arXiv subjects

Wentao Tang

Publications and source records attributed to Wentao Tang.

At least 19 recordsLinked to original sources

arXiv2026

Koopman--Lyapunov and Koopman--Riccati Controller Synthesis

While the Koopman operator-based lifted representations of nonlinear autonomous and controlled systems have been well covered in the literature, the direct controller synthesis problem largely remains open. As the controlled system is generally a bilinear (instead of fully linear) Koopman model, controller synthesis appears to lose the linear--quadratic structures of the classical Lyapunov and Riccati methods for finite-dimensional linear systems. However, in infinite dimensions, bilinearity in the feature map should be merely artifactual and hence reducible to linearity in principle. In this work, by considering the operator semigroups in the reproducing kernel Hilbert space with a linear--Sobolev kernel and utilizing the Yosida approximation of their generators, the synthesis problems of a stabilizing controller and an input-unconstrained optimal controller can be formulated as an operator Lyapunov inequality and an operator Riccati equation, respectively. These formulations recover the desirable linear--quadratic structures, and hence, with sample data, they are solvable efficiently in analogous ways to usual linear systems by semidefinite programming solvers and Kleinman iterations, respectively. In addition to proving control performance bounds dependent on the sampling denseness and Yosida regularization, through numerical comparison to linearized LQR, bilinear EDMD-based synthesis, nonlinear MPC, and Koopman MPC methods on numerical models and process control examples, this work demonstrates the proposed Koopman--Riccati synthesis as a computationally efficient approach to obtain a near-optimal state-feedback control law.

math.OC↗

arXiv2026

Stochastic MPC under Heavy-Tailed Disturbances: An Extreme Value Theory Approach

Safety-critical control systems must contend with disturbances whose extreme deviations occur far more frequently than classical light-tailed models predict. Existing stochastic MPC (SMPC) formulations tighten constraints using an assumed distribution, a moment bound, or a finite scenario sample, each of which degrades under an unknown heavy-tailed disturbance. This paper develops an SMPC formulation for linear systems under heavy-tailed disturbances that is only assumed to be regularly varying, which allows an explicit extreme value theory (EVT) characterization of the tube error tail that is asymptotically exact. We further show that closed-loop dynamics induce temporal clustering of rare excursions across the prediction horizon, and characterize this clustering through a closed-form extremal index estimable from data. The resulting clustering-corrected constraint bounds the probability of a rare-event episode over the horizon, rather than only the marginal per-step exceedance probability. Simulations of a linear two-CSTR-in-series process and of a nonlinear unicycle navigating past an obstacle under Student-$t$ disturbances validate both approaches and demonstrate reduced frequencies of safety constraint violations.

eess.SY↗

arXiv2026

A Decomposition-Based Data-Driven Branch-and-Bound Approach for Black-Box Global Optimization

Many scientific and engineering applications require the global optimization of expensive black-box functions. In high-dimensional settings, however, achieving computational scalability is a major challenge. To address this challenge, we propose a distributed spatial branch-and-bound framework that exploits partially separable structure for the global optimization of box-constrained black-box problems. The proposed framework adopts a two-layer structure in which branching is performed only on a lower-dimensional set of coupling variables in an outer layer. Within each outer node, the remaining non-overlapping (private) variables, which appear independently across blocks, have their domains partitioned and explored in parallel within an inner layer, resulting in a naturally parallelizable framework that is well suited for implementation on multi-core CPU architectures. At each node, valid upper bounds are obtained via sampling, with optional refinement using a local solver, while lower bounds are computed using data-driven convex underestimators constructed over partitions of the private variables. A residual-based correction and finite-sample validity analysis provide conditions under which the partitionwise underestimators are valid lower bounds, while the proposed branching and refinement mechanism establishes convergence to an $ε$-global optimum. Numerical studies on benchmark and ODE-constrained parameter-estimation problems demonstrate improvements in both sampling efficiency and computational performance relative to monolithic approaches.

