physics-informed control

This work addresses the low sample efficiency and inconsistent actions often observed in reinforcement learning for robotic control, which stem from neglecting known physical dynamics. To this end, the authors propose PIPER, a novel framework that seamlessly integrates physical priors into policy learning by incorporating a differentiable Lagrangian dynamics residual—computed via a standard simulator—as a soft regularization term directly into the policy objective. Crucially, this approach requires no modifications to the underlying simulator or reinforcement learning algorithm. By softly enforcing analytical physical constraints during policy updates, PIPER achieves a tight coupling between physical consistency and learning, significantly improving sample efficiency, training stability, and control accuracy. Empirical results across multiple robotic tasks demonstrate that policies trained with PIPER exhibit superior physical plausibility and overall performance compared to baseline methods.

This work addresses the challenge of ensuring safety in industrial cyber-physical systems when applying deep reinforcement learning, where black-box exploration may inadvertently violate hardware constraints and conventional reward shaping struggles to balance safety with task performance. To overcome this, the authors propose a physics-informed safety mechanism that embeds a differentiable dynamics model into the loss function of a Proximal Policy Optimization (PPO) policy network. By performing short-horizon forward simulations to predict trajectories, the method imposes soft penalties—decoupled from the task-specific reward—on potential safety violations. This approach regularizes the policy online without requiring intricate reward engineering. Evaluated on a one-degree-of-freedom helicopter simulation platform, the method significantly reduces pitch angle constraint violations while maintaining excellent trajectory tracking performance.

This paper addresses stochastic optimal control problems by proposing a physics-informed neural network (PINN)-based policy iteration framework for nonlinear stochastic systems governed by second-order Hamilton–Jacobi–Bellman (HJB) equations. The method parameterizes the value function using a neural network and performs value evaluation via L²-minimization of the linear PDE residual induced by a fixed policy. Crucially, it establishes, for the first time, an explicit Lipschitz-type bound quantifying how value gradient estimation error propagates to policy update error—enhancing both interpretability and training stability. Theoretical analysis preserves the global exponential convergence guarantee of classical policy iteration. Empirical evaluation on benchmark tasks—including stochastic CartPole, a nonlinear pendulum, and a 10-dimensional linear-quadratic regulator—demonstrates the method’s effectiveness and scalability to high-dimensional settings.

This work addresses the challenges of real-time optimal control in high-dimensional dynamical systems, where low sample efficiency, the curse of dimensionality in exploration, and gradient instability hinder performance. The authors propose the PEARL framework, which uniquely integrates the adjoint method with a neural network-based reward function. By exploiting the differentiability of system dynamics, PEARL employs an actor-adjoint algorithm that combines automatic differentiation with adjoint sensitivity analysis to efficiently compute policy gradients over short horizons. This approach enables physics-informed policy learning, significantly enhancing sample efficiency and generalization while operating directly in high-dimensional state-action spaces. Evaluated on unsteady flow navigation tasks, PEARL outperforms existing reinforcement learning methods and scales to high-dimensional control problems without requiring dimensionality reduction or multi-agent architectures.

To address the scalability limitations of centralized policies and the lack of coordination in independent policies for multi-robot systems, this paper proposes a scalable and physically consistent distributed reinforcement learning framework. Methodologically, it pioneers the integration of port-Hamiltonian system modeling with graph self-attention mechanisms, enabling efficient local information utilization under dynamic interaction graphs while enforcing energy conservation; it employs distributed policy parameterization—bypassing value function decomposition—and explicitly encodes inter-robot dependencies. Key contributions include: (1) a self-attention–enhanced port-Hamiltonian policy representation; (2) zero-shot post-training scalability to robot swarms six times larger than those used during training; and (3) cumulative rewards twice those of prior state-of-the-art methods across multiple tasks, demonstrating significant improvements in scalability and collaborative efficiency.

