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We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

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Among the infinite number of possible movements that can be produced, humans are commonly assumed to choose those that optimize criteria such as minimizing movement time, subject to certain movement constraints like signal-dependent and constant motor noise. While so far these assumptions have only been evaluated for simplified point-mass or planar models, we address the question of whether they can predict reaching movements in a full skeletal model of the human upper extremity. We learn a control policy using a motor babbling approach as implemented in reinforcement learning, using aimed movements of the tip of the right index finger towards randomly placed 3D targets of varying size. We use a state-of-the-art biomechanical model, which includes seven actuated degrees of freedom. To deal with the curse of dimensionality, we use a simplified second-order muscle model, acting at each degree of freedom instead of individual muscles. The results confirm that the assumptions of signal-dependent and constant motor noise, together with the objective of movement time minimization, are sufficient for a state-of-the-art skeletal model of the human upper extremity to reproduce complex phenomena of human movement, in particular Fitts' Law and the 2/3 Power Law. This result supports the notion that control of the complex human biomechanical system can plausibly be determined by a set of simple assumptions and can easily be learned.

We present a method to simulate movement in interaction with computers, using Model Predictive Control (MPC). The method starts from understanding interaction from an Optimal Feedback Control (OFC) perspective. We assume that users aim to minimize an internalized cost function, subject to the constraints imposed by the human body and the interactive system. In contrast to previous linear approaches used in HCI, MPC can compute optimal controls for nonlinear systems. This allows us to use state-of-the-art biomechanical models and handle nonlinearities that occur in almost any interactive system. Instead of torque actuation, our model employs second-order muscles acting directly at the joints. We compare three different cost functions and evaluate the simulated trajectories against user movements in a Fitts' Law type pointing study with four different interaction techniques. Our results show that the combination of distance, control, and joint acceleration cost matches individual users' movements best, and predicts movements with an accuracy that is within the between-user variance. To aid HCI researchers and designers, we introduce CFAT, a novel method to identify maximum voluntary torques in joint-actuated models based on experimental data, and give practical advice on how to simulate human movement for different users, interaction techniques, and tasks.

We apply a reinforcement meta-learning framework to optimize an integrated and adaptive guidance and flight control system for an air-to-air missile. The system is implemented as a policy that maps navigation system outputs directly to commanded rates of change for the missile's control surface deflections. The system induces intercept trajectories against a maneuvering target that satisfy control constraints on fin deflection angles, and path constraints on look angle and load. We test the optimized system in a six degrees-of-freedom simulator that includes a non-linear radome model and a strapdown seeker model, and demonstrate that the system adapts to both a large flight envelope and off-nominal flight conditions including perturbation of aerodynamic coefficient parameters and center of pressure locations, and flexible body dynamics. Moreover, we find that the system is robust to the parasitic attitude loop induced by radome refraction and imperfect seeker stabilization. We compare our system's performance to a longitudinal model of proportional navigation coupled with a three loop autopilot, and find that our system outperforms this benchmark by a large margin. Additional experiments investigate the impact of removing the recurrent layer from the policy and value function networks, performance with an infrared seeker, and flexible body dynamics.

Collision avoidance is a widely investigated topic in robotic applications. When applying collision avoidance techniques to a mobile robot, how to deal with the spatial structure of the robot still remains a challenge. In this paper, we design a configuration-aware safe control law by solving a Quadratic Programming (QP) with designed Control Barrier Functions (CBFs) constraints, which can safely navigate a mobile robotic arm to a desired region while avoiding collision with environmental obstacles. The advantage of our approach is that it correctly and in an elegant way incorporates the spatial structure of the mobile robotic arm. This is achieved by merging geometric restrictions among mobile robotic arm links into CBFs constraints. Simulations on a rigid rod and the modeled mobile robotic arm are performed to verify the feasibility and time-efficiency of proposed method. Numerical results about the time consuming for different degrees of freedom illustrate that our method scales well with dimension.

We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is held in canonical thermal equilibrium by weak coupling with a "super-bath". Our approach is a generalization of now standard typicality algorithms for computing the quantum expectation value of observables of bare quantum systems via trace estimators and Krylov subspace methods. In particular, our algorithm makes use of the fact that the reduced system density, when the bath is measured in a given random state, tends to concentrate about the corresponding thermodynamic averaged reduced system density. Theoretical error analysis and numerical experiments are given to validate the accuracy of our algorithm. Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long-range interaction systems.

