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We propose an enhanced semidefinite program (SDP) relaxation to enable the tight and efficient verification of neural networks (NNs). The tightness improvement is achieved by introducing a nonlinear constraint to existing SDP relaxations previously proposed for NN verification. The efficiency of the proposal stems from the iterative nature of the proposed algorithm in that it solves the resulting non-convex SDP by recursively solving auxiliary convex layer-based SDP problems. We show formally that the solution generated by our algorithm is tighter than state-of-the-art SDP-based solutions for the problem. We also show that the solution sequence converges to the optimal solution of the non-convex enhanced SDP relaxation. The experimental results on standard benchmarks in the area show that our algorithm achieves the state-of-the-art performance whilst maintaining an acceptable computational cost. 

The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent quantification of the closed-loop performance. Recent developments in model-free policy optimization for Linear Quadratic Gaussian (LQG) control have highlighted the importance of this question. In this paper, we first propose a new set of sufficient conditions ensuring that a perturbed controller remains internally stabilizing. Based on this result, we illustrate how to perform order reduction of general (non-observer based) output feedback controllers using balanced truncation and modal truncation. We also provide explicit bounds on the LQG performance of the reduced-order controller. Furthermore, for single-input-single-output (SISO) systems, we introduce a new controller reduction technique by truncating unstable modes. We illustrate our theoretical results with numerical simulations. Our results will serve as valuable tools to design direct policy search algorithms for control problems with partial observations. 

Objective: Robust neural decoding of intended motor output is crucial to enable intuitive control of assistive devices, such as robotic hands, to perform daily tasks. Few existing neural decoders can predict kinetic and kinematic variables simultaneously. The current study developed a continuous neural decoding approach that can concurrently predict fingertip forces and joint angles of multiple fingers. Methods: We obtained motoneuron firing activities by decomposing high-density electromyogram (HD EMG) signals of the extrinsic finger muscles. The identified motoneurons were first grouped and then refined specific to each finger (index or middle) and task (finger force and dynamic movement) combination. The refined motoneuron groups (separate matrix) were then applied directly to new EMG data in real-time involving both finger force and dynamic movement tasks produced by both fingers. EMG-amplitude-based prediction was also performed as a comparison. Results: We found that the newly developed decoding approach outperformed the EMG-amplitude method for both finger force and joint angle estimations with a lower prediction error (Force: 3.47±0.43 vs 6.64±0.69% MVC, Joint Angle: 5.40±0.50° vs 12.8±0.65°) and a higher correlation (Force: 0.75±0.02 vs 0.66±0.05, Joint Angle: 0.94±0.01 vs 0.5±0.05) between the estimated and recorded motor output. The performance was also consistent for both fingers. Conclusion: The developed neural decoding algorithm allowed us to accurately and concurrently predict finger forces and joint angles of multiple fingers in real-time. Significance: Our approach can enable intuitive interactions with assistive robotic hands, and allow the performance of dexterous hand skills involving both force control tasks and dynamic movement control tasks. 

Background: Myoelectric-based decoding has gained popularity in upper-limb neural-machine interfaces. Motor unit (MU) firings decomposed from surface electromyographic (EMG) signals can represent motor intent, but EMG properties at different arm configurations can change due to electrode shift and differing neuromuscular states. This study investigated whether isometric fingertip force estimation using MU firings is robust to forearm rotations from a neutral to either a fully pronated or supinated posture. Methods: We extracted MU information from high-density EMG of the extensor digitorum communis in two ways: (1) Decomposed EMG in all three postures (MU-AllPost); and (2) Decomposed EMG in neutral posture (MU-Neu), and extracted MUs (separation matrix) were applied to other postures. Populational MU firing frequency estimated forces scaled to subjects’ maximum voluntary contraction (MVC) using a regression analysis. The results were compared with the conventional EMG-amplitude method. Results: We found largely similar root-mean-square errors (RMSE) for the two MU-methods, indicating that MU decomposition was robust to postural differences. MU-methods demonstrated lower RMSE in the ring (EMG = 6.23, MU-AllPost = 5.72, MU-Neu = 5.64 %MVC) and pinky (EMG = 6.12, MU-AllPost = 4.95, MU-Neu = 5.36 %MVC) fingers, with mixed results in the middle finger (EMG = 5.47, MU-AllPost = 5.52, MU-Neu = 6.19% MVC). Conclusion: Our results suggest that MU firings can be extracted reliably with little influence from forearm posture, highlighting its potential as an alternative decoding scheme for robust and continuous control of assistive devices.