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We consider a cell-free massive multiple-input multiple-output (CF-mMIMO) system with joint unicast and multi-group multicast transmissions. We derive exact closed-form expressions for the downlink achievable spectral efficiency (SE) of both unicast and multicast users. Based on these expressions, we formulate a joint optimization problem of access point (AP) selection and power control subject to quality of service (QoS) requirements of all unicast and multicast users and per-AP maximum transmit power constraint. The challenging formulated problem is transformed into a tractable form and a novel accelerated projected gradient (APG)-based algorithm is developed to solve the optimization problem. Simulation results show that our joint optimization strategy enhances notably the sum SE (SSE) (up to 58%) compared to baseline schemes, while maintaining low complexity.

Lead-halide perovskite nanocrystals have recently emerged as desirable optical materials for applications such as coherent quantum light emitters and solid-state laser cooling due to their short radiative lifetime and near-unity photoluminescence quantum yield. Here, we investigate the effect of CsPbBr3 nanocrystal size on the radiative lifetime under ambient conditions. High-quality nanocrystals, with monoexponential time-resolved photoluminescence decay behaviors, unveil a non-monotonic trend in radiative lifetime. This non-monotonicity appears to reflect a behavior common among II-VI (CdSe) and perovskites semiconducting nanocrystals. We find that large nanocrystals in the weak quantum confinement regime exhibit long radiative lifetimes due to a thermally accessible population of dim states. Small nanocrystals within the strong quantum confinement regime, surprisingly, also show long radiative lifetimes, due however to a substantial reduction in oscillator strength. Nanocrystals in the intermediate quantum confinement regime displays the shortest radiative lifetime, as their oscillator strength is enhanced relative to particles in the strong confinement regime, but do not have sufficient low-lying dim states like the large particles to counteract this affect. These findings shed light on the impact of nanocrystal size on radiative lifetime and pave the way for tailored optical materials in various optical applications.

This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying (LPV) formulation and controlled using model predictive control (MPC). Our main focus is quantifying the uncertainty of the LPVMPC framework's forward error resulting from scheduling signal estimation mismatch. We compared our stochastic approach with a recent deterministic approach and observed improvements in conservatism and robustness. To validate our analysis and method, we solved the regulator problem of an unbalanced disk., Comment: 6pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2310.01049

Reference tracking and obstacle avoidance rank among the foremost challenging aspects of autonomous driving. This paper proposes control designs for solving reference tracking problems in autonomous driving tasks while considering static obstacles. We suggest a model predictive control (MPC) strategy that evades the computational burden of nonlinear nonconvex optimization methods after embedding the nonlinear model equivalently to a linear parameter-varying (LPV) formulation using the so-called scheduling parameter. This allows optimal and fast solutions of the underlying convex optimization scheme as a quadratic program (QP) at the expense of losing some performance due to the uncertainty of the future scheduling trajectory over the MPC horizon. Also, to ensure that the modeling error due to the application of the scheduling parameter predictions does not become significant, we propose the concept of scheduling trust region by enforcing further soft constraints on the states and inputs. A consequence of using the new constraints in the MPC is that we construct a region in which the scheduling parameter updates in two consecutive time instants are trusted for computing the system matrices, and therefore, the feasibility of the MPC optimization problem is retained. We test the method in different scenarios and compare the results to standard LPVMPC as well as nonlinear MPC (NMPC) schemes.

Identifying and controlling an unstable, underactuated robot to enable reference tracking is a challenging control problem. In this paper, a ballbot (robot balancing on a ball) is used as an experimental setup to demonstrate and test proposed strategies to tackle this control problem. A double-loop control system, including a state-feedback gain in the outer-loop and a Proportional-Integral-Derivative (PID) controller in the inner-loop, is presented to balance the system in its unstable equilibrium. Once stability is reached, the plant's response to a designed excitation signal is measured and interpreted to identify the system's dynamics. Hereby, the parameters of a linearized model of the ballbot are identified with prior knowledge about the structure of the nonlinear dynamics of the system. Based on an identified linear time-invariant (LTI) state-space model, a double-loop control strategy is considered to balance the real system and to allow reference tracking. A linear quadratic regulator (LQR) is designed offline and implemented in the inner-loop to ensure balance. In the outer-loop, the estimated dynamics forecast the system's behavior online using a model-predictive-control (MPC) design to find the optimal control input for reference tracking. The experimental results demonstrate the applicability of the proposed strategies., Comment: 6 pages, 10 figures

