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.

This paper presents the Adaptive Personalized Control System (APECS) architecture, a novel framework for shared autonomy that improves human performance while maintaining operator characteristics. 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 50% performance increase compared to an unconstrained feedforward neural network trained in the same way.

This paper presents a comprehensive approach to designing and optimizing a Hierarchical Rule-Base Reduction (HRBR) based Adaptive-Network-Based Fuzzy Inference System (ANFIS) for symmetric linguistic variables. Specifically, the linguistic joint membership functions that underlie the ANFIS are defined, focusing on symmetrical inputs/outputs and jointly optimized trapezoid membership functions to reduce the number of training parameters. Further optimizations for the ANFIS were derived based on design assumptions, including training the membership functions on closed or single-sided domains. The optimal output membership weights based on mean square error optimization were also symbolically obtained. The online training of the ANFIS’s input/output membership functions was performed using the DDPG (Deep Deterministic Policy Gradient) algorithm. A simulated skid-steered vehicle was used to validate the approach and performed waypoint-to-waypoint path following. Experimental results using the Clearpath Jackal demonstrated that the ANFIS model converged quickly, typically within 6 to 10 episodes of training, from an initial MAE and RMSE of 0.88 and 1.02 meters, respectively, to a final MAE and RMSE of 0.087 and 0.10 meters. The results highlight the effectiveness of the ANFIS approach for vehicular robotics applications and suggest promising avenues for future research and development.