This work uses SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings, alleviating the curse of dimensionality.
Abstract
Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require several system simulations, which are often computationally demanding due to the high-dimensionality of the underlying spatio-temporal dynamics. In this work, we exploit SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings. After training the model on a few optimal examples given by an expert demonstrator, SHRED-ROM mimics the expert behavior with effective distributed control actions in new scenarios, alleviating the curse of dimensionality. Moreover, a sensor forecaster is synthesized and used to close the loop at the latent level, thus efficiently mitigating possible sensor failures or delays. The performance of the proposed optimal control strategy is finally assessed on three challenging high-dimensional cases dealing with either parametric density control or fluid flow control.
Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems. However, RL algorithms are sample inefficient and require a large number of interaction with the environment to synthesize optimal control strategies. Consequently, applications of RL are typically limited to sparse sensors and actuators due to the curse of dimensionality entailed by the exploration-exploitation dilemma in high-dimensional spaces. In this work, we bridge RL and traditional optimal control for dynamical system with a novel Physics-EnhAnced Reinforcement Learning (PEARL) paradigm tailored to the control of high-dimensional and parametric dynamical systems, exploiting the differentibility of their dynamics. Specifically, PEARL employs an actor-adjoint algorithm that leverages automatic differentiation to compute policy gradients over short horizons and adjoint-based sensitivities of future returns approximated via neural networks, significantly reducing the number of environment interactions, while mitigating long-term gradient instabilities. Through two challenging parametric navigation problems in unsteady flows, we show that PEARL (i) effectively exploits differentiable environments to outperform state-of-the-art RL algorithms, (ii) is sample efficient, thanks to the physics-guided policy learning, (iii) generalizes across multiple scenarios, which is crucial when dealing with parametric systems, and (iv) enables scaling RL to high-dimensional state and action spaces, without requiring low-dimensional state representations or multi-agent strategies.
Matteo Tomasetto, Nicolò Botteghi, Gabriele Bruni et al.· 0 citations
Active flow control involves nonlinear dynamics, partial observations, and computationally expensive simulations, making controller design particularly challenging. Deep reinforcement learning (DRL) has emerged as a powerful framework for such problems, but its success typically relies on large numbers of simulator interactions and produces neural-network policies whose decision process often remains difficult to interpret. In this work, we investigate a different paradigm: instead of optimizing neural-network parameters, we use modern coding agents to search directly for explicit executable feedback laws. We introduce a constrained heuristic-learning protocol in which an agent iteratively proposes, evaluates, and revises controller implementations while interacting exclusively through the public benchmark interface. The proposed framework is evaluated on 13 active flow-control benchmarks spanning one, two, and three-dimensional problems and compared against the strongest available DRL baselines under identical simulation budgets. The discovered heuristic controllers match or outperform the best DRL policy in 10 of the 13 environments while remaining compact, interpretable, and directly inspectable. Beyond aggregate performance, the resulting controllers reveal physically meaningful feedback mechanisms, transfer successfully across more challenging configurations, and remain competitive under varying Reynolds and Rayleigh numbers, actuator counts, and observation sparsity. These results suggest that heuristic learning through coding agents constitutes a credible and complementary alternative to conventional reinforcement learning, combining competitive performance with physically interpretable controller representations. Prompts and source code are available at https://github.com/DonsetPG/fluid-heuristic-learning.
Multi-step rollouts are essential for model-based reinforcement learning (RL) and predictive control, yet learned dynamics models often become unstable when recursively applied, leading to divergence and unreliable policy updates. This paper proposes a model-agnostic hybrid dynamics framework that blends a provably contracting nominal model with a flexible excursion model through an uncertainty-guided switching law. The switching signal is derived from calibrated epistemic uncertainty and activates only when the system leaves the nominal region, ensuring that each model operates within its reliability regime. Under clearly stated smoothness and boundedness assumptions, we show that the resulting hybrid predictor yields globally bounded recursive multi-step rollouts: trajectories remain Lyapunov-stable in the nominal region and exhibit at most affine growth during excursions. To illustrate the theory in practice, we instantiate the hybrid dynamics framework within a model-based RL scheme that uses real one-step transitions for value learning and hybrid rollouts for policy improvement. Experiments on a nonlinear Duffing oscillator demonstrate stable long-horizon prediction and improved cost-effort trade-offs relative to a stabilizing baseline.
Learning continuous-time representations of dynamical systems from observation data has emerged as a cornerstone of data-driven control and scientific machine learning. However, existing neural differential equations either treat external control inputs heuristically without providing strict structural guarantees, or enforce stability properties under the restrictive assumption of constant or vanishing inputs. This paper proposes the Input-Contraction Neural Differential Model (ICNDM), a novel deep learning framework that seamlessly incorporates time-varying control inputs while ensuring incremental exponential convergence via input-dependent contraction regularization. By leveraging an embedded input encoder and a parameterized metric network, the proposed architecture learns both the non-autonomous neural vector fields and a generalized Riemannian contraction metric simultaneously. We derive sufficient conditions for input-dependent contraction and formally establish an input-to-state contraction property under bounded external excitations. Extensive numerical evaluations on highly nonlinear chaotic oscillators and experimental data from a Permanent Magnet Synchronous Motor (PMSM) drive system demonstrate that ICNDM yields substantial reductions in long-horizon rollout errors and exhibits superior structural robustness against input perturbations compared with state-of-the-art neural differential benchmarks.
Experimental results in simulation and on real hardware demonstrate that the decentralized–supervised architecture can achieve comparable or improved aggregate tracking performance relative to a centralized policy, while preserving decentralized proposal generation and enabling execution-time supervisory coordination under partial observability.
A. Bozzi, Matteo Aicardi, E. Zero et al.· IEEE Access· 0 citations
Decision-making in high-dimensional, nonlinear systems remains a central challenge in robotics. While model-based methods like Model Predictive Control (MPC) offer sample efficiency and interpretability, their performance degrades when the dynamics model is inaccurate or long-horizon predictions are required. Conversely, model-free reinforcement learning (RL) learns policies directly from interaction but suffers from high sample complexity and unstable optimization. Recent advances in sequence modeling have inspired transformer-based decision-making frameworks that can unify MPC and RL, but their training typically faces significant optimization challenges due to highly non-convex loss landscapes. In this work, we propose a novel framework that integrates MPC with RL in a sequence decision-making framework and leverages a curvature-aware optimization to efficiently tackle non-convex loss landscapes. MPC provides predictions of locally optimal trajectories that guide the decision transformer, removing the need for extensive offline pretraining. To address the slow and unstable convergence of traditional optimizers, we train the policy in a Riemannian parameter space using an efficient Riemannian (curvature-aware) method, leading to faster and more robust optimization. We evaluate our framework on high-dimensional quadruped control tasks and demonstrate consistent improvements over strong baselines, including TRPO, SAC, and Online Decision Transformer, achieving higher returns and faster convergence.