math.OC↗

arXiv2026

Koopman Observability of Nonlinear Systems and Data-Driven Koopman--Luenberger Observer

While nonlinear systems can be generally described as infinite-dimensional linear systems via their Koopman semigroups, the direct synthesis of state observers on the premise of learned Koopman operator models, in an analogous manner to finite-dimensional linear systems, remains an open problem. In this paper, the concepts of Koopman observability (exact and approximate), Koopman detectability (exponential and strong), and Koopman--Luenberger observer of nonlinear systems are provided. By defining the Koopman semigroup on a reproducing kernel Hilbert space (RKHS), the conditions for Koopman exponential detectability are established, which involves solving an operator Lyapunov inequality that only implicitly involves the the infinitesimal generator of the Koopman semigroup. Through the use of a finite-horizon Yosida approximation of the Koopman generator and an empirical sampling operator, the data-driven solution of the observer gain can be reduced to a finite-dimensional subspace specified by the sample and hence fulfilled by convex semidefinite programming. The state observation error is guaranteed to be bounded in mean squares, under closed-loop dissipation conditions on the sampling operator and its empirical operator.

math.OC↗

arXiv2026

Data-Driven State Observers for Measure-Preserving Systems

The use of data-driven control strategies on systems with not fully measurable states induces the problem of learning-based state observation. Motivated by this need, the present work proposes a data-driven approach for the synthesis of state observers for discrete-time nonlinear systems with measure-preserving dynamics. To this end, Kazantzis--Kravaris/Luenburger (KKL) observers are shown to be well-defined, where the observer design boils down to determining a nonlinear injective mapping of states and its pseudo-inverse. For its learning-based construction, the KKL observer is related to the Koopman operator, well-defined on the square-integrable function space and restrictable to a Sobolev-type reproducing kernel Hilbert space (RKHS). Hence, observer synthesis algorithms, based on kernel interpolation/regression routines for the desired injective mapping in the observer and its pseudo-inverse, are proposed in various settings of the available dataset -- (i) many orbits, (ii) single long orbit, and (iii) snapshots. Theoretical error analyses are provided, and numerical studies on a chaotic Lorenz system are demonstrated.

eess.SY↗

arXiv2026

Data-Driven Domain of Attraction Estimation via Convergent Koopman-Zubov Approximation

The computation of a domain of attraction (DOA) around an equilibrium point is a key issue in nonlinear stability analysis, which boils down to the difficult problem of searching for a Zubov function. With an operator-theoretical viewpoint of nonlinear systems, the concept of Zubov--Koopman operator has been introduced. However, due to the lack of convergence guarantee on the infinite-times action of Zubov--Koopman operator, the Zubov function estimate is unamenable to a theoretical bound under data-based learning errors. In this paper, considering a reproducing kernel Hilbert space (RKHS) with a linear--radial product kernel, the operator is proved to have a spectrum inside the unit circle. Hence, by augmenting this RKHS with constant-valued functions, the Zubov function that characterizes the DOA is obtained as the unique invariant element under the operator's action. This new RKHS formulation allows an efficient kernel-based estimation, which has an at most sectorially bounded error that scales down with the sample size. The proposed approach is tested with numerical examples, showing high accuracy of on-DOA/off-DOA classification of states, with two order-of-magnitude faster computation than neural networks.

eess.SY↗

arXiv2026

Koopman Operator for Stability Analysis: Theory with a Linear--Radial Product Reproducing Kernel