In this study, we are concerned with nonlinear model predictive control (NMPC) schemes that, through the linear parameter-varying (LPV) formulation, nonlinear systems can be embedded and with a sequential quadratic program (SQP) can provide efficient solutions for the NMPC. We revisit the different constrained optimization formulations known as simultaneous and sequential approaches tailored with the LPV predictor, constituting, in general, a nonlinear program (NLP). The derived NLPs are represented through the Lagrangian formulation, which enforces the Karush-Kuhn-Tucker (KKT) optimality conditions for the optimization problem to be solvable. The main novelty suggests that the problem can still be efficiently solvable with a significantly lower computational load by approximating certain terms to reduce the computational burden. The proposed method is compared with other state-of-the-art approaches on standard performance measures. Moreover, we provide convergence analysis that can assert further theoretical guarantees in control, such as stability and recursive feasibility. Finally, the method is tested through well-studied control benchmarks such as the forced Van der Pol oscillator and the dynamic unicycle., Comment: 8 pages, 2 figures

In this study, we implement a control method for stabilizing a ballbot that simultaneously follows a reference. A ballbot is a robot balancing on a spherical wheel where the single point of contact with the ground makes it omnidirectional and highly maneuverable but with inherent instability. After introducing the scheduling parameters, we start the analysis by embedding the nonlinear dynamic model derived from first principles to a linear parameter-varying (LPV) formulation. Continuously, and as an extension of a past study, we refine the parameters of the nonlinear model that enhance significantly its accuracy. The crucial advantages of the LPV formulation are that it consists of a nonlinear predictor that can be used in model predictive control (MPC) by retaining the convexity of the quadratic optimization problem with linear constraints and further evades computational burdens that appear in other nonlinear MPC methods with only a slight loss in performance. The LPVMPC control method can be solved efficiently as a quadratic program (QP) that provides timing that supports real-time implementation. Finally, to illustrate the method, we test the control designs on a two-set point 1D non-smooth reference with sudden changes, to a 2D nonstationary smooth reference known as Lissajous curves, and to a single-set point 1D non-smooth reference where for this case theoretical guarantees such as stability and recursive feasibility are provided., Comment: 8 pages, 6 figures

Lead halide perovskite nanocrystals demonstrate efficient up-conversion, although the precise mechanism remains a subject of active research. This study utilizes steady-state and time-resolved spectroscopy methods to unravel the mechanism driving the up-conversion process in CsPbBr3 nanocrystals. Employing above- and below-gap photoluminescence measurements, we extract a distinct phonon mode with an energy of ~7 meV and identify the Pb-Br-Pb bending mode as the phonon involved in the up-conversion process. This result was corroborated by Raman spectroscopy. We confirm an up-conversion efficiency reaching up to 75%. Transient absorption measurements under conditions of sub-gap excitation also unexpectedly reveal coherent phonons for the subset of nanocrystals undergoing up-conversion. This coherence implies that the up-conversion and subsequent relaxation is accompanied by a synchronized and phased lattice motion. This study reveals that efficient up-conversion in CsPbBr3 nanocrystals is powered by a unique interplay between the soft lattice structure, phonons, and excited states dynamics., Comment: Main text has 6 figures, supporting information has 7 figures. total number of pages 39

By means of the linear parameter-varying (LPV) Fundamental Lemma, we derive novel data-driven predictive control (DPC) methods for LPV systems. In particular, we present output-feedback and state-feedback-based LPV-DPC methods with terminal ingredients, which guarantee exponential stability and recursive feasibility. We provide methods for the data-based computation of these terminal ingredients. Furthermore, an in-depth analysis of the application and implementation aspects of the LPV-DPC schemes is given, including application for nonlinear systems and handling noisy data. We compare and demonstrate the performance of the proposed methods in a detailed simulation example involving a nonlinear unbalanced disc system., Comment: Submitted to IEEE-TAC. Extended version. 18 pages

We report the growth of high-quality GaN epitaxial thin films on graphene-coated c-sapphire substrates using pulsed-mode metalorganic vapor-phase epitaxy, together with the fabrication of freestanding GaN films by simple mechanical exfoliation for transferable light-emitting diodes (LEDs). High-quality GaN films grown on the graphene-coated sapphire substrates were easily lifted off using thermal release tape and transferred onto foreign substrates. Furthermore, we revealed that the pulsed operation of ammonia flow during GaN growth was a critical factor for the fabrication of high-quality freestanding GaN films. These films, exhibiting excellent single crystallinity, were utilized to fabricate transferable GaN LEDs by heteroepitaxially growing InxGa1-xN/GaN multiple quantum wells and a p-GaN layer on the GaN films, showing their potential application in advanced optoelectronic devices., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright 2023 American Chemical Society after peer review. To access the final edited and published work see https://doi.org/10.1021/acs.nanolett.3c03333

