QENDy learns quadratic dynamics from nonlinear systems data.
problem Identifying governing equations of highly nonlinear dynamical systems.
method QENDy embeds nonlinear dynamics into a quadratic feature space, requiring trajectory data and preselected basis functions.
result QENDy accurately identifies quadratic dynamics and outperforms SINDy and deep learning methods.
Paper classifies conic submanifolds in control systems.
problem Characterizing and classifying conic submanifolds in control systems.
method Feedback equivalence of control-affine and fully nonlinear systems.
result Complete description of non-degenerate conic submanifolds.
We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of R m {\Bbb R}^{m} R m , and establish 1 − 1 1-1 1 − 1 correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and orthogonal multiplications of the form $μ:{\Bbb R}^{n} \times {\Bbb R}^{m} \longrightarr…
Efficient online control algorithms for noisy systems with quadratic losses.
problem Controlling linear systems with known dynamics and adversarial losses.
method Novel SDP relaxation for steady-state distribution, ensuring strongly stable policies.
result Guaranteed O ( T ) O(\sqrt{T}) O ( T ) regret for online learning algorithms. The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.
problem Optimal transport problem in Linear Quadratic optimal control systems.
method Well-posedness of the Monge problem, regularity of optimal transport map, displacement interpolation of measures.
result Derivation of general interpolation inequalities for entropy functionals.
Solves new quadratic BSDE systems for market performance analysis.
problem Characterizing forward performance processes in regime switching markets.
method Introduces and solves ergodic BSDE systems in infinite time horizon.
result Connection between ergodic BSDE solutions and long-term growth rates of utility maximization.
Study shows certainty equivalent policy minimizes regret in continuous-time systems.
problem Minimizing regret in continuous-time stochastic linear-quadratic systems.
method Theoretical analysis of randomized certainty equivalent policy.
result Establishes square-root of time regret bounds and linear scaling with parameters.
Efficient algorithm reduces control system learning regret to sqrt(T).
problem Learning Linear-Quadratic Regulators with unknown dynamics efficiently.
method First computationally-efficient algorithm with sqrt(T) regret.
result Resolves open question on control system learning.
LqgOpt learns optimal control in unknown LQG systems with minimal regret.
problem Adaptive control in partially observable linear quadratic Gaussian systems with unknown dynamics.
method Optimism in the face of uncertainty, predictor state evolution, closed-loop system identification, confidence bounds.
result Proves a regret upper bound of i l d e O ( T ) ilde{\mathcal{O}}(\sqrt{T}) i l d e O ( T ) for LQG systems. Quantizes Stäckel integrable systems into self-adjoint operators.
problem Quantizing Stäckel integrable systems into self-adjoint operators.
method Constructs commutative self-adjoint operators from quadratic Hamiltonians in involution.
result Proves multiplicative separation of variables for Stäckel integrable systems.
We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only …
Safe control of systems with unknown dynamics using persistent excitation.
problem Tension between safety and exploration in data-driven control.
method System identification through persistent excitation, robust constraint satisfaction, and synthesis of feedback controllers.
result Non-asymptotic guarantees on estimation and controller performance.
Gradient model for memristive systems in neurophysiology and neuromorphic circuits.
problem Understanding and modeling memristive systems.
method Introducing a gradient modeling framework based on Chua's definition of memristive elements.
result Gradient properties of memristive systems have implications for neuromorphic circuit analysis and design.
Algorithm minimizes regret in adaptive control of unknown linear systems.
problem Adaptive control of unknown linear systems with quadratic costs.
method Provably polynomial time algorithm using recent developments in system estimation and robust controller synthesis.
result First algorithm with high probability guarantees of sub-linear regret.
The study sets limits on how well systems can be controlled adaptively.
problem Learning to control unknown linear Gaussian systems with quadratic costs.
method Combining ideas from experiment design, estimation theory, and perturbation bounds of information matrices.
result Regret lower bounds of the order of T \sqrt{T} T in the time horizon T T T accurately capture control-theoretic parameters. Optimism-based methods improve adaptive regulation of linear-quadratic systems.
problem Trade-off between identifying unknown dynamics and regulating the system.
method Optimism-based adaptive policies that favor optimistic approximations of true parameters.
result Established high probability upper bounds for worst-case regret of optimism-based adaptive policies.
