Papers

In the digital twin paradigm, online parameter updating is essential. Unlike a static model, a digital twin must continuously adapt to the evolving dynamics of the system it represents. Adaptive observers, which jointly estimate states and parameters from online data, are therefore an increasingly important tool. In this work, we formulate a mode-wise adaptive observer for a class of autonomous switched nonlinear systems with switched unknown parameters. The main challenges are twofold: removing the disturbance that switching injects into the parameter-error dynamics and guaranteeing persistence of excitation over a finite-time window without relying on an input signal. To address them, we assign a dedicated adaptive observer to each mode, active only on its corresponding interval, which directly removes the zero-input disturbance caused by switching. We then introduce a finite-window persistence-of-excitation condition together with a minimum dwell-time condition, under which the parameter estimation error is contractive and the state estimation error is bounded within the active interval of each mode. The performance of the proposed approach is illustrated with an academic example and with a practical example of evolutionary therapies.

Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling. In particular, score differences arise naturally in transfer learning, where the score difference provides the mechanism for adapting a pre-trained model to a new target distribution, and in diffusion model-based post-training methods such as discriminator guidance. Existing estimators for score differences in these settings either lack of statistical consistency or are difficult to scale up in high-dimensions. We propose a statistically consistent and scalable estimator for score differences based on Sobolev regularization, which plays a crucial role in ensuring consistency and stablizing the training in the small-sample regime. Mathematically, we establish a convergence rate of $O(n^{-\frac{s-1}{d+2s-2}})$ where $d$ is the dimension and $s$ denotes the smoothness of the underlying densities, and provide a minimax lower bound of $\tilde{\Omega}(n^{-\frac{2(s-1)}{d+2s}})$ (in mean-squared error). Empirically, our estimator exhibits significantly improved stability in small-sample regimes compared to existing methods. We demonstrate its effectiveness on real-world tasks, including transfer learning for ECG signal generation, where it substantially outperforms non-regularized score difference estimators in downstream classification performance.

District heating networks are a central tool to achieve low-carbon heat supplies. In this realm, they face the challenge of dealing with increasingly heterogeneous, partially time-varying renewable sources, thermal storage, and meshed topologies. This paper examines global optimization of the operation of such district heating networks over multiple time steps, based on a stationary, yet realistical nonlinear network model. To accelerate the solution performance of a spatial branch-and-bound algorithm for one time step, the following new methodological ingredients are introduced: exclusion of cyclic flow, symmetry exploitation between supply and return networks, reduction of temperature mixing constraints, novel primal heuristics and branching rules. The proposed methods are evaluated on a set of generated and real-world benchmark network instances with cycles and several suppliers. On the generated benchmark instances, using these methods more than doubles the number of solved instances and more than halves the runtime. For the real-world benchmark instances, the resulting algorithm produces solutions with guaranteed quality in reasonable run time. For multiple time steps that are coupled by a storage, a time decomposition approach is investigated. Under assumptions that are reasonable in practice, this approach is shown to yield an optimal solution. On a small example network, this decomposition is able to compute optimal solutions in less than a second, while solving the complete time-coupled problem is not possible within one hour.

Recent publications have started to explore the application of Geometric Algebra (GA) to the modeling, analysis and control of dynamical systems and, in particular, electrical circuits. Since a crucial element there is to transform the ordinary differential equations governing the dynamical system which models the systems' behavior from the real domain to the Laplace domain, a definition of the Laplace transform in GA is needed. In the present work, we extend previous works dealing with extension to some hiper-complex algebras by introducing a definition of the Laplace transform within the framework of Geometric Algebra (GA). In particular, our definition and its properties are applicable to geometric algebras with signature lower or equal than 5.

Gray elements and material overlaps at the interfaces limit density-based multi-material topology optimization. This article extends the level set-based negative-mapping interpolation to the multi-material proportional topology optimization of macro-scale structures in two and three dimensions. An alternating active-phase algorithm decomposes M-phase problems into two-phase sub-problems described by level set functions; an evolutionary strategy removes the need for sentitivity analysis; and the negative-mapping interpolation eliminates the overlaps of the phases in the interface elements. Cantilever and half-MBB beams in two dimensions and a cantilever beam in three dimensions, with three and four material phases, give smooth boundaries, no gray elements and overlap-free designs. The compliance lies below the SIMP value in four of the eight two-dimensional cases and 0.3%, 0.4%, 4.8% and 12.7% above it in the other four. The influence of the material properties, of the interface treatment and of the algorithmic parameters is also examined.