Koopman operator, as a fully linear representation of nonlinear dynamical systems, if well-defined on a reproducing kernel Hilbert space (RKHS), can be efficiently learned from data. For stability analysis and control-related problems, it is desired that the defining RKHS of the Koopman operator should account for both the stability of an equilibrium point (as a local property) and the regularity of the dynamics on the state space (as a global property). To this end, we show that by using the product kernel formed by the linear kernel and a Wendland radial kernel, the resulting RKHS is invariant under the action of Koopman operator (under certain smoothness conditions). Furthermore, when the equilibrium is asymptotically stable, the spectrum of Koopman operator is provably confined inside the unit circle, and escapes therefrom upon bifurcation. Thus, the learned Koopman operator with provable probabilistic error bound provides a stability certificate. In addition to numerical verification, we further discuss how such a fundamental spectrum--stability relation would be useful for Koopman-based control.

eess.SY↗

arXiv2026

Koopman--Nemytskii Operator of Nonlinear Controlled Systems and Its Learning for Controller Synthesis

While the Koopman operator represents a nonlinear system as a linear operator in a function space, its definition does not involve inputs. For controller synthesis, an operator model is needed to describe the effect of feedback laws on closed-loop systems, so that the desired state-feedback law can be computationally searched based on such a predictive model. To this end, this paper proposes a Koopman--Nemytskii operator, defined as a linear operator that maps canonical features of state--policy pairs in a reproducing kernel Hilbert space (RKHS) to that of succeeding states. Under regularity conditions on the dynamics and kernel selection, this operator is definable on suitable Sobolev-type RKHSs, and its data-based estimation guarantees bounded errors in single-step prediction, multi-step prediction, and accumulated cost under control. The controller synthesis problem is thus formulated as a convex kernel-based optimization one and efficiently solved in a sample-based manner.

eess.SY↗

arXiv2026

Koopman Modeling and Stabilization of Discrete-Time Nonlinear Control Systems: Bilinearity on a Reproducing Kernel Hilbert Space

Despite the popularity of Koopman modeling for nonlinear systems, in the presence of input variables, the evident nonexistence of a fully linear time-invariant model even in infinite dimensions makes Koopman-based control largely an open problem to date. Focusing on discrete-time systems in this paper, which eschews from using operator semigroup and infinitesimal generator notions, it is proven that nonlinear systems, if satisfying appropriate smoothness and regularity conditions, can be expressed exactly as bilinear dynamics, when the state variables and input variables are separately lifted into their reproducing kernel Hilbert spaces (RKHSs). To account for the knowledge of an equilibrium point at the origin, the RKHS is defined by a linear--radial product kernel, and hence the functions belonging to this RKHS are spanned by the multiplications of component functions and Sobolev functions. The stabilization problem, namely the determination of a feedback law that causes a Lyapunov function (expressed as a kernel sum-of-squares form) to decrease, is then posed as an infinite-dimensional optimization problem over state-dependent conditional probability measures over the input space, solved via a discretization scheme.

math.OC↗

arXiv2026

A constrained symbolic regression approach for Lyapunov function discovery

In this paper, we consider the data-driven discovery of Lyapunov functions for autonomous dynamical systems. We represent the Lyapunov function as an expression tree of fixed depth and formulate the Lyapunov discovery task as a constrained self-supervised symbolic regression problem. The constraints model the output of the Lyapunov function for a given input as well as the Lyapunov stability conditions. This modeling approach makes no a priori assumptions about the functional form of the Lyapunov function, is inherently interpretable since the function is obtained in a symbolic form, and, in principle, can be applied to any continuous dynamical system. We also develop a tailored branch-and-bound-and-check solution approach to efficiently solve the resulting learning task. Applications to several case studies show the ability of the proposed approach to discover Lyapunov functions.

eess.SY↗

arXiv2026

Convex Hybrid Modeling: An Operator-Based Approach

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear ones, promoting the use of operator theory, which ``universally'' represents a nonlinear system by a nonparametric operator. On the other hand, interpretability requires by a ``non-universal'', parametric nonlinear model family satisfying first principles; these constraints tend to complicate the learning procedure. This paper considers hybrid modeling by formulating convex learning problems that account for interpretability systematically and give surrogate models efficiently. Three settings are discussed -- (i) regularization around a particular ``reference model'', (ii) restriction on an ``interpretable subspace'', and more generally, (iii) restriction on a ``interpretable manifold'' that is nonlinearly parameterized. In the more general setting, by introducing an operator-theoretic technique to re-parameterize models in the ``lifted'' parameters (``canonical features'', potentially infinite-dimensional), the system is regarded as a kernel-based mixture of interpretable models. Application to both static and dynamic models are exemplified in numerical studies.

