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1. Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model

   Sangli Teng, Amit K. (July 2022, 2022 American Control Conference (ACC))

   Abstract— Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discretetime, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the inputdependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controller 

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2. A Hölder-continuous Extended State Observer for Model-free Position Tracking Control

   https://doi.org/10.23919/ACC50511.2021.9483268  

   Wang, Ningshan; Sanyal, Amit K. (May 2021, 2021 American Control Conference (ACC))

   null (Ed.)

   Position tracking control in three spatial dimensions in the presence of unknown or uncertain dynamics, is applicable to unmanned aerial, ground, (under)water and space vehicles. This work gives a new approach to model-free position tracking control by designing an extended state observer to estimate the states and the uncertain dynamics, with guaranteed accuracy of estimates. The estimated states and uncertainties can be used in a control scheme in real-time for position tracking control. The uncertainty (disturbance input) estimate is provided by an extended state observer (ESO) that is finite-time stable (FTS), to provide accuracy and robustness. The ideas of homogeneous vector fields and real-valued functions are utilized for the ESO design and to prove FTS. The estimated disturbance is then utilized for compensation of this uncertainty in real-time, and to enhance the stability and robustness of the feedback tracking control scheme. 

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3. MmWave Lens-based MIMO System for Suppressing Small-scale Fading and Shadowing

   https://doi.org/10.1109/TWC.2020.2991776  

   Almasi, Mojtaba Ahmadi; Amiri, Roohollah; Jafarkhani, Hamid; Mehrpouyan, Hani (January 2020, IEEE Transactions on Wireless Communications)

   In this paper, we propose a generalized millimeter-Wave (mmWave) reconfigurable antenna multiple-input multiple-output (RA-MIMO) architecture that takes advantage of lens antennas. The considered antennas can generate multiple independent beams simultaneously using a single RF chain. This property, together with RA-MIMO, is used to combat small-scale fading and shadowing in mmWave bands. To this end, first, we derive a channel matrix for RA-MIMO. Then, we use rate-one space-time block codes (STBCs), together with phase-shifters at the receive reconfigurable antennas, to suppress the effect of small-scale fading. We consider two kinds of phase shifters: i) ideal which is error-free and ii) digital which adds quantization error. The goal of phase-shifters is to convert a complex-valued channel matrix into real-valued. Hence, it is possible to use rate-one STBCs for any dimension of RA-MIMO. We investigate diversity gain and derive an upper bound for symbol error rate in cases of ideal and digital phase-shifters. We show that RA-MIMO achieves the full-diversity gain with ideal phase-shifters and the full-diversity gain for digital phase-shifters when the number of quantization bits is higher than one. We investigate RA-MIMO in the presence of shadowing. Our analysis demonstrates that, by increasing the dimension of RA-MIMO, the outage probability decreases which means the effect of shadowing decreases. Numerical results verify our theoretical derivations. 

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4. VLSI Design of a Nonparametric Equalizer for Massive MU-MIMO

   Jeon, Charles; Mirza, Gulnar; Maleki, Arian; Studer, Christoph (October 2017, Asilomar Conference on Signals, Systems, and Computers)

   Linear minimum mean-square error (L-MMSE) equalization is among the most popular methods for data detection in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. While L-MMSE equalization enables near-optimal spectral efficiency, accurate knowledge of the signal and noise powers is necessary. Furthermore, corresponding VLSI designs must solve linear systems of equations, which requires high arithmetic precision, exhibits stringent data dependencies, and results in high circuit complexity. This paper proposes the first VLSI design of the NOnParametric Equalizer (NOPE), which avoids knowledge of the transmit signal and noise powers, provably delivers the performance of L-MMSE equalization for massive MU-MIMO systems, and is resilient to numerous system and hardware impairments due to its parameter-free nature. Moreover, NOPE avoids computation of a matrix inverse and only requires hardware-friendly matrix-vector multiplications. To showcase the practical advantages of NOPE, we propose a parallel VLSI architecture and provide synthesis results in 28nm CMOS. We demonstrate that NOPE performs on par with existing data detectors for massive MU-MIMO that require accurate knowledge of the signal and noise powers. 

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5. Control-Coherent Koopman Modeling: A Physical Modeling Approach

   Asada, Harry; Solano--Castellanos, Jose (December 2024, IEEE)

   The modeling of nonlinear dynamics based on Koopman operator theory, originally applicable only to autonomous systems with no control, is extended to nonautonomous control system without approximation of the input matrix. Prevailing methods using a least square estimate of the input matrix may result in an erroneous input matrix, misinforming the controller. Here, a new method for constructing a Koopman model that yields the exact input matrix is presented. A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators. With these variables, a lifted linear model with the exact input matrix, called a Control-Coherent Koopman Model, is constructed by superposing control input terms, which are linear in local actuator dynamics, to the Koopman operator of the associated autonomous nonlinear system. As an example, the proposed method is applied to multi degree-of-freedom robotic arms, which are controlled with Model Predictive Control (MPC). It is demonstrated that the prevailing Dynamic Mode Decomposition with Control (DMDc) using an approximate input matrix does not provide a satisfactory result, while the Control-Coherent Koopman Model performs well with the correct input matrix, even performing better than the bilinear formulation of the Koopman operator. 

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