This paper introduces a robust W-infinity optimal control framework for linear Itô diffusions using a weighted Sobolev-space performance measure. Because the sample paths of Itô diffusions are nondifferentiable, the formulation leverages the weak derivative of the expected state. An LMI-based semidefinite program is developed for dynamic output-feedback synthesis, and a rigorous stability analysis guarantees mean-square ultimate boundedness with minimized ultimate bound. A numerical example demonstrates that the proposed approach provides effective disturbance attenuation with fast transient performance.

Bilevel optimization is a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications. Due to their nested structure, however, bilevel problems are intrinsically hard to solve, even if all variables are continuous and all parameters of the problem are exactly known. Further challenges arise if mixed-integer aspects and problems under uncertainty are considered. In this article, we summarize selected results from the author's dissertation. We study mixed-integer linear min-max problems with a $\Gamma$-robust treatment of uncertain data, for which we present exact and heuristic solution approaches. The performance of the methods is assessed in a computational study on 560 instances of the knapsack interdiction problem. Our results show that the heuristic closes the optimality gap for a significant portion of the considered instances and often practically outperforms both heuristic and exact benchmark approaches.

We derive duality-based $\textit{a posteriori}$ error identities for a broad class of subgradient flows induced by time-dependent convex integral functionals. Starting from the Brézis-Ekeland-Nayroles principle, we identify an unsteady primal energy functional and derive its Fenchel dual formulation, including strong duality and the corresponding optimality system under general normal-integrand assumptions. This Fenchel duality framework is used to derive $\textit{a posteriori}$ error identities for subgradient flows. In doing so, we depart from the usual duality-based $\textit{a posteriori}$ error control framework in the unsteady setting, since the Brézis-Ekeland-Nayroles formulation reveals the following unsteady feature: the minimal primal value and the maximal dual value are both prescribed by the initial datum. This allows us to pass from a combined primal-dual gap identity to separate primal and dual gap identities. These identities quantify the primal and dual errors independently and admit representations in terms of generalized Bregman divergences and, under a spatial convex conjugation formula, as non-negative time-space integral quantities suitable for localization. The abstract framework is applied to a number of variational problems of physical interest, including the unsteady heat equation, the unsteady Stokes equations, the unsteady Navier-Lamé equations, the unsteady Bingham flow through a pipe, the unsteady obstacle problem, and the unsteady elasto-plastic torsion problem.

Multi-armed bandit algorithms are evaluated by regret, yet comparable regret can coexist with different allocations across independent runs. We study the trade-off between worst-case regret $\mathcal{R}_{K,T}$ and instability $\mathcal S_{K,T}$, defined as the largest standard deviation of a terminal pull count, for $K$ arms and $T$ rounds. We prove the finite-time lower bound $\mathcal R_{K,T}\mathcal S_{K,T}\ge C T^{3/2}$, where $C$ is independent of $K$ and $T$, under a finite-time regret condition and without the regularity assumptions imposed in the prior asymptotic analysis. We also introduce Stabilized Lower-Envelope UCB (\textup{SLE-UCB}), a new tunable algorithm combining a running lower-envelope index with a decreasing pull-count stabilizer. \textup{SLE-UCB} satisfies $\mathcal R_{K,T}\mathcal S_{K,T}=O(T^{3/2}\log K)$, with an implicit constant independent of $K$ and $T$, matching the lower bound exactly in $T$ and within a logarithmic factor in $K$. To prove the instability bound, we develop a new offline top-prefix representation that removes path dependence from online decisions. Together with single-reward perturbations and the Efron–Stein inequality, this representation controls pull-count variance. Thus, regret and instability depend reciprocally on $K$, while their product has no polynomial dependence on $K$. These results resolve the open question raised in the literature concerning the sharp arm-dependent regret–instability frontier.

