arXiv subjects

Sunbochen Tang

Publications and source records attributed to Sunbochen Tang.

8 recordsLinked to original sources

arXiv2026

LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers

Linear matrix inequalities (LMIs) have played a central role in certifying stability, robustness, and forward invariance of dynamical systems. Despite rapid development in learning-based methods for control design and certificate synthesis, existing approaches often fail to preserve the hard matrix inequality constraints required for formal guarantees. We propose LMI-Net, an efficient and modular differentiable projection layer that enforces LMI constraints by construction. Our approach lifts the set defined by LMI constraints into the intersection of an affine equality constraint and the positive semidefinite cone, performs the forward pass via Douglas-Rachford splitting, and supports efficient backward propagation through implicit differentiation. We establish theoretical guarantees that the projection layer converges to a feasible point, certifying that LMI-Net transforms a generic neural network into a reliable model satisfying LMI constraints. Evaluated on experiments including invariant ellipsoid synthesis and joint controller-and-certificate design for a family of disturbed linear systems, LMI-Net substantially improves feasibility over soft-constrained models under distribution shift while retaining fast inference speed, bridging semidefinite-program-based certification and modern learning techniques.

cs.LG↗

arXiv2026

Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies

Diffusion and flow policies are gaining prominence in online reinforcement learning (RL) due to their expressive power, yet training them efficiently remains a critical challenge. A fundamental difficulty that distinguishes online RL from standard generative modeling is the lack of direct samples from the target Boltzmann distribution defined by the Q-function. To address this, two seemingly distinct families of methods have been proposed for diffusion policies: a noise-expectation family, which uses a weighted average of noise as the training target, and a gradient-expectation family, which employs a weighted average of Q-function gradients. However, it remains unclear how these objectives are formally related, or whether they can be synthesized into a more general formulation. In this paper, we propose a unified framework, reverse flow matching (RFM), which rigorously addresses the problem of training diffusion and flow models without direct target samples. By adopting a reverse inferential perspective, we formulate the training target as a posterior mean estimation problem given an intermediate noisy sample. Crucially, we introduce Langevin Stein operators to construct zero-mean control variates, deriving a general class of estimators that share the same expectation. We show that existing noise-expectation and gradient-expectation methods are simply two specific instances within this broader class. This unified view yields two key advancements: it extends the capability of targeting Boltzmann distributions from diffusion to flow policies, and it enables the principled combination of Q-value and Q-gradient information to form an effective estimator, thereby improving training efficiency and stability. We instantiate RFM to train a flow policy in online RL and demonstrate improved performance on continuous-control benchmarks compared to diffusion policy baselines.

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arXiv2025

ECO: Energy-Constrained Operator Learning for Chaotic Dynamics with Boundedness Guarantees

Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems are dissipative and ergodic, motivating data-driven models that aim to learn invariant statistical properties over long time horizons. While recent models have shown empirical success in preserving invariant statistics, they are prone to generating unbounded predictions, which prevent meaningful statistics evaluation. To overcome this, we introduce the Energy-Constrained Operator (ECO) that simultaneously learns the system dynamics while enforcing boundedness in predictions. We leverage concepts from control theory to develop algebraic conditions based on a learnable energy function, ensuring the learned dynamics is dissipative. ECO enforces these algebraic conditions through an efficient closed-form quadratic projection layer, which provides provable trajectory boundedness. To our knowledge, this is the first work establishing such formal guarantees for data-driven chaotic dynamics models. Additionally, the learned invariant level set provides an outer estimate for the strange attractor, a complex structure that is computationally intractable to characterize. We demonstrate empirical success in ECO's ability to generate stable long-horizon forecasts, capturing invariant statistics on systems governed by chaotic PDEs, including the Kuramoto--Sivashinsky and the Navier--Stokes equations.