Policy gradient converges to globally optimal policy in nearly linear-quadratic systems.
problem Finding optimal policies in nonlinear control systems with partial information.
method Policy gradient algorithm designed for nearly linear-quadratic regulators with small Lipschitz nonlinear components.
result Policy gradient algorithm converges to globally optimal policy with linear rate.
Study derivative-free methods for linear policies in linear-quadratic systems.
problem Optimizing policies in linear-quadratic systems with limited derivative information.
method Derivative-free methods applied to linear policies over various noise and reward feedback settings.
result These methods converge to near-optimal policies with a polynomial number of zero-order evaluations.
In this paper, the symmetry group of a differential system of n quadratic homogeneous first order ODEs of n variables is studied. For this purpose, we consider the action of both point and contact transformations to signify the corresponding Lie algebras. We also find the independent differential invariants of these ac…
Quadratic growth of intersecting curves on surfaces resolved.
problem Understanding the largest size of intersecting simple closed curves on surfaces.
method Introduced almost nibs, flowers, and stem systems to analyze curve intersections.
result The size of intersecting curves grows quadratically with the surface's Euler characteristic.
The paper studies quadratic Poisson structures on Lie algebras, finding a 10-parametric family.
problem Compatibility of quadratic Poisson structures with linear structures on Lie algebras.
method Developed general theory and studied families of functions in involution.
result Found a 10-parametric family of quadratic Poisson structures on $\gl(3)^*$ .
This research shows how quadratic models can recover tensors with fewer samples than traditional methods.
problem Predicting missing entries in tensors with limited observations.
method Examined non-convex methods for learning quadratic models and their sample complexity.
result All local minima of the mean squared error objective are global minima, recovering the original tensor with linear samples.
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under Möbius transformations. They can be obtained from discrete harmonic functions in the sense of the cotangent …
Develops a control framework for systemic risk under uncertainty.
problem Systemic risk under model uncertainty.
method Linear-quadratic mean-field control framework with viscosity solutions and verification theorems.
result Explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability.
Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from the Christoffel symbols. The procedure is extended for determining if a second …
The paper tackles control policy learning for unknown systems using convex optimization.
problem Learning control policies for unknown linear dynamical systems to maximize a quadratic reward function.
method Sequential convex programming to optimize expected reward over posterior system parameter distribution.
result The method achieves reliable local convergence and robust stability, demonstrated with strong performance and robustness in simulations and real-world applications.
The study connects triangulated surfaces to complex projective structures and circle patterns.
problem Understanding circle patterns on complex projective tori.
method Using discrete holomorphic quadratic differentials, the approach involves cross ratio systems and Delaunay angles.
result For any triangulated torus, the projection map is a covering map with at most one branch point.
Study optimizes resource allocation in noisy systems for better control.
problem Limited attention in stochastic systems with multiplicative noise.
method Analytical and numerical methods for optimal attention allocation.
result Effective resource allocation enhances noise estimation and control decisions.
New LQR kernels improve controller learning from data.
problem Optimal controller design for nonlinear systems from data is challenging.
method Developed LQR kernels for Bayesian optimization.
result LQR kernels lead to superior learning performance on uncertain systems.
New model-free algorithm achieves similar LQR regret guarantees.
problem Model-free control of linear dynamical systems under quadratic costs.
method Online policy gradient scheme with policy space cost analysis.
result Achieves regret scaling with √T, matching model-based methods.
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…
Algorithm reduces regret in partially observable systems by learning dynamics and using optimistic control.
problem Minimizing regret in partially observable linear quadratic control systems with unknown dynamics.
method ExpCommit algorithm that learns model parameters and uses optimism in uncertainty.
result End-to-end sublinear regret upper bound of O ~ ( T 2 / 3 ) \tilde{\mathcal{O}}(T^{2/3}) O ~ ( T 2/3 ) for ExpCommit. New algorithms achieve logarithmic regret in learning linear quadratic control systems.
problem Learning in Linear Quadratic Control systems with unknown parameters.
method Efficient algorithms for two scenarios: unknown A A A or B B B with certain conditions. result Regret scales logarithmically with the number of steps, not square root.