We consider a quadratic minmax problem with coupled inner constraints and propose a method to compute a class of stationary points. To motivate the need to compute such stationary points, we first show that they are meaningful, in the sense that they can be locally optimal for our problem under suitable{non-degeneracy} conditions. Then based on a suitable log barrier function, we build an infeasible interior point-type {single loop method} (which does not explicitly distinguish between the outer and inner problem) and prove that a non-degenerate stationary point is an attraction point as the algorithm moves along the designed central path. We show in particular that our method is polynomial in the special case where the inner feasible set of our constrained minmax problem is independent from outer variables. Our numerical experiments, on both synthetic data and a class of min-cost flow problems, showcase the behavior of our method and how it outperforms existing algorithms from the literature in terms of the quality of the computed stationary points.

We show that Integer Quadratic Programming is W[1]-hard parameterized by the number of variables. Thus, under standard complexity assumptions, Integer Quadratic Programming cannot be solved in f(n)|I|^{O(1)} time for any computable function f where |I| is the size of the encoding and n is the number of variables.

We develop simulation-based policy iteration for continuous-time portfolio choice with predictable returns and convex constraints. Each outer step re-evaluates a fixed-latent open-loop backpropagation-through-time (OL-BPTT) adjoint after deployment and solves the constrained update. Shifted-adjoint cancellation controls the adjoint–HJB Hamiltonian-gradient discrepancy by the policy-improvement residual. For CRRA portfolios, exact HJB policy iteration identifies the optimal reduced value factor, while population OL-BPTT iteration converges globally when the adjoint update is directionally improving and approximate stationarity is asymptotically HJB-compatible. A theorem-matched occupation audit yields maximal $95\%$ upper endpoints of $0.066$ for the primitive directional ratio and $0.074$ for a stronger norm-relative ratio, both against the half-step threshold $0.75$. In the high-precision $50$–$50$ occupancy/broad-anchor design of a three-factor, fifty-asset benchmark, current-policy re-evaluation outperforms matched pooled refinement under the on-policy and broad evaluation laws.

Phase equilibrium problems are central to chemical engineering, underpinning tasks ranging from separation process design to the development of thermodynamic models. A particularly challenging computational task is the generation of phase envelopes: rigorously fitting thermodynamic models to real world data with well behaved predictions requires solving a computationally expensive bilevel optimization problem. We present a geometric reformulation of this parameter estimation problem that restates the bilevel program as a single level problem that is significantly easier to solve. The solution of the single level problem is proven to be the globally optimal solution of the bilevel problem when specialized global optimization solvers are used. In addition, the method retains the constraints that guarantee a well behaved fitted model, such as enforcing the correct number of phase splits, excluding spurious phases, and ensuring stability in regions of instability. This allows the practitioner to reliably and efficiently fit mathematically complex thermodynamic models to data, and potentially enables highly accurate and rigorous modelling of problems in computational thermodynamics that were previously intractable. Finally, an algorithm is presented that is proven to converge for any black box thermodynamic model. Only an expression of the Gibbs free energy is required, no derivatives are needed, and convergence is guaranteed for the broadest class of non-smooth, non-continuous models.

This work proposes a novel robust optimal W-infinity controller for dynamic systems with Prandtl-Ishlinskii hysteresis. By utilizing weighted Sobolev spaces Wm,p,Gamma, the approach uses weak derivatives to rigorously handle the non-differentiable, input non-affine nature of hysteresis. This formulation recasts the Prandtl-Ishlinskii operator as a bounded uncertainty multiplying the input rate, enabling robust optimal controller design via linear matrix inequalities, while guaranteeing W3,2,Gamma-stability with a W-infinity-gain bound. A numerical study on a piezoelectric actuator model validates its effectiveness, demonstrating asymptotic tracking and the attenuation of both hysteresis and external disturbances through a straightforward implementation.

We consider the following model in the framework of Newtonian aerodynamics: a 2D convex body moves forward and slowly oscillates in a rarefied medium on the plane. The law of oscillations is given. The problem is to find a body of fixed area that has the smallest resistance. We solve this problem by reducing it to an isoperimetric problem for quasi-Finsler metrics. Further, we introduce two criteria of smallness of oscillations. We show that the optimal body has singularity at the front (back) part of its boundary iff the former (latter) criterion is satisfied. The rest of the boundary is smooth. Finally, we find exact optimal shapes in the case of uniform oscillations and construct several shapes explicitly.

