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1. Control of a Noncooperative Positive Nonlinear System by Augmented Positive Linear System Regulation

   https://doi.org/10.1109/LCSYS.2024.3522944  

   Liu, Guanyun; Menezes, Amor A (December 2024, IEEE Control Systems Letters)

   Positive systems, which are systems whose states are always non-negative, can have both positive linear and positive nonlinear approximations that are valid dynamical models in a prescribed domain. When a linearization of a nonlinear system in a domain near an operating point is equivalent to another linear system representation, a reference-tracking controller for that linear system should also achieve reference-tracking control of the nonlinear system in that domain. Here, we show that only if a linearized positive nonlinear system (PNS) is a positive system (i.e., the PNS is cooperative) will a reference-tracking controller for an equivalent positive linear system realization achieve similar results on the nonlinear system. For an example noncooperative PNS of human blood coagulation, where a published reference-tracking controller assumed a positive linear plant, we develop feedforward and feedback controllers that augment the prior controller to overcome noncooperativity and similarly control the positive nonlinear model. 

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2. Fast and Guaranteed Safe Controller Synthesis for Nonlinear Vehicle Models

   https://doi.org/10.1007/978-3-030-53288-8\_31  

   Fan, Chuchu; Miller, Kristina; Mitra, Sayan (July 2020, Computer Aided Verification - 32nd International Conference, {CAV} 2020, Los Angeles, CA, USA, July 21-24, 2020, Proceedings, Part {I})

   We address the problem of synthesizing a controller for nonlinear systems with reach-avoid requirements. Our controller consists of a reference controller and a tracking controller which drives the actual trajectory to follow the reference trajectory. We identify a type of reference trajectory such that the tracking error between the actual trajectory of the closed-loop system and the reference trajectory can be bounded. Moreover, such a bound on the tracking error is independent of the reference trajectory. Using such bounds on the tracking error, we propose a method that can find a reference trajectory by solving a satisfiability problem over linear constraints. Our overall algorithm guarantees that the resulting controller can make sure every trajectory from the initial set of the system satisfies the given reach-avoid requirement. We also implement our technique in a tool FACTEST. We show that FACTEST can find controllers for four vehicle models (3–6 dimensional state space and 2–4 dimensional input space) across eight scenarios (with up to 22 obstacles), all with running time at the sub-second range. 

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3. A High-Gain Observer Approach to Robust Trajectory Estimation and Tracking for a Multirotor Unmanned Aerial Vehicle

   https://doi.org/10.1115/1.4065758  

   Boss, Connor J; Srivastava, Vaibhav (January 2025, Journal of Dynamic Systems, Measurement, and Control)

   Abstract Using the context of trajectory estimation and tracking for multirotor unmanned aerial vehicles (UAVs), we explore the challenges in applying high-gain observers to highly dynamic systems. The multirotor will operate in the presence of external disturbances and modeling errors. At the same time, the reference trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume the only measurements that are available are the position and orientation of the multirotor and the position of the reference system. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the unmeasured multirotor states, modeling errors, external disturbances, and the reference trajectory. We design a robust output feedback controller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. The proposed control method is rigorously analyzed to establish its stability properties. Finally, we illustrate our theoretical results through numerical simulation and experimental validation in which a multirotor tracks a moving ground vehicle with an unknown trajectory and dynamics and successfully lands on the vehicle while in motion. 

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4. Dynamic wake modeling and state estimation for improved model-based receding horizon control of wind farms

   https://doi.org/10.23919/ACC.2017.7963036  

   Shapiro, Carl R.; Meyers, Johan; Meneveau, Charles; Gayme, Dennice F. (May 2017, American Control Conference)

   Power tracking is an emerging application for wind farm control designs that allows farms to participate in a wider range of grid services, such as secondary frequency regulation. Control designs that enable large wind farms to follow a time-varying power trajectory are complicated by aerodynamic interactions that make it impossible to decouple upstream wind turbine control actions from downstream power production. This coupling is particularly important in applications where the reference trajectory is changing faster than, or at a similar rate as, the propagation of turbine wakes through the farm. In this work we overcome these difficulties by using a dynamic wake model that accounts for wake expansion, advection, and multi-wake interactions within a model-based receding horizon controller for coordinated control of a large multi-turbine wind farm. An ensemble Kalman filter is employed for state estimation and error correction at the turbine level. We implement the controller in high-fidelity numerical simulations of a wind farm with 84 turbines and then test the controlled farm's ability to track a power reference signal. The results demonstrate the ability of the control algorithm to track two types of power reference signals used by a US independent system operator. 

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5. 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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