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We solve the feedback stabilization problem for a tank, with friction, containing a liquid modeled by the viscous Saint-Venant system of Partial Differential Equations. A spill-free exponential stabilization is achieved, with robustness to the wall friction forces. A Control Lyapunov Functional (CLF) methodology with two different Lyapunov functionals is employed. These functionals determine specific parameterized sets which approximate the state space. The feedback law is designed based only on one of the two functionals (which is the CLF) while the other functional is used for the derivation of estimates of the sup-norm of the velocity. The feedback law does not require the knowledge of the exact relation of the friction coefficient. Two main results are provided: the first deals with the special case of a velocity-independent friction coefficient, while the second deals with the general case. The obtained results are new even in the frictionless case., Comment: 39 pages, 2 figures, submitted to ESAIM-COCV for possible publication. arXiv admin note: text overlap with arXiv:2108.11052

An algorithm and a system of quantum circuits is developed and applied to compute accurately the S matrix for the transitions between vibrational states of H2 for collisions with H. The algorithm was applied to 100 eV laboratory collision energy at a quantum circuit simulator. The effects of the discretized dissociative continuum to the transition cross sections are carefully studied and accuracy and convergence of the results with the chosen parameters of the algorithm and the collision system are verified by comparison with a solution of the time-dependent Schrodinger equation using the classical algorithm as well as comparison with a few results from the literature., Comment: 21 pages, 12 figrues

We study the effects of quantum noise in hybrid quantum-classical solver for sparse systems of linear equations using quantum random walks, applied to stoquastic Hamiltonian matrices. In an ideal noiseless quantum computer, sparse matrices achieve solution vectors with lower relative error than dense matrices. However, we find quantum noise reverses this effect, with overall error increasing as sparsity increases. We identify invalid quantum random walks as the cause of this increased error and propose a revised linear solver algorithm which improves accuracy by mitigating these invalid walks.

We extend source seeking algorithms, in the absence of position and velocity measurements, and with tuning of the surge input, from velocity-actuated (unicycle) kinematic models to force-actuated generic Euler-Lagrange dynamic underactuated models. In the design and analysis, we employ a symmetric product approximation, averaging, passivity, and partial-state stability theory. The proposed control law requires only real-time measurement of the source signal at the current position of the vehicle and ensures semi-global practical uniform asymptotic stability (SPUAS) with respect to the linear motion coordinates for the closed-loop system. The performance of our source seeker with surge force tuning is illustrated with both numerical simulations and experiments of an underactuated boat.

In this work, we combine {Model Predictive Control} (MPC) and Control Barrier Function (CBF) design {methods} to create a hierarchical control law for simultaneous lane-keeping (LK) and obstacle avoidance (OA): at the low level, MPC performs LK via trajectory tracking during nominal operation; and at the high level, different CBF-based safety filters that ensure both LK and OA are designed and compared across some practical scenarios. In particular, we show that Exponential Safety (ESf) and Prescribed-Time Safety (PTSf) filters, which override the MPC control when necessary, result in feasible Quadratic Programs when safety is prioritized appropriately. We additionally investigate control designs subject to input constraints by using Input-Constrained-CBFs. Finally, we compare the performance of combinations of ESf, PTSf, and their input-constrained counterparts with respect to the LK and OA goals in two simulation studies for early- and late-detected obstacle scenarios.

All the existing source-seeking algorithms for unicycle models in GPS-denied settings guarantee at best an exponential rate of convergence over an infinite interval. Using the recently introduced time-varying feedback tools for prescribed-time stabilization, we achieve source seeking in prescribed time, i.e., the convergence to a small but bounded neighborhood of the source, without the measurements of the position and velocity of the unicycle, in as short a time as the user desires, starting from an arbitrary distance from the source. The practical convergence is established using a singularly perturbed version of the Lie bracket averaging method, combined with time dilation and time contraction operations. The algorithm is robust, provably, even to bounded nonvanishing perturbations and an arbitrarily strong gradient-dependent repulsive velocity drift emanating from the source.

Neurological injuries predominantly result in loss of functioning of neurons. These neurons may regain function after particular medical therapeutics, such as Chondroitinase ABC (ChABC), that promote axon elongation by manipulating the extracellular matrix, the network of extracellular macromolecules, and minerals that control the tubulin protein concentration, which is fundamental to axon elongation. We introduce an observer for the concentration of unmeasured tubulin along the axon, as well as in the growth cone, using the measurement of the axon length and the tubulin flux at the growth cone. We employ this observer in a boundary control law which actuates the tubulin concentration at the soma (nucleus), i.e., at the end of the axon distal from the measurement location. For this PDE system with a moving boundary, coupled with a two-state ODE system, we establish global exponential convergence of the observer and local exponential stabilization of the [axon, observer] system in the spatial $\mathcal{H}_1$-norm. The results require that the axon growth speed be bounded. For an open-loop observer, this is ensured by assumption (which requires that tubulin influx at the soma be limited), whereas for the output-feedback system the growth rate of the axon is ensured by assuming that the initial conditions of all the states, including the axon length, be sufficiently close to their setpoint values., Comment: Accepted for ACC 2022

Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to systems with deterministic and stochastic disturbances, has been solved by the second author and his coauthors. In this paper we develop homogeneous feedback laws for fixed-time nonovershooting stabilization for nonlinear systems that are input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of `fixed-time safety filters' (FxTSf filters) which keep the system within the closed safe set for all time but, in the case where the user's nominal control commands approach to the unsafe set, allow the system to reach the boundary of the safe set no later than a desired time that is independent of nominal control and independent of the value of the state at the time the nominal control begins to be overridden.

OpenQ$^\star$D code has been used by the RC$^\star$ collaboration for the generation of fully dynamical QCD+QED gauge configurations with C$^\star$ boundary conditions. In this talk, optimization of solvers provided with the openQ$^\star$D package relevant for porting the code on GPU-accelerated supercomputing platforms is discussed. We present the analysis of the current implementations of the GCR solver preconditioned with Schwarz alternating procedure for ill-conditioned Dirac-operators. With the goal of enabling support for GPUs from various vendors, a novel method of adaptive CPU/GPU-hybrid implementation is proposed.