We study a resource extraction problem of ergodic type, where harvesting quotas are imposed that restrict the harvesting rate by a function of the current biomass. In a setting with diffusive dynamics, we provide conditions under which the optimal harvesting strategy is of threshold type. In contrast with the unrestricted case with singular controls, the optimal threshold may be 0, which corresponds to harvesting at the maximal possible rate at all times. Furthermore, we establish the convergence of the solution to the corresponding singular control problem as the harvesting rate tends to infinity.

This paper investigates the well-posedness and hidden regularity of boundary-degenerate hyperbolic equations in a two-dimensional setting. The shape design method is employed, which approximates the original degenerate problem by a family of uniformly elliptic problems on truncated subdomains and passes to the limit through uniform estimates. Within this framework, the existence and uniqueness of weak solutions are established in suitable weighted Sobolev spaces. A hidden regularity estimate for the conormal derivative on the nondegenerate portion of the boundary is obtained, providing a uniform bound in terms of the natural weighted energy norms of the initial data and source term. This estimate yields the boundary trace information essential for observability and controllability of degenerate hyperbolic systems.

We study a dynamic coalition-formation process in the tradition of Konishi and Ray (2003): players repeatedly form and dissolve binding agreements, evaluate states by discounted long-term expected payoffs, and hold self-confirming beliefs about the process. States and payoff sharing follow Heitzig and Kornek (2018): a state is a hierarchy of nested agreements, and the members of a new agreement share the surplus it generates, measured against the state without that agreement. All payoff assumptions are structural. We prove that every grand state ever reached is absorbing, and that every absorbing state is grand, for every discount factor. A grand state is actually reached, almost surely, for small discount factors, for three players, and, at every discount factor, whenever distributional stakes are smaller than each player s share of the efficiency gain. Otherwise the process can fail only by cycling for ever among non-grand states. We give exact necessary conditions on such a cycle, decidable for a fixed candidate cycle by linear programming, and exhibit, under an earlier and weaker notion of profitability, a four-player payoff structure whose only closed class is a cycle of two pairs forming and dissolving alternately. Under the present definition, and under either termination rule, no equilibrium traverses a cycle on a fixed schedule: somebody always reaches a state they would rather not leave, and the axioms give them the floor. Whether arrival can fail by cycling at random is open. The axioms are not merely postulated: we exhibit a bargaining game proposal, amendment by substitutes voted on by their own signatories, final unanimity, and an arbitrarily small delay on failure whose equilibria satisfy them as the delay vanishes, and which settles each period in its first round.

Single-particle cryo-electron microscopy images a macromolecule as many noisy tomographic projections of its electrostatic potential. We reconstruct the protein backbone directly from such projections, as an atomic point cloud, without the intermediate step of reconstructing the 3D electrostatic potential map. We formulate this as an indirect shape matching problem: a point-cloud template of the backbone is deformed until its simulated projections agree with the data, with the structure observed only through the imaging operator. The deformation is computed via a gradient flow on a Lie group, and we derive the resulting framework in a general geometric setting before adapting it for single-particle cryo-electron microscopy. On synthetic data, we recover single- and multichain proteins and capture conformational transitions.

Mobile robots that operate in side by side with humans and critical facilities must reach their goals at low cost, despite often unknown true traversal costs of the map apriori and imperfect actuation. Planners that solve the underlying stochastic shortest path problem exactly, such as value iteration, require computation that grows with the diameter of the map, whereas Dijkstra's algorithm is fast but is usually considered inexact once transitions are stochastic. This study shows that Dijkstra's algorithm can remain an exact planning engine under a condition that is much weaker than the causality condition often invoked in the literature, namely nonnegativity of a reduced cost defined on the determinized map. Building on this characterization, an online learner DORA (Dijkstra Oracle Reduced-cost Algorithm) is proposed for robot navigation that calls a shortest path oracle a fixed number of times per episode, never estimates a transition kernel, and adds a logarithmic survival weight when the probability of contact with a dynamic obstacle must stay within a budget. In the numerical experiments involving three other benchmarks that cover grid world navigation, directional drilling, and drone surveillance, the learner matches optimistic value iteration that is given the true transition kernel while performing 4.5 to 19.3 times less planner work, reduces contacts during learning by a factor of seventeen relative to determinize and replan, and keeps the contact rate within budgets that span two orders of magnitude. These results indicate that shortest path search supports safe and efficient online navigation and path planning tasks.

