arXiv subjects

Anders Hansson

Publications and source records attributed to Anders Hansson.

At least 19 recordsLinked to original sources

arXiv2026

Sparse Feedback Implementation for Sender-Receiver Transportation Linear-Quadratic Control

We study a sparse linear-quadratic problem for transportation dynamics. The sparsity pattern has a natural directed-graph representation in which vertices are storage locations and edges are transportation links. The goal is to compute the optimal control signal without applying the usually dense optimal feedback gain directly. We show that the optimal feedback gain can be factorized as the product of a sparse matrix and the inverse of another sparse matrix from the right. In contrast to an existing factorization that uses an inverse from the left, the proposed factors use graph-adapted state coordinates. When the underlying graph is a tree, we give, for every edge orientation, a closed formula for the Riccati matrix that determines these factors and a graph-based bound on their possible nonzero entries. This factorization can reduce the online cost relative to dense feedback multiplication and permits distributed evaluation. The main message is that linear quadratic control need not appear dense when expressed in graph-adapted coordinates, and that these coordinates can reveal intrinsic sparsity.

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arXiv2026

Performance Bounds for Rollout Policies in Stochastic Shortest Path Problems

This paper concerns rollout and certainty-equivalent rollout policies for stochastic shortest path problems with absorbing terminal states. The main result provides a direct non-asymptotic performance certificate for a fixed rollout policy: the loss relative to the optimal value is controlled by the uniform accuracy of the value approximation and by the expected time for which the rollout closed loop remains away from the terminal state. Thus, in the undiscounted transient setting, the expected hitting time plays the role of a discount or finite-horizon parameter in more standard approximate dynamic programming bounds. This paper also gives a performance-difference identity showing that suboptimality is exactly accumulated through the transient occupation measure, and a deterministic sharpness example showing that the hitting-time factor is unavoidable. Finally, consequences under uniform hitting-time and Foster-Lyapunov drift conditions are given, and extend the argument to certainty-equivalent rollout by adding a separate local model-mismatch term.

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arXiv2026

A characteristic function framework for chance constraint programming in stochastic model predictive control

The computation of chance constraints in stochastic model predictive control is often numerically challenging due to the non-Gaussian nature of the disturbances. To overcome this problem, we propose an optimization computational framework applicable to non-Gaussian disturbances. This framework employs a numerical inversion method, utilizing the characteristic function of the disturbance distribution to compute the probability in the chance constraint as well as its gradient. To improve efficiency, it vectorizes integral points and reuses intermediate computations in Gauss-Kronrod quadrature. The framework is implemented within the YALMIP toolbox to perform chance constraint calculations for arbitrary non-Gaussian disturbances, applicable to both single-component distributions and mixture models. It allows the user to simply specify a distribution type and its parameters for the disturbance and directly compute the probability and its gradient to solve the optimization problem. The method is validated through a numerical example of a stochastic model predictive control application.

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arXiv2026

Informativity and Identifiability for Identification of Networks of Dynamical Systems

In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gr\"obner bases. We provide a sufficient condition for informativity in terms of positive definiteness of the spectrum of external signals and full generic rank of the transfer function relating the external signals to the inputs of the predictor. Moreover, we show how generic local network identifiability can be investigated by computing the dimension of the fiber associated with the closed loop transfer function from external measurable signals to the measured outputs.

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arXiv2025

Maximum Likelihood Estimation of Dynamic Sub-Networks with Missing Data

Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of sub-networks within complex interconnected systems without estimating the entire network. The key insight is that under specific topological conditions, a sub-network's parameters can be estimated using only local measurements: signals within the target sub-network and those in the directly connected to the so-called separator sub-network. This approach significantly reduces computational complexity while enhancing privacy by eliminating the need to share sensitive internal data across organizational boundaries. We establish theoretical conditions for network separability, derive the probability density function for the sub-network, and demonstrate the method's effectiveness through numerical examples.

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arXiv2025

Repeater Swarm-Assisted Cellular Systems: Interaction Stability and Performance Analysis

We consider a cellular massive MIMO system where swarms of wireless repeaters are deployed to improve coverage. These repeaters are full-duplex relays with small form factors that receive and instantaneously retransmit signals. They can be deployed in a plug-and-play manner at low cost, while being transparent to the network--conceptually they are active channel scatterers with amplification capabilities. Two fundamental questions need to be addressed in repeater deployments: (I) How can we prevent destructive effects of positive feedback caused by inter-repeater interaction (i.e., each repeater receives and amplifies signals from others)? (ii) How much performance improvement can be achieved given that repeaters also inject noise and may introduce more interference? To answer these questions, we first derive a generalized Nyquist stability criterion for the repeater swarm system, and provide an easy-to-check stability condition. Then, we study the uplink performance and develop an efficient iterative algorithm that jointly optimizes the repeater gains, user transmit powers, and receive combining weights to maximize the weighted sum rate while ensuring system stability. Numerical results corroborate our theoretical findings and show that the repeaters can significantly improve the system performance, both in sub-6 GHz and millimeter-wave bands. The results also warrant careful deployment to fully realize the benefits of repeaters, for example, by ensuring a high probability of line-of-sight links between repeaters and the base station.

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arXiv2025

Maximum Likelihood Estimation for System Identification of Networks of Dynamical Systems

This paper investigates maximum likelihood estimation for direct system identification in networks of dynamical systems. We establish that the proposed approach is both consistent and efficient. In addition, it is more generally applicable than existing methods, since it can be employed even when measurements are unavailable for all network nodes, provided that network identifiability is satisfied. Finally, we demonstrate that the maximum likelihood problem can be formulated without relying on a predictor, which is key to achieving computationally efficient numerical solutions.

