Luigi Romano

Luigi Romano, Ole Morten Aamo, Miroslav Krstić et al.

This paper presents an adaptive observer design for semilinear hyperbolic rolling contact ODE-PDE systems with uncertain friction characteristics parameterized by a matrix of unknown coefficients appearing in the nonlinear (and possibly non-smooth) PDE source terms. Under appropriate assumptions of forward completeness and boundary sensing, an adaptive observer is synthesized to simultaneously estimate the lumped and distributed states, as well as the uncertain friction parameters, using only boundary measurements. The observer combines a finite-dimensional parameter estimator with an infinite-dimensional description of the state error dynamics, and achieves exponential convergence under persistent excitation. The effectiveness of the proposed design is demonstrated in simulation by considering a relevant example borrowed from road vehicle dynamics.

Luigi Romano, Ole Morten Aamo, Miroslav Krstić et al.

This paper addresses the local stabilization problem for semilinear single-track vehicle models with distributed tire friction dynamics, represented as interconnections of ordinary differential equations (ODEs) and hyperbolic partial differential equations (PDEs). A passivity-exploiting backstepping design is presented, which leverages the strict dissipativity properties of the PDE subsystem to achieve exponential stabilization of the considered ODE-PDE interconnection around a prescribed equilibrium. Sufficient conditions for local well-posedness and exponential convergence are derived by constructing a Lyapunov functional combining the lumped and distributed states. Both state-feedback and output-feedback controllers are synthesized, the latter relying on a cascaded observer. The theoretical results are corroborated with numerical simulations, considering non-ideal scenarios and accounting for external disturbances and uncertainties. Simulation results confirm that the proposed control strategy can effectively and robustly stabilize oversteer vehicles at high speeds, demonstrating the relevance of the approach for improving the safety and performance in automotive applications.

Luigi Romano, Ole Morten Aamo, Jan Åslund et al.

In [1], a new modeling paradigm for developing rate-and-state-dependent, control-oriented friction models was introduced. The framework, termed Friction with Bristle Dynamics (FrBD), combines nonlinear analytical expressions for the friction coefficient with constitutive equations for bristle-like elements. Within the FrBD framework, this letter introduces two novel formulations based on the two most general linear viscoelastic models for solids: the Generalized Maxwell (GM) and Generalized Kelvin-Voigt (GKV) elements. Both are analyzed in terms of boundedness and passivity, revealing that these properties are satisfied for any physically meaningful parametrization. An application of passivity for control design is also illustrated, considering an example from robotics. The findings of this letter systematically integrate rate-and-state dynamic friction models with linear viscoelasticity.

Luigi Romano

This paper extends the distributed rolling contact FrBD framework to linear viscoelasticity by considering classic derivative Generalised Maxwell and Kelvin-Voigt rheological representations of the bristle element. With this modelling approach, the dynamics of the bristle, generated friction forces, and internal deformation states are described by a system of 2(n+1) hyperbolic partial differential equations (PDEs), which can capture complex relaxation phenomena originating from viscoelastic behaviours. By appropriately specifying the analytical expressions for the transport and rigid relative velocity, three distributed formulations of increasing complexity are introduced, which account for different levels of spin excitation. For the linear variants, well-posedness and passivity are analysed rigorously, showing that these properties hold for any physically meaningful parametrisation. Numerical experiments complement the theoretical results by illustrating steady-state characteristics and transient relaxation effects. The findings of this paper substantially advance the FrBD paradigm by enabling a unified and systematic treatment of linear viscoelasticity.