Supply chains are interconnected networks of processes and operations producing and delivering high-value products. These chains are increasingly subjected to structural changes from the energy transition and other external factors. To address this, this work develops mixed-integer programming formulations to identify optimal reconfigurations that preserve industrial operations and profitability. We propose products and spatial neighborhoods to restrict the feasible search space and enable fast heuristic solutions. Furthermore, this restriction combines structural and product-based information, thus allowing to explore and define multiple reconfiguration scenarios. We demonstrate the approach using an agricultural waste case study, showing its ability to quickly produce good quality solutions.

We propose a data-driven method for designing state-feedback gains that achieve stabilization, $H_2$-control, and $H_\infty$-control for continuous-time systems. The state-input data are assumed to be corrupted by process noise, measurement noise, and input disturbances. We first characterize the set of all systems consistent with the noisy data using operator-based data embedding. This characterization yields necessary and sufficient conditions for data informativity under a certain class of noise. These conditions are formulated as linear matrix inequalities, and the feedback gains are constructed from their solutions. To enable direct controller design from noisy sampled data for continuous-time systems, we also obtain an upper bound on the reconstruction error of continuous-time signals.

Sparse optimal control is considered in the infinite horizon. In the literature, sparse control has been considered mostly in a finite horizon for its formulation into a finite-dimensional optimization problem. It is shown in this paper that an optimal solution of the infinite-horizon sparse control problem can be obtained through a solution of some finite-horizon subproblem. This is due to sparsity of the optimal solution in the sense that the optimal control input is constantly equal to zero at its tail. An estimate is given on the horizon length required by this subproblem and its adaptive choice is also discussed. Implementation with a receding-horizon technique is considered and its optimality and sparsity are guaranteed.

Purcell's swimmer is a well-known planar model of a swimming microorganism, governed by low Reynolds number hydrodynamics, which is comprised of three rigid links connected by actuated rotary joints. This model has been analyzed as a robotic locomotion system governed by first-order nonlinear dynamics with a periodic input (gait) of the two joint angles. In this work, we present a robotic macro-scale realization of this three-link swimmer moving in a highly viscous fluid. We propose a simple variant of Purcell's theoretical model with non-slender links and a central rigid sphere which represents the added drag of the robot's central flotation block, and calibrate the model's parameters to fit experimental measurements. Next, we apply optimal control formulation based on Pontryagin's Maximum Principle (PMP) in order to find optimal gaits that maximize the displacement per cycle under bounds on the joint angles. Employing a differential geometric method that transforms the problem to area integral enclosed by the gait trajectory in the plane of joint angles, enables visual interpretation which explains topological changes in displacement-optimal gaits upon varying the bound on the joint angles. We then apply PMP formulation to the problem of maximizing Lighthill's energy efficiency in order to obtain a boundary value problem (BVP) whose solution gives efficiency-optimal gaits for Purcell's swimmer model, as well as its variant with a central sphere. Finally, we utilize numerical methods such as parameterizing the input gait as a truncated Fourier series, as well as GPOPS-II solver, to produce sufficient initial guess values for solving the BVPs and obtaining efficiency-optimal gaits.

We demonstrate that, with a suitable rescaling, using Johnson-Lindenstrauss transforms (JLTs) in the random subspace model-based derivative-free optimization (DFO) algorithm from [Cartis & Roberts, Math. Prog. 199 (2023)] achieves an improved worst-case evaluation complexity bound compared to 'unscaled' JLTs. This improved bound does not require any modification to the original algorithm or complexity analysis, and matches the best-known bound in terms of dimension dependence for model-based DFO (e.g. achieved by [Scheinberg & Chaudhry, ICM 2026] using Haar matrices in a similar framework).

Maximal Lyapunov functions encode the entire domain of attraction of an asymptotically stable equilibrium, but preserving strict decrease under neural approximation is difficult because its margin vanishes at the equilibrium. For systems locally dominated by an asymptotically stable homogeneous vector field, we construct a continuously differentiable maximal target and an anchored, positivity-preserving neural family. We prove semiglobal universal approximation: strict neural Lyapunov functions and their first derivatives can approximate the target on nested invariant sublevel sets that exhaust the domain of attraction. We also provide directly verifiable conditions under which a candidate neural Lyapunov function can be formally certified, and illustrate the effectiveness of the proposed neural architecture through numerical examples.

