Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs.

"stitches" together the local solutions to learn the cost; it thereby avoids the "curse

Classical techniques suffer from limited applicability or huge computational costs.

We consider solutions to the linear quadratic Gaussian (LQG) regulator problem via policy gradient (PG) methods. Although PG methods have demonstrated strong theoretical guarantees in solving the linear quadratic regulator (LQR) problem, despite its nonconvex landscape, their theoretical understanding in the LQG setting remains limited. Notably, the LQG problem lacks gradient dominance in the classical parameterization, i.e., with a dynamic controller, which hinders global convergence guarantees. In this work, we study PG for the LQG problem by adopting an alternative parameterization of the set of stabilizing controllers and employing a lifting argument. We refer to this parameterization as a history representation of the control input as it is parameterized by past input and output data from the previous p time-steps. This representation enables us to establish gradient dominance and approximate smoothness for the LQG cost. We prove global convergence and per-iteration stability guarantees for policy gradient LQG in model-based and model-free settings. Numerical experiments on an open-loop unstable system are provided to support the global convergence guarantees and to illustrate convergence under different history lengths of the history representation.

Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and plan near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution.

Modeling and controlling cable-driven snake robots is a challenging problem due to nonlinear mechanical properties such as hysteresis, variable stiffness, and unknown friction between the actuation cables and the robot body. This challenge is more significant for snake robots in ophthalmic surgery applications, such as the Improved Integrated Robotic Intraocular Snake (I$^2$RIS), given its small size and lack of embedded sensory feedback. Data-driven models take advantage of global function approximations, reducing complicated analytical models' challenge and computational costs. However, their performance might deteriorate in case of new data unseen in the training phase. Therefore, adding an adaptation mechanism might improve these models' performance during snake robots' interactions with unknown environments. In this work, we applied a model predictive path integral (MPPI) controller on a data-driven model of the I$^2$RIS based on the Gaussian mixture model (GMM) and Gaussian mixture regression (GMR). To analyze the performance of the MPPI in unseen robot-tissue interaction situations, unknown external disturbances and environmental loads are simulated and added to the GMM-GMR model. These uncertainties of the robot model are then identified online using a radial basis function (RBF) whose weights are updated using an extended Kalman filter (EKF). Simulation results demonstrated the robustness of the optimal control solutions of the MPPI algorithm and its computational superiority over a conventional model predictive control (MPC) algorithm.

End-to-end autonomous driving research currently faces a critical challenge in bridging the gap between open-loop training and closed-loop deployment. Current approaches are trained to predict trajectories in an open-loop environment, which struggle with quick reactions to other agents in closed-loop environments and risk generating kinematically infeasible plans due to the gap between open-loop training and closed-loop driving. In this paper, we introduce Hydra-NeXt, a novel multi-branch planning framework that unifies trajectory prediction, control prediction, and a trajectory refinement network in one model. Unlike current open-loop trajectory prediction models that only handle general-case planning, Hydra-NeXt further utilizes a control decoder to focus on short-term actions, which enables faster responses to dynamic situations and reactive agents. Moreover, we propose the Trajectory Refinement module to augment and refine the planning decisions by effectively adhering to kinematic constraints in closed-loop environments. This unified approach bridges the gap between open-loop training and closed-loop driving, demonstrating superior performance of 65.89 Driving Score (DS) and 48.20% Success Rate (SR) on the Bench2Drive dataset without relying on external experts for data collection. Hydra-NeXt surpasses the previous state-of-the-art by 22.98 DS and 17.49 SR, marking a significant advancement in autonomous driving. Code will be available at https://github.com/woxihuanjiangguo/Hydra-NeXt.

Designing controllers that are both safe and performant is inherently challenging. This co-optimization can be formulated as a constrained optimal control problem, where the cost function represents the performance criterion and safety is specified as a constraint. While sampling-based methods, such as Model Predictive Path Integral (MPPI) control, have shown great promise in tackling complex optimal control problems, they often struggle to enforce safety constraints. To address this limitation, we propose DualGuard-MPPI, a novel framework for solving safety-constrained optimal control problems. Our approach integrates Hamilton-Jacobi reachability analysis within the MPPI sampling process to ensure that all generated samples are provably safe for the system. On the one hand, this integration allows DualGuard-MPPI to enforce strict safety constraints; at the same time, it facilitates a more effective exploration of the environment with the same number of samples, reducing the effective sampling variance and leading to better performance optimization. Through several simulations and hardware experiments, we demonstrate that the proposed approach achieves much higher performance compared to existing MPPI methods, without compromising safety.