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1. A Hybrid PID Design for Asymptotic Stabilization with Intermittent Measurements

   https://doi.org/10.1109/CDC.2018.8619150  

   Lavell, Daniel; Phillips, Sean; Sanfelice, Ricardo G. (December 2018, 2018 IEEE Conference on Decision and Control)

   In this paper, we propose a modeling and design technique for a proportional-integral-derivative (PID) controller in the presence of aperiodic intermittent sensor measurements. Using classical control design methods, PID controllers can be designed when measurements are available periodically, at discrete time instances, or continuously. Unfortunately, such design do not apply when measurements are available intermittently. Using the hybrid inclusions framework, we model the continuous-time plant to control, the mechanism triggering intermittent measurements, and a hybrid PID control law defining a hybrid closed-loop system. We provide sufficient conditions for uniform global asymptotic stability using Lyapunov set stability methods. These sufficient conditions are used for the design of the gains of the hybrid PID controller. Also, we propose relaxed sufficient conditions to provide a computationally tractable design method leveraging a polytopic embedding approach. The results are illustrated via numerical examples. 

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2. A hybrid feedback control strategy for autonomous waypoint transitioning and loitering of unmanned aerial vehicles

   Smith, Dean A; Sanfelice, Ricardo G (November 2017, Nonlinear analysis. Hybrid systems)

   We consider the problem of autonomously controlling a fixed-wing aerial vehicle to visit a neighborhood of a pre-defined waypoint, and when nearby it, loiter around it. To solve this problem, we propose a hybrid feedback control strategy that unites two state-feedback controllers: a transit controller capable of steering or transitioning the vehicle to nearby the waypoint and a loiter controller capable of steering the vehicle about a loitering radius. The aerial vehicle is modeled on a level flight plane with system performance characterized in terms of the aerodynamic, propulsion, and mass properties. Thrust and bank angle are the control inputs. Asymptotic stability properties of the individual control algorithms, which are designed using backstepping, as well as of the closed-loop system, which includes a hybrid algorithm uniting the two controllers, are established. In particular, for this application of hybrid feedback control, Lyapunov functions and hybrid systems theory are employed to establish stability properties of the set of points defining loitering. The analytical results are confirmed numerically by simulations. 

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3. Robust hybrid supervisory control for rendezvous and docking of a spacecraft

   https://doi.org/10.1109/CDC.2016.7798769  

   Malladi, Bharani P.; Sanfelice, Ricardo G.; Butcher, Eric; Wang, Jingwei (December 2016, 2016 IEEE 55th Conference on Decision and Control (CDC))

   We consider the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft. The problem can be conveniently divided into four phases: 1) rendezvous with angles-only measurements; 2) rendezvous with range measurements; 3) docking phase; and 4) docked phase. Due to the different constraints, available measurements, and tasks to perform on each phase, we study this problem using a hybrid systems approach, in which the system has different modes of operation for which a suitable controller is to be designed. Following this approach, we characterize the family of individual controllers and the required properties they should induce to the closed-loop system to solve the problem within each phase of operation. Furthermore, we propose a supervisor that robustly coordinates the individual controllers so as to provide a solution to the problem. Due to the stringent mission requirements, the solution requires hybrid controllers that induce convergence, invariance, or asymptotic stability properties, which can be designed using recent techniques in the literature of hybrid systems. In addition, we outline specific controller designs that appropriately solve the control problems for individual phases and validate them numerically1. 

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4. Analysis and design of event-triggered control algorithms using hybrid systems tools

   https://doi.org/10.1109/CDC.2017.8264574  

   Chai, Jun; Casau, Pedro; Sanfelice, Ricardo G. (December 2017, Proceedings of 2017 IEEE 56th Annual Conference on Decision and Control (CDC 2017))

   This paper proposes a general framework for analyzing continuous-time systems controlled by event-triggered algorithms. Closed-loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event-triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions and studied using recently developed tools for robust stability. Properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated in several event-triggered strategies available in the literature. 

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5. Using Energy Shaping and Regulation for Limit Cycle Stabilization, Generation, and Transition in Simple Locomotive Systems

   https://doi.org/10.1115/1.4051589  

   Yeatman, Mark; Gregg, Robert D. (September 2021, Journal of Computational and Nonlinear Dynamics)

   Abstract This paper explores new ways to use energy shaping and regulation methods in walking systems to generate new passive-like gaits and dynamically transition between them. We recapitulate a control framework for Lagrangian hybrid systems, and show that regulating a state varying energy function is equivalent to applying energy shaping and regulating the system to a constant energy value. We then consider a simple one-dimensional hopping robot and show how energy shaping and regulation control can be used to generate and transition between nearly globally stable hopping limit cycles. The principles from this example are then applied on two canonical walking models, the spring loaded inverted pendulum (SLIP) and compass gait biped, to generate and transition between locomotive gaits. These examples show that piecewise jumps in control parameters can be used to achieve stable changes in desired gait characteristics dynamically/online. 

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