This paper considers robust nonadaptive regulation for general nonlinear systems in an output-feedback setting with arbitrarily high relative degree. We develop a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law, thereby recasting the regulation problem as the robust input-to-state stabilization of an augmented error system. Unlike adaptive schemes, the proposed method does not rely on linearly parameterized regressors and does not require the construction of Lyapunov functions having merely nonpositive derivatives. Under standard assumptions on the exosystem, including purely imaginary and simple eigenvalues, together with a minimum-phase input-to-state stability condition on the internal dynamics, we establish global asymptotic regulation and derive explicit, verifiable inequalities for selecting the design gains. The resulting nonadaptive framework guarantees convergence of the estimation and tracking errors even when the controlled-system dynamics are complex or only partially known. The effectiveness of the theoretical results is demonstrated using a benchmark controlled Duffing system.

First-order methods typically require a specific step-size that depends on the regularity conditions of the objective function, such as the smoothness, Lipschitz continuity, or strong convexity constants. The Polyak step-size is a classical alternative for subgradient descent on convex functions that only uses knowledge of the optimal value of the objective function and automatically adapts to the above-mentioned regimes. However, many optimization problems are better described by non-Euclidean geometries and are more amenable to mirror descent. Extending this adaptivity to mirror descent is subtle. Some existing generalizations of the Polyak step-size rely on norms instead of purely on relative geometry, excluding many of the use cases of mirror descent. In this work, we revisit a variant of the Polyak step-size based on Bregman projections due to Kiwiel (1997), which we call mirror Polyak. This method is known to converge asymptotically, but its convergence rate is not known. We show that mirror Polyak enjoys guarantees similar to its Euclidean counterpart, automatically adapting to relative notions of smoothness, Lipschitz continuity, or strong convexity. We then leverage mirror Polyak to avoid having to know the optimal value in some structured optimization problems such as regularized linear and logistic regression. We propose a lifted formulation based on convex duality with optimal value exactly zero and a natural mirror map given by the problem's structure. Mirror Polyak applied to the lifted problem enjoys the same worst-case guarantees as the Polyak step-size in the original problem if we knew the optimal value.

This paper addresses the limitations of Gaussian distribution assumptions in statistical sparse learning, particularly in modeling correlated and heterogeneous data. Conventional Gaussian models often lack robustness towards outliers and underlying distribution assumptions. To overcome these limitations, we propose the use of the $q$Gaussian distribution, derived from Tsallis entropy maximization, as a robust alternative. This is notably relevant in biostatistics, where the presence of correlated observations and heterogeneity, such as in genetic and longitudinal studies, is prevalent. Our contributions include modeling of correlated data through the re-derived multivariate probability density function from Tsallis entropy maximization, thereby addressing the limitations inherent in conventional Gaussian models. Furthermore, we introduce a novel framework that adapts numerical methods designed to find equilibria in flows to tackle composite optimization problems prevalent in statistical sparse learning. Applying this framework to the Hager-Zhang conjugate gradient algorithm \cite{Hager2005}, we develop a numerically stable and efficient algorithm for sparse statistical learning. The $q$Gaussian distribution, informed by the principle of maximizing Tsallis entropy, presents a viable and flexible alternative to Gaussian-based methods. This paper not only contributes to the theoretical understanding of statistical distributions and optimization techniques, but also paves the way for practical data analysis.

We explore the problem of asymptotically stabilizing a class of interacting particle systems to a prescribed particle configuration with zero velocity. The class of interacting particle systems is motivated by the Cucker-Smale model on the mean-field level. Rather than designing a feedback by manually solving an IDA-PBC matching equation, we derive a feedback using an instantaneous rolling horizon control algorithm. We show that this feedback preserves the port-Hamiltonian structure of the interacting particle system and therefore allows for an interpretation in the IDA-PBC framework. Additionally, the energy balance of the closed-loop Hamiltonian provides an important tool to prove convergence of the particles' velocities and interaction forces in discrete and continuous time. If the control operator is surjective, we additionally prove convergence of the particle positions to the prescribed configuration.