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1. Hybrid Regional Stabilization of Linear Systems with Actuator Saturation and Multi-Rate Samplers

   https://doi.org/10.23919/ECC.2018.8550561  

   Ferrante, Francesco; Sanfelice, Ricardo G.; Tarbouriech, Sophie (June 2018, European Control Conference)

   Regional stability analysis of linear systems with multi-rate samplers and actuator saturation is studied. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant. When a new measurement is available, the controller state undergoes a jump. The resulting system is analyzed in a hybrid system framework. Sufficient conditions in the form of matrix inequalities are given to determine estimates of the basin of attraction of the closed-loop system. Finally, the effectiveness of the proposed methodology is shown in an example. 

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2. A Barrier Certificate-Based Simplex Architecture for Systems With Approximate and Hybrid Dynamics

   https://doi.org/10.1109/ACCESS.2025.3599459  

   Damare, Amol; Roy, Shouvik; Sharma, Roshan; DSouza, Keith; Smolka, Scott A; Stoller, Scott D (August 2025, IEEE Access)

   This paper presents Barrier-based Simplex (Bb-Simplex), a new, provably correct design for runtime assurance of continuous dynamic systems. Bb-Simplex is centered around the Simplex control architecture, which consists of a high-performance advanced controller that is not guaranteed to maintain safety of the plant, a verified-safe baseline controller, and a decision module that switches control of the plant between the two controllers to ensure safety without sacrificing performance. In Bb-Simplex, Barrier certificates are used to prove that the baseline controller ensures safety. Furthermore, Bb-Simplex features a new automated method for deriving, from the barrier certificate, the conditions for switching between the controllers. Our method is based on the Taylor expansion of the barrier certificate and yields computationally inexpensive switching conditions. We also propose extensions to Bb-Simplex to enable its use in hybrid systems, which have multiple modes each with its own dynamics, and to support its use when only approximate dynamics (not exact dynamics) are available, for both continuous and hybrid dynamic systems. We consider significant applications of Bb-Simplex to microgrids featuring advanced controllers in the form of neural networks trained using reinforcement learning. These microgrids are modeled in RTDS, an industry-standard high-fidelity, real-time power systems simulator. Our results demonstrate that Bb-Simplex can automatically derive switching conditions for complex continuous and hybrid dynamic systems, the switching conditions are not overly conservative, and Bb-Simplex ensures safety even in the presence of adversarial attacks on the neural controller when only approximate dynamics (with an error bound) are available. Our experiments to evaluate conservativeness of the switching conditions show that switches from an unsafe advanced controller to a baseline controller occur on average only a few control periods before a safety violation would have occurred. 

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3. Proportional Integral Derivative Control in Spark Plasma Sintering Simulations

   https://doi.org/10.3390/ma14071779  

   Jiang, Runjian; Torresani, Elisa; Cui, Guodong; Olevsky, Eugene A. (April 2021, Materials)

   null (Ed.)

   The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS. 

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4. Series-elastic actuator with two degree-of-freedom PID control improves torque control in a powered knee exoskeleton

   https://doi.org/10.1017/wtc.2023.20  

   Sarkisian, Sergei V.; Gabert, Lukas; Lenzi, Tommaso (January 2023, Wearable Technologies)

   Abstract Powered exoskeletons need actuators that are lightweight, compact, and efficient while allowing for accurate torque control. To satisfy these requirements, researchers have proposed using series elastic actuators (SEAs). SEAs use a spring in series with rotary or linear actuators. The spring compliance, in conjunction with an appropriate control scheme, improves torque control, efficiency, output impedance, and disturbance rejection. However, springs add weight to the actuator and complexity to the control, which may have negative effects on the performance of the powered exoskeleton. Therefore, there is an unmet need for new SEA designs that are lighter and more efficient than available systems, as well as for control strategies that push the performance of SEA-based exoskeletons without requiring complex modeling and tuning. This article presents the design, development, and testing of a novel SEA with high force density for powered exoskeletons, as well as the use of a two degree-of-freedom (2DOF) PID system to improve output impedance and disturbance rejection. Benchtop testing results show reduced output impedance and damping values when using a 2DOF PID controller as compared to a 1DOF PID controller. Human experiments with three able-bodied subjects (N = 3) show improved torque tracking with reduced root-mean-square error by 45.2% and reduced peak error by 49.8% when using a 2DOF PID controller. Furthermore, EMG data shows a reduction in peak EMG value when using the exoskeleton in assistive mode compared to the exoskeleton operating in transparent mode. 

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5. Adaptive Robust Tracking Control for Hybrid Models of Three-Dimensional Bipedal Robotic Walking Under Uncertainties

   https://doi.org/10.1115/1.4050259  

   Gu, Yan; Yuan, Chengzhi (August 2021, Journal of Dynamic Systems, Measurement, and Control)

   Abstract This paper introduces an adaptive robust trajectory tracking controller design to provably realize stable bipedal robotic walking under parametric and unmodeled uncertainties. Deriving such a controller is challenging mainly because of the highly complex bipedal walking dynamics that are hybrid and involve nonlinear, uncontrolled state-triggered jumps. The main contribution of the study is the synthesis of a continuous-phase adaptive robust tracking control law for hybrid models of bipedal robotic walking by incorporating the construction of multiple Lyapunov functions into the control Lyapunov function. The evolution of the Lyapunov function across the state-triggered jumps is explicitly analyzed to construct sufficient conditions that guide the proposed control design for provably guaranteeing the stability and tracking the performance of the hybrid system in the presence of uncertainties. Simulation results on fully actuated bipedal robotic walking validate the effectiveness of the proposed approach in walking stabilization under uncertainties. 

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