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1. Existence, uniqueness, and stabilization results for parabolic variational inequalities

   Kröner, Axel; Rautenberg, Carlos N.; Rodrigues, Sérgio S. (January 2021, ArXivorg)

   null (Ed.)

   In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories. Based on a Moreau--Yosida approximation, a feedback operator is established using a finite (and uniform in the approximation index) number of actuators leading to exponential decay of given rate of the state variable. Several numerical examples are presented addressing smooth and nonsmooth obstacle functions. 

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2. A Hybrid Adaptive Feedback Law for Robust Obstacle Avoidance and Coordination in Multiple Vehicle Systems

   https://doi.org/10.23919/ACC.2018.8431064  

   Poveda, Jorge I.; Benosman, Mouhacine; Teel, Andrew R.; Sanfelice, Ricardo G. (June 2018, American Control Conference)

   This paper presents an adaptive hybrid feedback law designed to robustly steer a group of autonomous vehicles toward the source of an unknown but measurable signal, at the same time that an obstacle is avoided and a prescribed formation is maintained. The hybrid law overcomes the limitations imposed by the topological obstructions induced by the obstacle, which precludes the robust stabilization of the source of the signal by using smooth feedback. The control strategy implements a leader-follower approach, where the followers track, in a coordinated way, the position of the leader. 

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3. Global sampled‐data stabilization via static output feedback for a class of nonlinear uncertain systems

   https://doi.org/10.1002/rnc.6542  

   Cao, Kecai; Qian, Chunjiang; Gu, Juping (December 2022, International Journal of Robust and Nonlinear Control)

   Summary This paper proposes some novel compensating strategies in output feedback controller design for a class of nonlinear uncertain system. With Euler approximation introduced for unmeasured state and coordinate transformation constructed for continuous system, sampled‐data stabilization under arbitrary sampling period is firstly realized for linear system using compensation between sampling period and scaling gain. Then global sampled‐data stabilization for a class of nonlinear system is studied using linear feedback domination of Lyapunov functions. Extension of obtained results to three‐dimensional system or systems under general assumptions are also presented. With the compensation schemes proposed in controller design, the sufficiently small sampling period or approximating step previously imposed is not required any more. The proposed controllers can be easily implemented using output measurements sampled at the current step and delayed output measurements sampled at the previous step without constructing state observers which has been illustrated by the numerical studies. 

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4. Duality-Based Nested Controller Synthesis from STL Specifications for Stochastic Linear Systems

   https://doi.org/10.1007/978-3-030-00151-3  

   Jha, Susmit; Raj, Sunny; Jha, Sumit Kumar; Shankar, Natarajan (January 2018, 16th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2018)

   We propose an automatic synthesis technique to generate provably correct controllers of stochastic linear dynamical systems for Signal Temporal Logic (STL) specifications. While formal synthesis problems can be directly formulated as exists-forall constraints, the quantifier alternation restricts the scalability of such an approach. We use the duality between a system and its proof of correctness to partially alleviate this challenge. We decompose the controller synthesis into two subproblems, each addressing orthogonal concerns - stabilization with respect to the noise, and meeting the STL specification. The overall controller is a nested controller comprising of the feedback controller for noise cancellation and an open loop controller for STL satisfaction. The correct-by-construction compositional synthesis of this nested controller relies on using the guarantees of the feedback controller instead of the controller itself. We use a linear feedback controller as the stabilizing controller for linear systems with bounded additive noise and over-approximate its ellipsoid stability guarantee with a polytope. We then use this over-approximation to formulate a mixed-integer linear programming (MILP) problem to synthesize an open-loop controller that satisfies STL specifications. 

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5. Pushing revisited: Differential flatness, trajectory planning, and stabilization

   https://doi.org/10.1177/0278364919872532  

   Zhou, Jiaji; Hou, Yifan; Mason, Matthew_T (September 2019, The International Journal of Robotics Research)

   We prove that quasi-static pushing with a sticking contact and ellipsoid approximation of the limit surface is differential flat. Both graphical and algebraic derivations are given. A major conclusion is that the pusher–slider system is reducible to the Dubins car problem where the sticking contact constraints translate to bounded curvature. Planning is as easy as computing a Dubins curve with the additional benefit of time-optimality. For trajectory stabilization, we design closed-loop control using dynamic feedback linearization or open-loop control using two contact points as a form of mechanical feedback. We conduct robotic experiments using objects with different pressure distributions, shape, and contact materials placed at different initial poses that require difficult switching action maneuvers to the goal pose. The average error is within 1.67 mm in translation and 0.5° in orientation over 60 experimental trials. We also show an example of pushing among obstacles using a RRT planner with exact steering. 

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