More Like this

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. 

   more » « less
2. Chapter 14 - Adaptive Hinfinity Tracking Control of Nonlinear Systems Using Reinforcement Learning

   https://doi.org/10.1016/b978-0-12-812976-0.00018-x  

   Hamidreza Modares, Bahare Kiumarsi (January 2018, Adaptive Learning Methods for Nonlinear System Modeling (Book))

   his chapter presents online solutions to the optimal Hinfinity tracking of nonlinear systems to attenuate the effect of disturbance on the performance of the systems. To obviate the requirement of the complete knowledge of the system dynamics, reinforcement learning (RL) is used to learn the solutions to the Hamilton–Jacobi–Isaacs equations arising from solving the tracking problem. Off-policy RL algorithms are designed for continuous-time systems, which allows the reuse of data for learning and consequently leads to data efficient RL algorithms. A solution is first presented for the Hinfinity optimal tracking control of affine nonlinear systems. It is then extended to a special class of nonlinear nonaffine systems. It is shown that for the nonaffine systems existence of a stabilizing solution depends on the performance function. A performance function is designed to assure the existence of the solution to a class of nonaffine system, while taking into account the input constraints. 

   more » « less
3. Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

   Richards, S. M.; Azizan, N.; Slotine, J.-J. E.; Pavone, M. (July 2021, Robotics science and systems)

   null (Ed.)

   Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control. 

   more » « less
4. Distributed Model Predictive Control for Connected and Automated Vehicles in the Presence of Uncertainty

   https://doi.org/10.1115/1.4054696  

   HomChaudhuri, Baisravan; Bhattacharyya, Viranjan (January 2022, Journal of Autonomous Vehicles and Systems)

   Abstract This article focuses on the development of distributed robust model predictive control (MPC) methods for multiple connected and automated vehicles (CAVs) to ensure their safe operation in the presence of uncertainty. The proposed layered control framework includes reference trajectory generation, distributionally robust obstacle occupancy set computation, distributed state constraint set evaluation, data-driven linear model representation, and robust tube-based MPC design. To enable distributed operation among the CAVs, we present a method, which exploits sampling-based reference trajectory generation and distributed constraint set evaluation methods, that decouples the coupled collision avoidance constraint among the CAVs. This is followed by data-driven linear model representation of the nonlinear system to evaluate the convex equivalent of the nonlinear control problem. Finally, to ensure safe operation in the presence of uncertainty, this article employs a robust tube-based MPC method. For a multiple CAV lane change problem, simulation results show the efficacy of the proposed controller in terms of computational efficiency and the ability to generate safe and smooth CAV trajectories in a distributed fashion. 

   more » « less
5. Global-Position Tracking Control for Three-Dimensional Bipedal Robots Via Virtual Constraint Design and Multiple Lyapunov Analysis

   https://doi.org/10.1115/1.4054732  

   Gu, Yan; Gao, Yuan; Yao, Bin; Lee, C. S. (November 2022, Journal of Dynamic Systems, Measurement, and Control)

   Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking. 

   more » « less