze circuits as interconnections of passive components. We illustrate that when used differentially, the same concept leads to an interconnection theory for electrical circuits that switch and oscillate as interconnections of passive components with operational amplifiers (op-amps). The approach builds on recent results on dominance and p-passivity aimed at generalizing dissipativity theory to the analysis of non-equilibrium nonlinear systems. Our paper shows how those results apply to basic and well-known nonlinear circuit architectures. They illustrate the potential of dissipativity theory to design and analyze switching and oscillating circuits quantitatively, very much like their linear counterparts.

Fulvio Forni, Alexandre Mauroy, Rodolphe Sepulchre

The paper shows that normally hyperbolic one-dimensional compact attractors of smooth dynamical systems are characterized by differential positivity, that is, the pointwise infinitesimal contraction of a smooth cone field. The result is analog to the characterization of zero-dimensional hyperbolic attractors by differential stability, which is the pointwise infinitesimal contraction of a Riemannian metric.

Yongkang Huo, Fulvio Forni, Rodolphe Sepulchre

This paper introduces the ``rebound Winner-Take-All (RWTA)" motif as the basic element of a scalable neuromorphic control architecture. From the cellular level to the system level, the resulting architecture combines the reliability of discrete computation and the tunability of continuous regulation: it inherits the discrete computation capabilities of winner-take-all state machines and the continuous tuning capabilities of excitable biophysical circuits. The proposed event-based framework addresses continuous rhythmic generation and discrete decision-making in a unified physical modeling language. We illustrate the versatility, robustness, and modularity of the architecture through the nervous system design of a snake robot.

Omar Faris, Sławomir Tadeja, Fulvio Forni

Object handover is a common form of interaction that is widely present in collaborative tasks. However, achieving it efficiently remains a challenge. We address the problem of ensuring resilient robotic actions that can adapt to complex changes in object pose during human-to-robot object handovers. We propose the use of Virtual Model Control to create an interaction layer that controls the robot and adapts to the dynamic changes in the handover process. Additionally, we propose the use of augmented reality to facilitate bidirectional communication between humans and robots during handovers. We assess the performance of our controller in a set of experiments that demonstrate its resilience to various sources of uncertainties, including complex changes to the object's pose during the handover. Finally, we performed a user study with 16 participants to understand human preferences for different robot control profiles and augmented reality visuals in object handovers. Our results showed a general preference for the proposed approach and revealed insights that can guide further development in adapting the interaction with the user.

Dimitris Kousoulidis, Fulvio Forni

We design and test a cone finding algorithm to robustly address nonlinear system analysis through differential positivity. The approach provides a numerical tool to study multi-stable systems, beyond Lyapunov analysis. The theory is illustrated on two examples: a consensus problem with some repulsive interactions and second order agent dynamics, and a controlled duffing oscillator.

Yi Zhang, Zixing Wang, Fulvio Forni

We present a passive, data-driven velocity control method for nonlinear robotic manipulators that achieves better tracking performance than optimized PID with comparable design complexity. Using only three minutes of probing data, a VRFT-based design identifies passive iFIR controllers that (i) preserve closed-loop stability via passivity constraints and (ii) outperform a VRFT-tuned PID baseline on the Franka Research 3 robot in both joint-space and Cartesian-space velocity control, achieving up to a 74.5% reduction in tracking error for the Cartesian velocity tracking experiment with the most demanding reference model. When the robot end-effector dynamics change, the controller can be re-learned from new data, regaining nominal performance. This study bridges learning-based control and stability-guaranteed design: passive iFIR learns from data while retaining passivity-based stability guarantees, unlike many learning-based approaches.