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1. Concurrent Learning and Lyapunov-Based Updates of Deep Neural Networks for Euler-Lagrange Dynamic Systems

   https://doi.org/10.23919/ACC60939.2024.10644154  

   Basyal, Sujata; Ting, Jonathan; Mishra, Kislaya; Allen, Brendon C (July 2024, IEEE)

   This paper presents a deep neural network (DNN)-and concurrent learning (CL)-based adaptive control architecture for an Euler-Lagrange dynamic system that guarantees system performance for the first time. The developed controller includes two DNNs with the same output-layer weights to ensure feasibility of the control system. In this work, a Lyapunov-and CL-based update law is developed to update the output-layer DNN weights in real-time; whereas, the inner-layer DNN weights are updated offline using data that is collected in real-time. A Lyapunov-like analysis is performed to prove that the proposed controller yields semi-global exponential convergence to an ultimate bound for the output-layer weight estimation errors and for the trajectory tracking errors. 

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2. Experimental and Analytical Prescribed-Time Trajectory Tracking Control of a 7-DOF Robot Manipulator

   https://doi.org/10.23919/ACC53348.2022.9867788  

   Bertino, Alexander; Naseradinmousavi, Peiman; Krstic, Miroslav (June 2022, American Control Conference (ACC))

   We present an analytical design and experimental verification of trajectory tracking control of a 7-DOF robot manipulator, which achieves convergence of all tracking errors to the origin within a finite terminal time. A key feature of this control strategy is that this terminal convergence time is explicitly prescribed by the control designer, and is thus independent of the initial conditions of the tracking errors. In order to achieve this beneficial property of the proposed controller, a scaling of the state by a function of time that grows unbounded towards the terminal time is employed. Through Lyapunov analysis, we first demonstrate that the proposed controller achieves regulation of all tracking errors within the prescribed time as well as the uniform boundedness of the joint torques, even in the presence of a matched, non-vanishing disturbance. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of converging to the desired trajectory within the prescribed time, despite large initial conditions of the tracking errors and a sinusoidal disturbance being applied in each joint. 

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3. Adaptive Ankle Torque Control for Bipedal Humanoid Walking on Surfaces with Unknown Horizontal and Vertical Motion

   Stewart, Jacob; Chang, I-Chia; Gu, Yan; Ioannou, Petros A (July 2025, IEEE; American Control Conference)

   Achieving stable bipedal walking on surfaces with unknown motion remains a challenging control problem due to the hybrid, time-varying, partially unknown dynamics of the robot and the difficulty of accurate state and surface motion estimation. Surface motion imposes uncertainty on both system parameters and non-homogeneous disturbance in the walking robot dynamics. In this paper, we design an adaptive ankle torque controller to simultaneously address these two uncertainties and propose a step-length planner to minimize the required control torque. Typically, an adaptive controller is used for a continuous system. To apply adaptive control on a hybrid system such as a walking robot, an intermediate command profile is introduced to ensure a continuous error system. Simulations on a planar bipedal robot, along with comparisons against a baseline controller, demonstrate that the proposed approach effectively ensures stable walking and accurate tracking under unknown, time-varying disturbances. 

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4. Lie Algebraic Cost Function Design for Control on Lie Groups

   Sangli Teng, William Clark (January 2022, Proc. IEEE CDC 2022)

   This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to design the control objective on a Lie group and then derive the gradient for controller design are non-trivial and can result in slow convergence in tracking control. We show that with a proper left-invariant metric, setting the gradient of the cost function as the tracking error in the Lie algebra leads to a quadratic Lyapunov function that enables globally exponential convergence. In the PD control case, we show that our controller can maintain an exponential convergence rate even when the initial error is approaching π in SO(3). We also show the merit of this proposed framework in trajectory optimization. The proposed cost function enables the iterative Linear Quadratic Regulator (iLQR) to converge much faster than the Differential Dynamic Programming (DDP) with a well-adopted cost function when the initial trajectory is poorly initialized on SO(3). 

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5. Vision-Based Safety-Critical Landing Control of Quadrotors With External Uncertainties and Collision Avoidance

   Lin, J; Miao, Zhiqiang; Wang, Yaonan; Wang, Hesheng; Wang, Xiangke; Fierro, Rafael (July 2024, IEEE Transactions on Control Systems Technology)

   This article addresses the quadrotors’ safety-critical landing control problem with external uncertainties and collision avoidance. A geometrically robust hierarchical control strategy is proposed for an underactuated quadrotor, which consists of a slow outer loop controlling the position and a fast inner loop regulating the attitude. First, an estimation error quantified (EEQ) observer is developed to identify and compensate for the target’s linear acceleration and the translational disturbances, whose estimation error has a nonnegative upper bound. Furthermore, an outer-loop controller is designed by embedding the EEQ observer and control barrier functions (CBFs), in which the negative effects of external uncertainties, collision avoidance, and input saturation are thoroughly considered and effectively attenuated. For the inner-loop subsystem, a geometric controller with a robust integral of the sign of the error (RISE) control structure is developed to achieve disturbances rejection and asymptotic attitude tracking. Based on Lyapunov techniques and the theory of cascade systems, it is rigorously proven that the closed-loop system is uniformly ultimately bounded. Finally, the effectiveness of the proposed control strategy is demonstrated through numerical simulations and hardware experiments. 

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