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1. A Hybrid Predictive Control Approach to Trajectory Tracking for a Fully Actuated Biped

   https://doi.org/10.23919/ACC.2018.8431254  

   Short, Brendan E.; Sanfelice, Ricardo G. (June 2018, 2018 Annual American Control Conference (ACC))

   We model a three-link fully actuated biped as a hybrid system and propose a prediction-based control algorithm for global tracking of reference trajectories. The proposed control strategy consists of a reference system that generates the desired periodic gait, a virtual system that generates a suitable reference trajectory using prediction, and a tracking control law that steers the biped to the virtual trajectory. The proposed algorithms achieves, in finite time, tracking in two steps. We present mathematical properties that define the main elements in the hybrid predictive controller for achieving convergence to the reference within the first two steps. The results are validated through numerical simulations. 

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2. Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems

   https://doi.org/10.1002/acs.3631  

   L'Afflitto, Andrea (August 2023, International Journal of Adaptive Control and Signal Processing)

   M. Grimble (Ed.)

   Summary This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem. 

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3. A Hybrid Model Reference Adaptive Control System for Multi-Rotor Unmanned Aerial Vehicles

   https://doi.org/10.2514/6.2024-0755  

   Gramuglia, Mattia; Kumar, Giri Mugundan; L'Afflitto, Andrea (January 2024, SciTech)

   AIAA (Ed.)

   In this paper, a novel model reference adaptive control (MRAC) architecture for nonlinear, time-varying, hybrid dynamical systems is applied for the first time to design the control system of a multi-rotor unmanned aerial vehicle (UAV). The proposed control system is specifically designed to address problems of practical interests involving autonomous UAVs transporting unknown, unsteady payloads and subject to instantaneous variations both in their state and in their dynamics. These variations can be due, for instance, to the payload’s dynamics, impacts between the payload and its casing, and sudden payload dropping and pickup. The proposed hybrid MRAC architecture improves the UAV’s trajectory tracking performance over classical MRAC also in the presence of motor failures. The applicability of the proposed framework is validated numerically through the first use of the high-fidelity simulation environment PyChrono for autonomous UAV control system testing. 

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4. 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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5. A Hybrid Filtered Basis Functions Approach for Tracking Control of Linear Systems with Unmodeled Nonlinear Dynamics

   https://doi.org/10.1109/CASE49439.2021.9551476  

   Chou, Cheng-Hao; Duan, Molong; Okwudire, Chinedum E. (August 2021, 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE))

   A hybrid filtered basis function (FBF) approach is proposed in this paper for feedforward tracking control of linear systems with unmodeled nonlinear dynamics. Unlike most available tracking control techniques, the FBF approach is very versatile; it is applicable to any type of linear system, regardless of its underlying dynamics. The FBF approach expresses the control input to a system as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through a linear model of the system's dynamics and the unknown coefficients are selected such that tracking error is minimized. The linear models used in existing implementations of the FBF approach are typically physics-based representations of the linear dynamics of a system. The proposed hybrid FBF approach expands the application of the FBF approach to systems with unmodeled nonlinearities by learning from data. A hybrid model is formulated by combining a physics-based model of the system's linear dynamics with a data-driven linear model that approximates the unmodeled nonlinear dynamics. The hybrid model is used online in receding horizon to compute optimal control commands that minimize tracking errors. The proposed hybrid FBF approach is shown in simulations on a model of a vibration-prone 3D printer to improve tracking accuracy by up to 65.4%, compared to an existing FBF approach that does not incorporate data. 

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