More Like this

1. A hybrid predictive control algorithm for tracking in a single-phase DC/AC inverter

   https://doi.org/10.1109/CCTA.2017.8062574  

   Torquati, Luca; Sanfelice, Ricardo G.; Zaccarian, Luca (August 2017, Proceedings of 2017 IEEE Conference on Control Technology and Applications (CCTA))

   In this paper we design a hybrid predictive controller for the tracking of a sinusoidal reference signal. The stability and forward invariance of a set of points around the reference state, named the tracking ellipse, is established by using tools for hybrid dynamical systems. Moreover, prediction of solutions for a finite number of switching events is used to minimize the number of switches. The control algorithm is shown to be robust to small perturbations and input disturbances. Simulations illustrating the main results are included. 

   more » « less
2. Control barrier functionals: Safety‐critical control for time delay systems

   https://doi.org/10.1002/rnc.6751  

   Kiss, Adam K.; Molnar, Tamas G.; Ames, Aaron D.; Orosz, Gabor (August 2023, International Journal of Robust and Nonlinear Control)

   Abstarct This work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples. 

   more » « less
3. iLQR for Piecewise-Smooth Hybrid Dynamical Systems

   https://doi.org/10.1109/CDC45484.2021.9683506  

   Kong, Nathan J.; Council, George; Johnson, Aaron M. (December 2021, IEEE Conference on Decision and Control)

   Trajectory optimization is a popular strategy for planning trajectories for robotic systems. However, many robotic tasks require changing contact conditions, which is difficult due to the hybrid nature of the dynamics. The optimal sequence and timing of these modes are typically not known ahead of time. In this work, we extend the Iterative Linear Quadratic Regulator (iLQR) method to a class of piecewise-smooth hybrid dynamical systems with state jumps by allowing for changing hybrid modes in the forward pass, using the saltation matrix to update the gradient information in the backwards pass, and using a reference extension to account for mode mismatch. We demonstrate these changes on a variety of hybrid systems and compare the different strategies for computing the gradients. 

   more » « less
4. Immersion and Invariance-based Disturbance Observer and Its Application to Safe Control

   https://doi.org/10.1109/TAC.2024.3416323  

   Wang, Yujie; Xu, Xiangru (January 2024, IEEE Transactions on Automatic Control)

   When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance relative degree, which can pose significant limitations. This note introduces a systematic approach for designing an Immersion and Invariance-based Disturbance Observer (IIDOB) that circumvents these strong assumptions. The proposed IIDOB ensures the disturbance estimation error is globally uniformly ultimately bounded by approximately solving a partial differential equation while compensating for the approximation error. Furthermore, by integrating IIDOB into the framework of control barrier functions, a filter-based safe control design method for control affine systems with disturbances is established where the filter is used to generate an alternative disturbance estimation signal with a known derivative. Sufficient conditions are established to guarantee the safety of the disturbed systems. Simulation results demonstrate the effectiveness of the proposed method. 

   more » « less
5. A model-constrained discontinuous Galerkin Network (DGNet) for compressible Euler equations with out-of-distribution generalization

   https://doi.org/10.1016/j.cma.2025.117912  

   Nguyen, Hai Van; Chen, Jau-Uei; Bui-Thanh, Tan (May 2025, Computer Methods in Applied Mechanics and Engineering)

   Real-time accurate solutions of large-scale complex dynamical systems are critically needed for control, optimization, uncertainty quantification, and decision-making in practical engineering and science applications, particularly in digital twin contexts. Recent research on hybrid approaches combining numerical methods and machine learning in end-to-end training has shown significant improvements over either approach alone. However, using neural networks as surrogate models generally exhibits limitations in generalizability over different settings and in capturing the evolution of solution discontinuities. In this work, we develop a model-constrained discontinuous Galerkin Network DGNet approach, a significant extension to our previous work, for compressible Euler equations with out-of-distribution generalization. The core of DGNet is the synergy of several key strategies: (i) leveraging time integration schemes to capture temporal correlation and taking advantage of neural network speed for computation time reduction. This is the key to the temporal discretization-invariant property of DGNet; (ii) employing a model-constrained approach to ensure the learned tangent slope satisfies governing equations; (iii) utilizing a DG-inspired architecture for GNN where edges represent Riemann solver surrogate models and nodes represent volume integration correction surrogate models, enabling capturing discontinuity capability, aliasing error reduction, and mesh discretization generalizability. Such a design allows DGNet to learn the DG spatial discretization accurately; (iv) developing an input normalization strategy that allows surrogate models to generalize across different initial conditions, geometries, meshes, boundary conditions, and solution orders. In fact, the normalization is the key to spatial discretization-invariance for DGNet; and (v) incorporating a data randomization technique that not only implicitly promotes agreement between surrogate models and true numerical models up to second-order derivatives, ensuring long-term stability and prediction capacity, but also serves as a data generation engine during training, leading to enhanced generalization on unseen data. To validate the theoretical results, effectiveness, stability, and generalizability of our novel DGNet approach, we present comprehensive numerical results for 1D and 2D compressible Euler equation problems, including Sod Shock Tube, Lax Shock Tube, Isentropic Vortex, Forward Facing Step, Scramjet, Airfoil, Euler Benchmarks, Double Mach Reflection, and a Hypersonic Sphere Cone benchmark. 

   more » « less