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1. A Hybrid PID Design for Asymptotic Stabilization with Intermittent Measurements

   https://doi.org/10.1109/CDC.2018.8619150  

   Lavell, Daniel; Phillips, Sean; Sanfelice, Ricardo G. (December 2018, 2018 IEEE Conference on Decision and Control)

   In this paper, we propose a modeling and design technique for a proportional-integral-derivative (PID) controller in the presence of aperiodic intermittent sensor measurements. Using classical control design methods, PID controllers can be designed when measurements are available periodically, at discrete time instances, or continuously. Unfortunately, such design do not apply when measurements are available intermittently. Using the hybrid inclusions framework, we model the continuous-time plant to control, the mechanism triggering intermittent measurements, and a hybrid PID control law defining a hybrid closed-loop system. We provide sufficient conditions for uniform global asymptotic stability using Lyapunov set stability methods. These sufficient conditions are used for the design of the gains of the hybrid PID controller. Also, we propose relaxed sufficient conditions to provide a computationally tractable design method leveraging a polytopic embedding approach. The results are illustrated via numerical examples. 

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2. Adaptive greedy algorithms based on parameter‐domain decomposition and reconstruction for the reduced basis method

   https://doi.org/10.1002/nme.6544  

   Jiang, Jiahua; Chen, Yanlai (October 2020, International Journal for Numerical Methods in Engineering)

   Abstract The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline–online decomposition, a.k.a. a learning‐execution process. A key feature of the method is a greedy algorithm repeatedly scanning the training set, a fine discretization of the parameter domain, to identify the next dimension of the parameter‐induced solution manifold along which we expand the surrogate solution space. Although successfully applied to problems with fairly high parametric dimensions, the challenge is that this scanning cost dominates the offline cost due to it being proportional to the cardinality of the training set which is exponential with respect to the parameter dimension. In this work, we review three recent attempts in effectively delaying this curse of dimensionality, and propose two new hybrid strategies through successive refinement and multilevel maximization of the error estimate over the training set. All five offline‐enhanced methods and the original greedy algorithm are tested and compared on two types of problems: the thermal block problem and the geometrically parameterized Helmholtz problem. 

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3. ARCH-COMP20 Repeatability Evaluation Report

   https://doi.org/10.29007/8dp4  

   Johnson, Taylor T (September 2020, EPiC Series in Computing)

   This report presents the results of the repeatability evaluation for the 4th International Competition on Verifying Continuous and Hybrid Systems (ARCH-COMP’20). The competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2020, affiliated with the IFAC World Congress. In its fourth edition, twenty-eight tools submitted artifacts through a Git repository for the repeatability evaluation, applied to solve benchmark problems for seven competition categories. The majority of participants adhered to the requirements for this year’s repeatability evaluation, namely to submit scripts to automatically install and execute tools in containerized virtual environments (specifically Dockerfiles to execute within Docker), and several categories used performance evaluation information from a common execution platform. The repeatability results represent a snapshot of the current landscape of tools and the types of benchmarks for which they are particularly suited and for which others may repeat their analyses. Due to the diversity of problems in verification of continuous and hybrid systems, as well as basing on standard practice in repeatability evaluations, we evaluate the tools with pass and/or failing being repeatable. 

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4. Extended Mean Field Control Problems: stochastic maximum principle and transport perspective

   Beatrice Acciaio, Julio Backhoff-Veraguas (June 2018, arXiv.org)

   We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic maximum principle, both in necessary and in sufficient form, which extend the known conditions to this general framework. Furthermore, we suggest a variational approach to study a weak formulation of these control problems. We show a natural connection between this weak formulation and optimal transport on path space, which inspires a novel discretization scheme. 

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5. Barrier Function Certificates for Forward Invariance in Hybrid Inclusions

   https://doi.org/10.1109/CDC.2018.8618998  

   Maghenem, Mohamed; Sanfelice, Ricardo G. (December 2018, IEEE Conference on Decision and Control)

   This paper proposes barrier functions for the study of forward invariance in hybrid systems modeled by hybrid inclusions. After introducing an appropriate notion of a barrier function, we propose sufficient conditions to guarantee forward invariance properties of a set for hybrid systems with nonuniqueness of solutions, solutions terminating prematurely, and Zeno solutions. Our conditions involve infinitesimal conditions on the barrier certificate and Minkowski functionals. Examples illustrate the results. 

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