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled multi-physics PDEs and mainly consists of a framework of underground heat exchange pipelines to extract the geothermal heat from the geothermal reservoir. This method is a natural combination of Galerkin Method and machine learning with the solution approximated by a neural network instead of a linear combination of basis functions. We train the neural network by randomly sampling the spatiotemporal points and minimize loss function to satisfy the differential operators, initial condition, boundary and interface conditions. Moreover, the approximate ability of the neural network is proved by the convergence of the loss function and the convergence of the neural network to the exact solution in L^2 norm under certain conditions. Finally, some numerical examples are carried out to demonstrate the approximation ability of the neural networks intuitively.

Cyclic motions are fundamental patterns in robotic applications including industrial manipulation and legged robot locomotion. This paper proposes an approach for the online modulation of cyclic motions in robotic applications. For this purpose, we present an integrated programmable Central Pattern Generator (CPG) for the online generation of the reference joint trajectory of a robotic system out of a library of desired periodic motions. The reference trajectory is then followed by the lower-level controller of the robot. The proposed CPG generates a smooth reference joint trajectory convergence to the desired one while preserving the position and velocity joint limits of the robot. The integrated programmable CPG consists of one novel bounded output programmable oscillator. We design the programmable oscillator for encoding the desired multidimensional periodic trajectory as a stable limit cycle. We also use the state transformation method to ensure that the oscillator's output and its first-time derivative preserve the joint position and velocity limits of the robot. With the help of Lyapunov-based arguments, We prove that the proposed CPG provides the global stability and convergence of the desired trajectory. The effectiveness of the proposed integrated CPG for trajectory generation is shown in a passive rehabilitation scenario on the Kuka iiwa robot arm, and also in a walking simulation on a seven-link bipedal robot.

We present DeepCSI, a novel approach to Wi-Fi radio fingerprinting (RFP) which leverages standard-compliant beamforming feedback matrices to authenticate MU-MIMO Wi-Fi devices on the move. By capturing unique imperfections in off-the-shelf radio circuitry, RFP techniques can identify wireless devices directly at the physical layer, allowing low-latency low-energy cryptography-free authentication. However, existing Wi-Fi RFP techniques are based on software-defined radio (SDRs), which may ultimately prevent their widespread adoption. Moreover, it is unclear whether existing strategies can work in the presence of MU-MIMO transmitters - a key technology in modern Wi-Fi standards. Conversely from prior work, DeepCSI does not require SDR technologies and can be run on any low-cost Wi-Fi device to authenticate MU-MIMO transmitters. Our key intuition is that imperfections in the transmitter's radio circuitry percolate onto the beamforming feedback matrix, and thus RFP can be performed without explicit channel state information (CSI) computation. DeepCSI is robust to inter-stream and inter-user interference being the beamforming feedback not affected by those phenomena. We extensively evaluate the performance of DeepCSI through a massive data collection campaign performed in the wild with off-the-shelf equipment, where 10 MU-MIMO Wi-Fi radios emit signals in different positions. Experimental results indicate that DeepCSI correctly identifies the transmitter with an accuracy of up to 98%. The identification accuracy remains above 82% when the device moves within the environment. To allow replicability and provide a performance benchmark, we pledge to share the 800 GB datasets - collected in static and, for the first time, dynamic conditions - and the code database with the community.

This extensive revision of my paper "Description of an $O(\text{poly}(n))$ Algorithm for NP-Complete Combinatorial Problems" will dramatically simplify the content of the original paper by solving subset-sum instead of $3$-SAT. I will first define the "product-derivative" method which will be used to generate a system of equations for solving unknown polynomial coefficients. Then I will describe the "Dragonfly" algorithm usable to solve subset-sum in $O(n^{16}\log(n))$ which is itself composed of a set of symbolic algebra steps on monic polynomials to convert a subset, $S_T$, of a set of positive integers, $S$, with a given target sum, $T$ into a polynomial with roots corresponding to the elements of $S_T$.

The success of deep learning attracted interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals, which is problematic in biologically realistic noisy environments and at odds with experimental evidence in neuroscience showing that top-down feedback can significantly influence neural activity. Building upon deep feedback control (DFC), a recently proposed credit assignment method, we combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization. Instead of gradually changing the network weights towards configurations with low output loss, weight updates gradually minimize the amount of feedback required from a controller that drives the network to the supervised output label. Moreover, we show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using a learning rule fully local in space and time. We complement our theoretical results with experiments on standard computer-vision benchmarks, showing competitive performance to backpropagation as well as robustness to noise. Overall, our work presents a fundamentally novel view of learning as control minimization, while sidestepping biologically unrealistic assumptions.

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