In this work, we provide deterministic error bounds for the actual state evolution of nonlinear systems embedded with the linear parametric variable (LPV) formulation and steered by model predictive control (MPC). The main novelty concerns the explicit derivation of these deterministic bounds as polytopic tubes using linear differential inclusions (LDIs), which provide exact error formulations compared to linearization schemes that introduce additional error and deteriorate conservatism. The analysis and method are certified by solving the regulator problem of an unbalanced disk that stands as a classical control benchmark example., Comment: 7 pages, 3 figures

In this study, we are concerned with autonomous driving missions when a static obstacle blocks a given reference trajectory. To provide a realistic control design, we employ a model predictive control (MPC) utilizing nonlinear state-space dynamic models of a car with linear tire forces, allowing for optimal path planning and tracking to overtake the obstacle. We provide solutions with two different methodologies. Firstly, we solve a nonlinear MPC (NMPC) problem with a nonlinear optimization framework, capable of considering the nonlinear constraints. Secondly, by introducing scheduling signals, we embed the nonlinear dynamics in a linear parameter varying (LPV) representation with adaptive linear constraints for realizing the nonlinear constraints associated with the obstacle. Consequently, an LPVMPC optimization problem can be solved efficiently as a quadratic programming (QP) that constitutes the main novelty of this work. We test the two methods for a challenging obstacle avoidance task and provide qualitative comparisons. The LPVMPC shows a significant reduction in terms of the computational burden at the expense of a slight loss of performance.

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points., Comment: Accepted to the 22nd IFAC World Congress 2023 (IFAC2023)

The framework of linear parameter-varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow to synthesize LPV state-feedback controllers directly from a single sequence of data and guarantee stability and performance of the closed-loop system, without knowing the model of the plant. We show that if the measured open-loop data from the system satisfies a persistency of excitation condition, then the full open-loop and closed-loop input-scheduling-state behavior can be represented using only the data. With this representation, we formulate synthesis problems that yield controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of the closed-loop system. The controllers are synthesized by solving an SDP with a finite set of LMI constraints. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data-driven synthesis methods is demonstrated w.r.t. model-based synthesis that have complete knowledge of the true system model in multiple simulation studies, including a nonlinear unbalanced disc system., Comment: 27 pages

Gaussian Process (GP) regressions have proven to be a valuable tool to predict disturbances and model mismatches and incorporate this information into a Model Predictive Control (MPC) prediction. Unfortunately, the computational complexity of inference and learning on classical GPs scales cubically, which is intractable for real-time applications. Thus GPs are commonly trained offline, which is not suited for learning disturbances as their dynamics may vary with time. Recently, state-space formulation of GPs has been introduced, allowing inference and learning with linear computational complexity. This paper presents a framework that enables online learning of disturbance dynamics on quadcopters, which can be executed within milliseconds using a state-space formulation of GPs. The obtained disturbance predictions are combined with MPC leading to a significant performance increase in simulations with jMAVSim. The computational burden is evaluated on a Raspberry Pi 4 B to prove the real-time applicability., Comment: Published at American Control Conference (ACC 2022), Atlanta, GA, USA, June 8 to 10, 2022

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modeled in linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and used to generate scenarios which ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance., Comment: Accepted and to be published by International Journal of Control

Based on the extension of the behavioral theory and the Fundamental Lemma for Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven Predictive Control (DPC) scheme capable to ensure reference tracking and satisfaction of Input-Output (IO) constraints for an unknown system under the conditions that (i) the system can be represented in an LPV form and (ii) an informative data-set containing measured IO and scheduling trajectories of the system is available. It is shown that if the data set satisfies a persistence of excitation condition, then a data-driven LPV predictor of future trajectories of the system can be constructed from the IO data set and online measured data. The approach represents the first step towards a DPC solution for nonlinear and time-varying systems due to the potential of the LPV framework to represent them. Two illustrative examples, including reference tracking control of a nonlinear system, are provided to demonstrate that the data-based LPV-DPC scheme, achieves similar performance as LPV model-based predictive control., Comment: Accepted to 4th IFAC Workshop on Linear Parameter-Varying Systems

This paper introduces a systematic approach to synthesize linear parameter-varying (LPV) representations of nonlinear (NL) systems which are described by input affine state-space (SS) representations. The conversion approach results in LPV-SS representations in the observable canonical form. Based on the relative degree concept, first the SS description of a given NL representation is transformed to a normal form. In the SISO case, all nonlinearities of the original system are embedded into one NL function, which is factorized, based on a proposed algorithm, to construct an LPV representation of the original NL system. The overall procedure yields an LPV model in which the scheduling variable depends on the inputs and outputs of the system and their derivatives, achieving a practically applicable transformation of the model in case of low order derivatives. In addition, if the states of the NL model can be measured or estimated, then a modified procedure is proposed to provide LPV models scheduled by these states. Examples are included to demonstrate both approaches.