eess.SY↗

arXiv2026

Neural Luenberger state observer for nonautonomous nonlinear systems

This work proposes a method for model-free synthesis of a state observer for nonlinear systems with manipulated inputs, where the observer is trained offline using a historical or simulation dataset of state measurements. We use the structure of the Kazantzis-Kravaris/Luenberger (KKL) observer, extended to nonautonomous systems by adding an additional input-affine term to the linear time-invariant (LTI) observer-state dynamics, which determines a nonlinear injective mapping of the true states. Both this input-affine term and the nonlinear mapping from the observer states to the system states are learned from data using fully connected feedforward multi-layer perceptron neural networks. Furthermore, we theoretically prove that trained neural networks, when given new input-output data, can be used to observe the states with a guaranteed error bound. To validate the proposed observer synthesis method, case studies are performed on a bioreactor and a Williams-Otto reactor.

eess.SY↗

arXiv2026

EDMD-Based Robust Observer Synthesis for Nonlinear Systems

This paper presents a data-driven approach for designing state observers for continuous-time nonlinear systems, where an extended dynamic mode decomposition (EDMD) procedure is used to identify an approximate linear lifted model. Since such a model on a finite-dimensional space spanned by the dictionary functions has an inevitable mismatch, we first establish, based on our theory of reproducing kernel Hilbert space with a linear--radial kernel, that the nonlinear error magnitude in the approximate linear model is sectorially bounded by the lifted state. The sector bound comprises a deterministic part due to the finite dictionary and a stochastic part due to the random data samples, and the observer design needs to account for both of these errors in a robust formulation. Hence, the observer synthesis is performed using linear matrix inequalities (LMIs), specified by the desired exponential decay rate of the observation error (when the system is asymptotically stable) or the L2 gain from the modeling error to the observation error. Numerical studies demonstrate the effectiveness and flexibility of the proposed method. As such, this work entails an explicit elementary use of linear systems theory for nonlinear state observation in a Koopman operator-theoretic framework.

eess.SY↗

arXiv2026

Dissipativity Analysis of Nonlinear Systems: A Linear--Radial Kernel-based Approach

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system on a reproducing kernel Hilbert space (RKHS), the storage function and supply rate functions are expressed as kernel quadratic forms, through which the dissipative inequality is expressed as a linear operator inequality. The RKHS is specified by a linear--radial kernel, which inherently encode the information of equilibrium point, thus ensuring that all functions in the RKHS are locally at least linear around the origin and that kernel quadratic forms are locally at least quadratic, which expressively generalize conventional quadratic forms including sum-of-squares polynomials. Based on the kernel matrices of the sampled data, the dissipativity estimation can be posed as a finite-dimensional convex optimization problem, and a statistical learning bound can be derived on the kernel quadratic form for the probabilistic approximate correctness of dissipativity estimation.

eess.SY↗

arXiv2026

MovieTeller: Tool-augmented Movie Synopsis with ID Consistent Progressive Abstraction

