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1. On the Zeros of An Undamped Three-DoF Flexible System

   Rath, Siddharth; Cui, Leqing; Awtar, Shorya (October 2020, Proceedings of the ASME Dynamic Systems and Control Conference)

   null (Ed.)

   This paper presents an investigation of zeros in the SISO dynamics of an undamped three-DoF LTI flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros – marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP) and complex non-minimum phase (CNMP) – that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. And, that the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a three-DoF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped three-DoF system considered in this paper comprises of one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros. (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero. (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system. 

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2. A Multirate Adaptive Control for MIMO Systems with Application to Cyber-Physical Security

   https://doi.org/10.1109/CDC.2018.8619570  

   Jafarnejadsani, Hamidreza; Lee, Hanmin; Hovakimyan, Naira; Voulgaris, Petros (December 2018, 2018 IEEE Conference on Decision and Control)

   This paper proposes a multirate output-feedback controller for multi-input multi-output (MIMO) systems, possibly with non-minimum-phase zeros, using the L1 adaptive control structure. The analysis of stability and robustness of the sampled-data controller reveals that under certain conditions the performance of a continuous-time reference system is uniformly recovered as the sampling time goes to zero. The controller is designed for detection and mitigation of actuator attacks. By considering a multirate formulation, stealthy zero-dynamics attacks become detectable. The experimental results from the flight test of a small quadrotor are provided. The tests show that the multirate L1 controller can effectively detect the zero-dynamics actuator attack and recover stability of the quadrotor. 

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3. Combining simulations and experiments for the molecular engineering of multifunctional collagen mimetic peptide-based materials

   https://doi.org/10.1039/D0SM01562H  

   Hilderbrand, Amber M.; Taylor, Phillip A.; Stanzione, Francesca; LaRue, Mark; Guo, Chen; Jayaraman, Arthi; Kloxin, April M. (February 2021, Soft Matter)

   null (Ed.)

   Assembling peptides allow the creation of structurally complex materials, where amino acid selection influences resulting properties. We present a synergistic approach of experiments and simulations for examining the influence of natural and non-natural amino acid substitutions via incorporation of charged residues and a reactive handle on the thermal stability and assembly of multifunctional collagen mimetic peptides (CMPs). Experimentally, we observed inclusion of charged residues significantly decreased the melting temperature of CMP triple helices with further destabilization upon inclusion of the reactive handle. Atomistic simulations of a single CMP triple helix in explicit water showed increased residue-level and helical structural fluctuations caused by the inclusion of the reactive handle; however, these atomistic simulations cannot be used to predict changes in CMP melting transition. Coarse-grained (CG) simulations of CMPs at experimentally relevant solution conditions, showed, qualitatively, the same trends as experiments in CMP melting transition temperature with CMP design. These simulations show that when charged residues are included electrostatic repulsions significantly destabilize the CMP triple helix and that an additional inclusion of a reactive handle does not significantly change the melting transition. Based on findings from both experiments and simulations, the sequence design was refined for increased CMP triple helix thermal stability, and the reactive handle was utilized for the incorporation of the assembled CMPs within covalently crosslinked hydrogels. Overall, a unique approach was established for predicting stability of CMP triple helices for various sequences prior to synthesis, providing molecular insights for sequence design towards the creation of bulk nanostructured soft biomaterials. 

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4. Upper-bounding the regularization constant for convex sparse signal reconstruction

   Gu, Renliang; Dogandzic, Aleksandar (February 2017, arXiv.org)

   Consider reconstructing a signal x by minimizing a weighted sum of a convex differentiable negative log-likelihood (NLL) (data-fidelity) term and a convex regularization term that imposes a convex-set constraint on x and enforces its sparsity using ℓ1-norm analysis regularization.We compute upper bounds on the regularization tuning constant beyond which the regularization term overwhelmingly dominates the NLL term so that the set of minimum points of the objective function does not change. Necessary and sufficient conditions for irrelevance of sparse signal regularization and a condition for the existence of finite upper bounds are established. We formulate an optimization problem for finding these bounds when the regularization term can be globally minimized by a feasible x and also develop an alternating direction method of multipliers (ADMM) type method for their computation. Simulation examples show that the derived and empirical bounds match. 

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5. An integral quadratic constraint framework for real-time steady-state optimization of linear time-invariant systems

   https://doi.org/10.23919/ACC.2018.8431231  

   Nelson, Zachary E.; Mallada, Enrique (June 2018, 2018 Annual American Control Conference (ACC))

   Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. We logically divide the proposed solution into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component calculates an input to the LTI system that aims to drive the system toward the optimal steady-state. We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using Integral Quadratic Constraints (IQCs), the proposed framework can translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed-loop system. We illustrate several resulting controller designs using a numerical example. 

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