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1. A Unified Framework for Data-Driven Optimal Control of Connected Vehicles in Mixed Traffic

   https://doi.org/10.1109/TIV.2023.3287131  

   Liu, Tong; Cui, Leilei; Pang, Bo; Jiang, Zhong-Ping (August 2023, IEEE Transactions on Intelligent Vehicles)

   This paper presents a unified approach to the problem of learning-based optimal control of connected human-driven and autonomous vehicles in mixed-traffic environments including both the freeway and ring road settings. The stabilizability of a string of connected vehicles including multiple autonomous vehicles (AVs) and heterogeneous human-driven vehicles (HDVs) is studied by a model reduction technique and the Popov-Belevitch-Hautus (PBH) test. For this problem setup, a linear quadratic regulator (LQR) problem is formulated and a solution based on adaptive dynamic programming (ADP) techniques is proposed without a priori knowledge on model parameters. To start the learning process, an initial stabilizing control law is obtained using the small-gain theorem for the ring road case. It is shown that the obtained stabilizing control law can achieve general Lp string stability under appropriate conditions. Besides, to minimize the impact of external disturbance, a linear quadratic zero-sum game is introduced and solved by an iterative learning-based algorithm. Finally, the simulation results verify the theoretical analysis and the proposed methods achieve desirable performance for control of a mixed-vehicular network. 

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2. Virtual Enriching Operators

   https://doi.org/10.1007/s10092-019-0338-z  

   Brenner, Susanne C; Sung, Li-yeng (October 2019, Calcolo)

   We construct bounded linear operators that map H1 conforming Lagrange finite element spaces to H2 conforming virtual element spaces in two and three dimensions. These operators are useful for the analysis of nonstandard finite element methods. 

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3. Limit Cycle Oscillation Suppression Using a Closed-loop Nonlinear Active Flow Control Technique

   https://doi.org/10.1109/CDC42340.2020.9303839  

   Kidambi, Krishna Bhavithavya; MacKunis, William; Jayaprakash, Anu Kossery (December 2020, IEEE Conference on Decision and Control)

   null (Ed.)

   This paper presents a nonlinear control method, which achieves simultaneous fluid flow velocity control and limit cycle oscillation (LCO) suppression in a flexible airfoil. The proposed control design is based on a dynamic model that incorporates the fluid structure interactions (FSI) in the airfoil. The FSI describe how the flow field velocity at the surface of a flexible structure gives rise to fluid forces acting on the structure. In the proposed control method, the LCO are controlled via control of the flow field velocity near the surface of the airfoil using surface-embedded synthetic jet actuators. Specifically, the flow field velocity profile is driven to a desired time-varying profile, which results in a LCO-stabilizing fluid forcing function acting on the airfoil. A Lyapunov-based stability analysis is used to prove that the active flow control system asymptotically converges to the LCO-stabilizing forcing function that suppresses the LCO. Numerical simulation results are provided to demonstrate the performance of the proposed active flow-and-LCO suppression method. 

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4. Doubly isogenous genus-2 curves with 𝐷₄-action

   https://doi.org/10.1090/mcom/3891  

   Arul, Vishal; Booher, Jeremy; Groen, Steven; Howe, Everett; Li, Wanlin; Matei, Vlad; Pries, Rachel; Springer, Caleb (January 2024, Mathematics of Computation)

   Abstract. We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C ′ are curves over a finite field K, with K-rational base points P and P ′ , and let D and D ′ be the pullbacks (via the Abel–Jacobi map) of the multiplication-by-2 maps on their Jacobians. We say that (C, P) and (C ′ , P ′ ) are doubly isogenous if Jac(C) and Jac(C ′ ) are isogenous over K and Jac(D) and Jac(D ′ ) are isogenous over K. For curves of genus 2 whose automorphism groups contain the dihedral group of order eight, we show that the number of pairs of doubly isogenous curves is larger than na¨ıve heuristics predict, and we provide an explanation for this phenomenon. 

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5. Self-triggered MPC with Performance Guarantee for Tracking Piecewise Constant Reference Signals

   https://doi.org/10.23919/ECC54610.2021.9655178  

   Lu, Liang; Limon, Daniel; Kolmanovsky, Ilya (June 2021, Proceedings of European Control Conference, Doelen ICC Rotterdam, Netherlands, July 29-July 2, 2021)

   This paper considers a self-triggered MPC controller design strategy for tracking piecewise constant reference signals. The proposed triggering scheme is based on the relaxed dynamic programming inequality and the idea of reference governor; such a scheme computes both the updated control action and the next triggering time. The resulting self-triggered tracking MPC control law preserves stability and constraint satisfaction and also satisfies certain a priori chosen performance requirements without the need to impose stabilizing terminal conditions. An illustrative example shows the effectiveness of this self-triggered tracking MPC implementation. 

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