This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for human-in-the-loop control. An architecture is developed which defines appropriate constraints for the system objectives. A method for enacting Lipschitz and sector bounds on the resulting controller is derived to ensure desirable control properties. An analysis of worst-case loss functions and the optimal loss function weighting is made to implement an effective training scheme. Finally, simulations are carried out to demonstrate the effectiveness of the proposed architecture. This architecture resulted in a 4.5% performance increase compared to the human operator and 9% to an unconstrained feedforward neural network trained in the same way.

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural networks has emerged as an essential area of research for enhancing adversarial robustness and network certifiability. This paper uses a rigorous approach to design $\mathcal{L}$-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. The ResNet architecture was reformulated as a pseudo-tri-diagonal LMI with off-diagonal elements and derived closed-form constraints on network parameters to ensure $\mathcal{L}$-Lipschitz continuity. To address the lack of explicit eigenvalue computations for such matrix structures, the Gershgorin circle theorem was employed to approximate eigenvalue locations, guaranteeing the LMI's negative semi-definiteness. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained networks and a compositional framework for managing recursive systems within hierarchical architectures. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. However, a limitation was identified in the Gershgorin-based approximations, which over-constrain the system, suppressing non-linear dynamics and diminishing the network's expressive capacity.

--This paper discusses the weight parametrization of two standard 1-Lipschitz network structure methodologies, the Almost-Orthogonal-Layers (AOL) and the SDP-based Lipschitz Layers (SLL), and derives their impact on the initialization for deep 1-Lipschitz feedforward networks in addition to discussing underlying issues surrounding this initialization. These networks are mainly used in certifiably robust classification applications to combat adversarial attacks by limiting the effects of perturbations on the output classification result. An exact and an upper bound for the parameterized weight variance was calculated assuming a standard Normal distribution initialization; additionally, an upper bound was computed assuming a Generalized Normal Distribution, generalizing the proof for Uniform, Laplace, and Normal distribution weight initializations. It is demonstrated that the weight variance holds no bearing on the output variance distribution and that only the dimension of the weight matrices matters. Additionally, this paper demonstrates that the weight initialization always causes deep 1-Lipschitz networks to decay to zero.

Soldiers in the field often need to cross negative obstacles, such as rivers or canyons, to reach goals or safety. Military gap crossing involves on-site temporary bridges construction. However, this procedure is conducted with dangerous, time and labor intensive operations, and specialized machinery. We envision a scalable robotic solution inspired by advancements in force-controlled and Cable Driven Parallel Robots (CDPRs); this solution can address the challenges inherent in this transportation problem, achieving fast, efficient, and safe deployment and field operations. We introduce the embodied vision in Co3MaNDR, a solution to the military gap crossing problem, a distributed robot consisting of several modules simultaneously pulling on a central payload, controlling the cables' tensions to achieve complex objectives, such as precise trajectory tracking or force amplification. Hardware experiments demonstrate teleoperation of a payload, trajectory following, and the sensing and amplification of operators' applied physical forces during slow operations. An operator was shown to manipulate a 27.2 kg (60 lb) payload with an average force utilization of 14.5\% of its weight. Results indicate that the system can be scaled up to heavier payloads without compromising performance or introducing superfluous complexity. This research lays a foundation to expand CDPR technology to uncoordinated and unstable mobile platforms in unknown environments.

A novel, learning-based method for in situ estimation of soil properties using a physics-infused neural network (PINN) is presented. The network is trained to produce estimates of soil cohesion, angle of internal friction, soil-tool friction, soil failure angle, and residual depth of cut which are then passed through an earthmoving model based on the fundamental equation of earthmoving (FEE) to produce an estimated force. The network ingests a short history of kinematic observations along with past control commands and predicts interaction forces accurately with average error of less than 2kN, 13% of the measured force. To validate the approach, an earthmoving simulation of a bladed vehicle is developed using Vortex Studio, enabling comparison of the estimated parameters to pseudo-ground-truth values which is challenging in real-world experiments. The proposed approach is shown to enable accurate estimation of interaction forces and produces meaningful parameter estimates even when the model and the environmental physics deviate substantially.