This work proposes a hybrid control framework that integrates physics-informed neural networks (PINNs) with model predictive control (MPC) to address the limitations of both traditional and purely data-driven approaches for satellite attitude control. Traditional methods rely on high-fidelity dynamical models that are complex and computationally expensive, whereas data-driven strategies often suffer from poor generalization and inadequate stability guarantees. By embedding physical priors into neural network training, the proposed approach constructs a robust and accurate surrogate model of attitude dynamics, which is then combined with a linear nominal model to form a nonlinear–linear hybrid MPC architecture. Experimental results demonstrate that, compared to purely data-driven methods, the proposed framework reduces the mean relative prediction error by 68.17% and shortens closed-loop settling time by 61.52%–76.42% under measurement noise and reaction wheel friction disturbances, while ensuring stable convergence.

This work addresses the challenge of efficiently learning and controlling actuator-to-configuration mappings defined by implicit equilibrium relations in physical AI tasks, particularly in multistable systems. The authors propose a boundary control framework that, for the first time, integrates the adjoint method into implicit equilibrium systems. By differentiating the equilibrium conditions, the approach yields trajectory-dependent surrogate gradients without unrolling iterative solvers, enabling memory-efficient and trajectory-sensitive gradient estimation. Coupled with receding-horizon model predictive control (MPC), the method substantially enhances long-horizon control robustness and effectively mitigates issues associated with switching between metastable energy basins. In manipulation tasks involving deformable linear objects, both simulation and real-world experiments demonstrate significant performance improvements over gradient-free baselines such as SPSA and CEM.

Modeling inconsistency arises in complex cyber-physical systems where unknown dynamics coexist with known algebraic invariants. Method: We propose physics-embedded neural network frameworks—HRPINN and PHRPINN—that hard-embed known differential equations into a recurrent integrator and enforce algebraic invariants via a prediction-projection mechanism. Our approach integrates physics-informed neural networks, differential-algebraic equation modeling, and projection-based regularization to learn residual dynamics while preserving physical consistency. Contribution/Results: Theoretical analysis and numerical experiments demonstrate high accuracy and data efficiency on battery lifetime prediction and standard constrained benchmarks. Notably, this work is the first to systematically characterize the intrinsic trade-off among physical consistency, computational cost, and numerical stability—providing foundational insights for robust, interpretable learning in constrained dynamical systems.

To address the challenge of simultaneously ensuring safety, energy efficiency, and trajectory smoothness for UAVs operating in dynamic wind fields, this paper proposes a physics-informed neural network (PINN) framework. The method explicitly encodes the UAV’s six-degree-of-freedom dynamics, wind disturbance models, and obstacle constraints into the neural architecture, enabling unsupervised end-to-end optimization via minimization of physical residuals and a risk-aware objective—without requiring ground-truth trajectory labels. Its key innovation lies in the synergistic integration of PINN-based modeling with gradient-free sampling strategies, unifying model-driven and data-driven paradigms. Experimental results demonstrate that the proposed approach reduces energy consumption by 12.7%, decreases trajectory jitter by 38.5%, and improves minimum safety distance by a factor of 2.1, while maintaining flight efficiency comparable to Kino-RRT*. It significantly outperforms A* and conventional sampling-based planners.

To address the poor stability and weak adaptability of conventional PID controllers in nonlinear systems, this paper proposes a physics-informed neural network (PINN)-based adaptive PID control method. The approach embeds a PINN within a closed-loop control framework, leveraging automatic differentiation to precisely compute system gradients and jointly integrating model predictive control with gradient-based optimization to minimize, online, a weighted cost function comprising tracking error and control effort—thereby enabling real-time adaptation of PID gains. Its key innovation lies in the first-ever construction of an adaptive PID architecture that deeply fuses data-driven learning with first-principles modeling, simultaneously ensuring superior dynamic response, steady-state accuracy, and robustness. Numerical experiments demonstrate that the proposed method significantly outperforms both conventional PID and purely data-driven approaches in time-domain tracking precision and frequency-domain disturbance rejection, while exhibiting strong resilience to model mismatch and external disturbances.