Unified analysis of SAGA, Finito, SDCA using jump systems and quadratic constraints.
problem Analyzing convergence rates of stochastic optimization methods.
method Incorporating jump system theory and quadratic constraints to derive convergence rate certifications.
result Derives linear matrix inequalities (LMIs) for convergence rates of SAGA, Finito, and SDCA.
Study Laplace operator spectra on Lie groups with specific root systems.
problem Calculating Laplace operator spectra on Lie groups.
method Explicit calculations for Lie groups with root systems B 4 B_4 B 4 , C 4 C_4 C 4 , and D 4 D_4 D 4 . result Established connection with number theory and quadratic forms.
Solves optimal control with constraints for stochastic systems.
problem Optimal control of constrained stochastic linear-quadratic systems.
method State separation theorem and Riccati equations for explicit solution.
result Explicit piecewise affine optimal control policy.
Paper addresses quadratic feasibility problems and their sample complexity.
problem Recovering complex vectors from quadratic measurements.
method Analyzes conditions for identifiability and explores optimization landscape.
result Gradient algorithms can converge to globally optimal solutions with high probability.
Geodesic flows with diagonalisable integrals are orthogonal.
problem Understanding geodesic flows with specific integrals.
method Analyzing quadratic integrals for geodesic flows.
result Diagonalisable integrals imply orthogonal separation of variables.
New integrable systems constructed for non-diagonal Killing tensors.
problem Constructing integrable Hamiltonian systems with quadratic momenta.
method Using Nijenhuis geometry and gl-regular Nijenhuis operators.
result Reproduces classical Stäckel construction and finds new systems for n≥3.
We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case R 4 ⟶ R 3 {\Bbb R}^{4}\longrightarrow {\Bbb R}^{3} R 4 ⟶ R 3 , we determine all quadr…
Hurwitz transformations are defined as specific automorphisms of a Cayley-Dickson algebra. These transformations generate quadratic and nonquadratic forms. We investigate here the Hurwitz transformations corresponding to Cayley-Dickson algebras of dimensions 2m = 2, 4 and 8. The Hurwitz transformations which lead to qu…
We consider the fundamental problem of solving quadratic systems of equations in n n n variables, where y i = ∣ ⟨ a i , x ⟩ ∣ 2 y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2 y i = ∣ ⟨ a i , x ⟩ ∣ 2 , i = 1 , … , m i = 1, \ldots, m i = 1 , … , m and x ∈ R n \boldsymbol{x} \in \mathbb{R}^n x ∈ R n is unknown. We propose a novel method, which starting with an initial guess computed by means of a …
Paper tackles robust control policy learning for uncertain systems.
problem Learning control policies for an unknown linear dynamical system with quadratic cost.
method Convex optimization method balancing exploitation and exploration.
result Minimizes worst-case cost by reducing uncertainty in model parameters.
Survey of quadratic form signatures in topology and dynamics.
problem Understanding quadratic form signatures in manifold and dynamical systems.
method Historical survey and expanded with new Appendix.
result Expanded understanding of quadratic form signatures in algebraic L-theory.
Time-inconsistent game solved with differential equations.
problem Time inconsistency in stochastic linear-quadratic games.
method Defined and derived equilibrium strategies via FBSDEs.
result Explicit equilibrium strategy found for 1D deterministic case.
Article explores G2-structures with quadratic conditions, finding new ERP and complete solitons.
problem Investigating closed G2-structures satisfying quadratic conditions.
method Analyzing a second-order PDE system involving parameter λ, producing new examples of ERP and complete solitons.
result First examples of ERP G2-structures, including complete inhomogeneous ERP G2-structure.
New algorithm reduces learning regret in multi-agent systems with unknown dynamics.
problem Challenges in decentralized learning due to unknown dynamics and lack of communication.
method Proposed MARL algorithm for two-agent LQ systems with unknown dynamics and one-directional communication.
result Achieved O ( T ) O(\sqrt{T}) O ( T ) regret bound for multi-agent LQ systems with certain communication patterns. 2-compatible Lie algebras are quadratic deformations of Lie algebras with specific constraints.
problem Classifying contact Lie algebras using quadratic deformations.
method Defining 2-compatible Lie algebras as quadratic deformations of Lie algebras and studying the constraints on these deformations.
result Any (2p+1)-dimensional contact Lie algebra is isomorphic to a quadratic deformation of the Heisenberg algebra.