With the explosive growth of digital entertainment, automated video summarization has become indispensable for applications such as content indexing, personalized recommendation, and efficient media archiving. Automatic synopsis generation for long-form videos, such as movies and TV series, presents a significant challenge for existing Vision-Language Models (VLMs). While proficient at single-image captioning, these general-purpose models often exhibit critical failures in long-duration contexts, primarily a lack of ID-consistent character identification and a fractured narrative coherence. To overcome these limitations, we propose MovieTeller, a novel framework for generating movie synopses via tool-augmented progressive abstraction. Our core contribution is a training-free, tool-augmented, fact-grounded generation process. Instead of requiring costly model fine-tuning, our framework directly leverages off-the-shelf models in a plug-and-play manner. We first invoke a specialized face recognition model as an external "tool" to establish Factual Groundings--precise character identities and their corresponding bounding boxes. These groundings are then injected into the prompt to steer the VLM's reasoning, ensuring the generated scene descriptions are anchored to verifiable facts. Furthermore, our progressive abstraction pipeline decomposes the summarization of a full-length movie into a multi-stage process, effectively mitigating the context length limitations of current VLMs. Experiments demonstrate that our approach yields significant improvements in factual accuracy, character consistency, and overall narrative coherence compared to end-to-end baselines.

cs.CV↗

arXiv2026

Koopman-based Estimation of Lyapunov Functions: Theory on a Reproducing Kernel Hilbert Space

Koopman operator provides a general linear description of nonlinear systems, whose estimation from data (via extended dynamic mode decomposition) has been extensively studied. However, the elusiveness between the Koopman spectrum and the stability of equilibrium point poses a challenge to utilizing the Koopman operator for stability analysis, which further hinders the construction of a universal theory of Koopman-based control. In our prior work, we defined the Koopman operator on a reproducing kernel Hilbert space (RKHS) using a linear--radial product kernel, and proved that the Koopman spectrum is confined in the unit disk of the complex plane when the origin is an asymptotically stable equilibrium point. Building on this fundamental spectrum--stability relation, here we consider the problem of Koopman operator-based Lyapunov function estimation with a given decay rate function. The decay rate function and the Lyapunov function are both specified by positive operators on the RKHS and are related by an operator algebraic Lyapunov equation (ALE), whose solution exists uniquely. The error bound of such a Lyapunov function estimate, obtained via kernel extended dynamic mode decomposition (kEDMD), are established based on statistical learning theory and verified by a numerical study.

eess.SY↗

arXiv2025

Machine Learning-based Optimal Control for Colloidal Self-Assembly

Achieving precise control of colloidal self-assembly into specific patterns remains a longstanding challenge due to the complex process dynamics. Recently, machine learning-based state representation and reinforcement learning-based control strategies have started to accumulate popularity in the field, showing great potential in achieving an automatable and generalizable approach to producing patterned colloidal assembly. In this work, we adopted a machine learning-based optimal control framework, combining unsupervised learning and graph convolutional neural work for state observation with deep reinforcement learning-based optimal control policy calculation, to provide a data-driven control approach that can potentially be generalized to other many-body self-assembly systems. With Brownian dynamics simulations, we demonstrated its superior performance as compared to traditional order parameter-based state description, and its efficacy in obtaining ordered 2-dimensional spherical colloidal self-assembly in an electric field-mediated system with an actual success rate of 97%.

cond-mat.soft↗

arXiv2025

Distributed Derivative-Free Optimization Using Inexact ADMM and Trust-Region Methods

To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject to linear equality constraints. The approach is built upon the alternating direction method of multipliers (ADMM) as the distributed optimization framework. To handle general, potentially complicating linear equality constraints beyond the standard ADMM formulation, we employ a two-level ADMM structure: an inner layer that performs sequential ADMM updates, and an outer layer that drives an introduced slack variable to zero via the method of multipliers. In addition, each subproblem is solved inexactly using a derivative-free trust-region solver, ensuring suboptimality within a decreasing, theoretically controlled error tolerance. This inexactness is critical for both computational efficiency and practical applicability in black-box settings, where exact solutions are impractical or overly expensive. We establish theoretical convergence of the proposed approach to an approximate solution, and demonstrate improved computational efficiency over monolithic derivative-free optimization approaches on challenging high-dimensional benchmarks, as well as effective performance on a distributed learning problem.

math.OC↗