eess.SY↗

arXiv2024

Learning Dissipative Chaotic Dynamics with Boundedness Guarantees

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven models that attempt to preserve invariant statistics over long horizons since many chaotic systems exhibit dissipative behaviors and ergodicity. Despite the recent progress in such models, they are still often prone to generating unbounded trajectories, leading to invalid statistics evaluation. To address this fundamental challenge, we introduce a modular framework that provides formal guarantees of trajectory boundedness for neural network chaotic dynamics models. Our core contribution is a dissipative projection layer that leverages control-theoretic principles to ensure the learned system is dissipative. Specifically, our framework simultaneously learns a dynamics emulator and an energy-like function, where the latter is used to construct an algebraic dissipative constraint within the projection layer. Furthermore, the learned invariant level set provides an outer estimate for the system's strange attractor, which is known to be difficult to characterize due to its complex geometry. We demonstrate our model's ability to produce bounded long-horizon forecasts that preserve invariant statistics for chaotic dynamical systems, including Lorenz 96 and a reduced-order model of the Kuramoto-Sivashinsky equation.

eess.SY↗

arXiv2024

Meta-Learning for Adaptive Control with Automated Mirror Descent

Adaptive control achieves concurrent parameter learning and stable control under uncertainties that are linearly parameterized with known nonlinear features. Nonetheless, it is often difficult to obtain such nonlinear features. To address this difficulty, recent progress has been made in integrating meta-learning with adaptive control to learn such nonlinear features from data. However, these meta-learning-based control methods rely on classical adaptation laws using gradient descent, which is confined to the Euclidean geometry. In this paper, we propose a novel method that combines meta-learning and adaptation laws based on mirror descent, a popular generalization of gradient descent, which takes advantage of the potentially non-Euclidean geometry of the parameter space. In our approach, meta-learning not only learns the nonlinear features but also searches for a suitable mirror-descent potential function that optimizes control performance. Through numerical simulations, we demonstrate the effectiveness of the proposed method in learning efficient representations and real-time tracking control performance under uncertain dynamics.

eess.SY↗

arXiv2023

Indirect Adaptive Optimal Control in the Presence of Input Saturation

In this paper, we propose a combined Magnitude Saturated Adaptive Control (MSAC)-Model Predictive Control (MPC) approach to linear quadratic tracking optimal control problems with parametric uncertainties and input saturation. The proposed MSAC-MPC approach first focuses on a stable solution and parameter estimation, and switches to MPC when parameter learning is accomplished. We show that the MSAC, based on a high-order tuner, leads to parameter convergence to true values while providing stability guarantees. We also show that after switching to MPC, the optimality gap is well-defined and proportional to the parameter estimation error. We demonstrate the effectiveness of the proposed MSAC-MPC algorithm through a numerical example based on a linear second-order, two input, unstable system.

math.OC↗

arXiv2021

Continuous Optimization-Based Drift Counteraction Optimal Control: A Spacecraft Attitude Control Case Study

This paper presents a continuous optimization approach to DCOC and its application to spacecraft high-precision attitude control. The approach computes a control input sequence that maximizes the time-before-exit by solving a nonlinear programming problem with an exponentially weighted cost function and purely continuous variables. Based on results from sensitivity analysis and exact penalty method, we prove the optimality guarantee of our approach. The practical application of our approach is demonstrated through a spacecraft high-precision attitude control example. A nominal case with three functional reaction wheels (RWs) and an underactuated case with only two functional RWs were considered. Simulation results illustrate the effectiveness of our approach as a contingency method for extending spacecraft's effective mission time in the case of RW failures.

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arXiv2021

Online Algorithms and Policies Using Adaptive and Machine Learning Approaches

This paper considers the problem of real-time control and learning in dynamic systems subjected to parametric uncertainties. We propose a combination of a Reinforcement Learning (RL) based policy in the outer loop suitably chosen to ensure stability and optimality for the nominal dynamics, together with Adaptive Control (AC) in the inner loop so that in real-time AC contracts the closed-loop dynamics towards a stable trajectory traced out by RL. Two classes of nonlinear dynamic systems are considered, both of which are control-affine. The first class of dynamic systems utilizes equilibrium points %with expansion forms around these points and a Lyapunov approach while second class of nonlinear systems uses contraction theory. AC-RL controllers are proposed for both classes of systems and shown to lead to online policies that guarantee stability using a high-order tuner and accommodate parametric uncertainties and magnitude limits on the input. In addition to establishing a stability guarantee with real-time control, the AC-RL controller is also shown to lead to parameter learning with persistent excitation for the first class of systems. Numerical validations of all algorithms are carried out using a quadrotor landing task on a moving platform.

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