Ricardo G. Sanfelice

Francesco Ferrante, Frédéric Gouaisbaut, Ricardo G. Sanfelice et al.

This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability with a given decay rate to a set wherein the estimation error is equal to zero. Robustness with respect to external perturbations and $\mathcal{L}_2$-external stability from the plant perturbation to a given performance output are considered. Moreover, computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in three examples.

Ricardo G. Sanfelice, Laurent Praly

In [1], it is established that a convergent observer with an infinite gain margin can be designed for a given nonlinear system when a Riemannian metric showing that the system is differentially detectable (i.e., the Lie derivative of the Riemannian metric along the system vector field is negative in the space tangent to the output function level sets) and the level sets of the output function are geodesically convex is available. In this paper, we propose techniques for designing a Riemannian metric satisfying the first property in the case where the system is strongly infinitesimally observable (i.e., each time-varying linear system resulting from the linearization along a solution to the system satisfies a uniform observability property) or where it is strongly differentially observable (i.e. the mapping state to output derivatives is an injective immersion) or where it is Lagrangian. Also, we give results that are complementary to those in [1]. In particular, we provide a locally convergent observer and make a link to the existence of a reduced order observer. Examples illustrating the results are presented.

Jan de Priester, Ricardo G. Sanfelice, Nathan van de Wouw

Reinforcement learning (RL) is a promising approach for deriving control policies for complex systems. As we show in two control problems, the derived policies from using the Proximal Policy Optimization (PPO) and Deep Q-Network (DQN) algorithms may lack robustness guarantees. Motivated by these issues, we propose a new hybrid algorithm, which we call Hysteresis-Based RL (HyRL), augmenting an existing RL algorithm with hysteresis switching and two stages of learning. We illustrate its properties in two examples for which PPO and DQN fail.

Ricardo G. Sanfelice, Berk Altin

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.

Yasar Yanik, Himadri Basu, Ricardo G. Sanfelice et al.

Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practical settings, however, this task is challenged by low observability, weak excitation, nonlinear dynamics, and noisy or biased measurements. In this work, we develop a new mathematical framework that integrates Weighted Flow Matching (WFM) generative modeling with physics-informed nonlinear filtering to enhance parameter estimation in DTs. WFM relies on dynamic reweighting of training samples, which guides the generative model toward parameter regimes most informative of the evolving system state. This generative component is tightly coupled with a physics-informed filtering architecture based on the Unscented Kalman Filter (UKF), yielding a unified DT framework that combines data-driven probability transport with physically consistent state and parameter estimation. The effectiveness of the new integrated framework is demonstrated within a spacecraft DT architecture, where stable moment of inertia estimation is achieved under uncertain and noisy sensing, with significant performance improvements over established approaches such as Extended Kalman Filtering (EKF) and Ensemble Kalman Filtering (EnKF). These results highlight the potential of weighted generative modeling as a core mechanism for real-time DT synchronization in operational and mission-critical systems.

Nan Wang, Ricardo G. Sanfelice

This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in hybrid time until an overlap between the forward and backward propagation results is detected. Then, HyRRT-Connect constructs a motion plan through the reversal and concatenation of functions defined on hybrid time domains, ensuring that the motion plan satisfies the given hybrid dynamics. To address the potential discontinuity along the flow caused by tolerating some distance between the forward and backward partial motion plans, we reconstruct the backward partial motion plan by a forward-in-hybrid-time simulation from the final state of the forward partial motion plan. effectively eliminating the discontinuity. The proposed algorithm is applied to an actuated bouncing ball system and a walking robot example to highlight its computational improvement.

Ricardo G. Sanfelice, Laurent Praly

We study how convergence of an observer whose state lives in a copy of the given system's space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the system vector field is conditionally negative. Moreover, we establish that the existence of this metric is related to the observability of the system's linearization along its solutions. Moreover, if the observer has an infinite gain margin then the level sets of the output function are geodesically convex. Conversely, we establish that, if a complete Riemannian metric has a Lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property, then there exists an observer with an infinite gain margin.