Arthur C. B. de Oliveira

Arthur C. B. de Oliveira, Ruigang Wang, Ian R. Manchester et al.

This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose, among all functions that (approximately) interpolate a given data set, one with a minimal Lipschitz constant. The paper establishes rigorous generalization bounds over practically relevant classes of approximators, including deep neural networks. It also presents a neural network implementation based on Lipschitz-bounded network layers and an augmented Lagrangian method. The results are illustrated for a problem of learning the dynamics of an input-to-state stable system with certified bounds on simulation error.

Moh Kamalul Wafi, Arthur C. B. de Oliveira, Eduardo D. Sontag

We study the monotonicity of the cumulative dose response (cDR) for a class of incoherent feedforward motifs (IFFM) systems with linear intermediate dynamics and nonlinear output dynamics. While the instantaneous dose response (DR) may be nonmonotone with respect to the input, the cDR can still be monotone. To analyze this phenomenon, we derive an integral representation of the sensitivity of cDR with respect to the input and establish general sufficient conditions for both monotonicity and non-monotonicity. These results reduce the problem to verifying qualitative sign properties along system trajectories. We apply this framework to four canonical IFFM systems and obtain a complete characterization of their behavior. In particular, IFFM1 and IFFM3 exhibit monotone cDR despite potentially non-monotone DR, while IFFM2 is monotone already at the level of DR, which implies monotonicity of cDR. In contrast, IFFM4 violates these conditions, leading to a loss of monotonicity. Numerical simulations indicate that these properties persist beyond the structured initial conditions used in the analysis. Overall, our results provide a unified framework for understanding how network structure governs monotonicity in cumulative input-output responses.

Andreas Oliveira, Arthur C. B. de Oliveira, Mario Sznaier et al.

The Łojasiewicz inequality characterizes objective-value convergence along gradient flows and, in special cases, yields exponential decay of the cost. However, such results do not directly give rates of convergence in the state. In this paper, we use contraction theory to derive state-space guarantees for gradient systems satisfying generalized Łojasiewicz inequalities. We first show that, when the objective has a unique strongly convex minimizer, the generalized Łojasiewicz inequality implies semi-global exponential stability; on arbitrary compact subsets, this yields exponential stability. We then give two curvature-based sufficient conditions, together with constraints on the Łojasiewicz rate, under which the nonconvex gradient flow is globally incrementally exponentially stable.

Moh Kamalul Wafi, Arthur C. B. de Oliveira, Eduardo D. Sontag

This paper studies whether solutions of a class of nonlinear feedback systems remain bounded over time. The systems we consider arise naturally in synthetic biology, where the antithetic feedback controller regulates a biological process through a delayed feedback loop. Our main result is that every trajectory of such a system is bounded. The key insight is simple: if the regulated state grows too large for too long, the feedback loop will eventually respond and push it back down. More precisely, we show that whenever the state exceeds a threshold and remains there long enough, the feedback signal becomes strong enough to force the state to decrease. We then show that once this happens, the feedback remains strong enough to keep the state from growing unbounded. The proof works directly with differential inequalities and does not require constructing a Lyapunov function, making the mechanism transparent and easy to interpret. The boundedness result can be understood as a time-domain small-gain effect, where the delayed feedback ultimately counteracts any persistent growth in the system.

Arthur C. B. de Oliveira, Alireza Ramezani

This work tries to contribute to the design of legged robots with capabilities boosted through thruster-assisted locomotion. Our long-term goal is the development of robots capable of negotiating unstructured environments, including land and air, by leveraging legs and thrusters collaboratively. These robots could be used in a broad number of applications including search and rescue operations, space exploration, automated package handling in residential spaces and digital agriculture, to name a few. In all of these examples, the unique capability of thruster-assisted mobility greatly broadens the locomotion designs possibilities for these systems. In an effort to demonstrate thrusters effectiveness in the robustification and efficiency of bipedal locomotion gaits, this work explores their effects on the gait limit cycles and proposes new design paradigms based on shaping these center manifolds with strong foliations. Unilateral contact force feasibility conditions are resolved in an optimal control scheme.