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arXiv2025

Path planning with moving obstacles using stochastic optimal control

Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the full problem is computationally demanding, we introduce a tractable approximation whose Bellman equation can be solved efficiently. The resulting value function is then incorporated as a terminal penalty in an online rollout framework. We construct a trade-off curve between safety and performance to identify an appropriate weighting between them, and compare the performance with other methods. Simulation results show that the proposed rollout approach can be tuned to reach the target in nearly the same expected time as receding horizon $A^\star$ while maintaining a larger expected minimum distance to the moving obstacle. The results also show that the proposed method outperforms the considered CBF-based methods when a larger obstacle clearance is desired, while achieving comparable performance otherwise.

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arXiv2024

Direct System Identification of Dynamical Networks with Partial Measurements: a Maximum Likelihood Approach

This paper introduces a novel direct approach to system identification of dynamic networks with missing data based on maximum likelihood estimation. Dynamic networks generally present a singular probability density function, which poses a challenge in the estimation of their parameters. By leveraging knowledge about the network's interconnections, we show that it is possible to transform the problem into a more tractable form by applying linear transformations. This results in a nonsingular probability density function, enabling the application of maximum likelihood estimation techniques. Our preliminary numerical results suggest that when combined with global optimization algorithms or a suitable initialization strategy, we are able to obtain a good estimate of the dynamics of the internal systems.

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arXiv2023

Time-Optimal Path Tracking for Cooperative Manipulators: A Convex Optimization Approach

This paper studies the time-optimal path tracking problem for a team of cooperating robotic manipulators carrying an object. Considering the problem for rigidly grasped objects, we show that it can be cast as a convex optimization problem and solved efficiently with a guarantee of optimality. When formulating the problem, we avoid using a particular wrench distribution and exploit the full actuation available to the system. Then, we consider the problem for grasps using frictional forces and show that this problem also, under a force-closure grasp assumption, can be formulated as a convex optimization problem and solved efficiently and to optimality. To ensure a firm grasp, internal forces have been taken into account in this approach.

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arXiv2021

Learning the Step-size Policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno Algorithm

We consider the problem of how to learn a step-size policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. This is a limited computational memory quasi-Newton method widely used for deterministic unconstrained optimization but currently avoided in large-scale problems for requiring step sizes to be provided at each iteration. Existing methodologies for the step size selection for L-BFGS use heuristic tuning of design parameters and massive re-evaluations of the objective function and gradient to find appropriate step-lengths. We propose a neural network architecture with local information of the current iterate as the input. The step-length policy is learned from data of similar optimization problems, avoids additional evaluations of the objective function, and guarantees that the output step remains inside a pre-defined interval. The corresponding training procedure is formulated as a stochastic optimization problem using the backpropagation through time algorithm. The performance of the proposed method is evaluated on the training of classifiers for the MNIST database for handwritten digits and for CIFAR-10. The results show that the proposed algorithm outperforms heuristically tuned optimizers such as ADAM, RMSprop, L-BFGS with a backtracking line search, and L-BFGS with a constant step size. The numerical results also show that a learned policy can be used as a warm-start to train new policies for different problems after a few additional training steps, highlighting its potential use in multiple large-scale optimization problems.

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arXiv2021

On the Search for Equilibrium Points of Switched Affine Systems

One of the main aspects of switched affine systems that makes their stabilizability study intricate is the existence of (generally) infinitely many equilibrium points in the state space. Thus, prior to designing the switched control, the user must specify one of these equilibrium points to be the goal or reference. This can be a cumbersome task, especially if this goal is partially given or only defined as a set of constraints. To tackle this issue, in this paper we describe algorithms that can determine whether a given goal is an equilibrium point of the system and also jointly search for equilibrium points and design globally stabilizing switching functions.

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arXiv2020

Task-similarity Aware Meta-learning through Nonparametric Kernel Regression

This paper investigates the use of nonparametric kernel-regression to obtain a tasksimilarity aware meta-learning algorithm. Our hypothesis is that the use of tasksimilarity helps meta-learning when the available tasks are limited and may contain outlier/ dissimilar tasks. While existing meta-learning approaches implicitly assume the tasks as being similar, it is generally unclear how this task-similarity could be quantified and used in the learning. As a result, most popular metalearning approaches do not actively use the similarity/dissimilarity between the tasks, but rely on availability of huge number of tasks for their working. Our contribution is a novel framework for meta-learning that explicitly uses task-similarity in the form of kernels and an associated meta-learning algorithm. We model the task-specific parameters to belong to a reproducing kernel Hilbert space where the kernel function captures the similarity across tasks. The proposed algorithm iteratively learns a meta-parameter which is used to assign a task-specific descriptor for every task. The task descriptors are then used to quantify the task-similarity through the kernel function. We show how our approach conceptually generalizes the popular meta-learning approaches of model-agnostic meta-learning (MAML) and Meta-stochastic gradient descent (Meta-SGD) approaches. Numerical experiments with regression tasks show that our algorithm outperforms these approaches when the number of tasks is limited, even in the presence of outlier or dissimilar tasks. This supports our hypothesis that task-similarity helps improve the metalearning performance in task-limited and adverse settings.

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arXiv2018

Efficient Robust Model Predictive Control using Chordality

In this paper we show that chordal structure can be used to devise efficient optimization methods for robust model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for distributing all the other computations in an interior-point method for solving the problem. The framework enables efficient parallel computations.

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arXiv2017

Exploiting Chordality in Optimization Algorithms for Model Predictive Control

In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for distributing all the other computations in an interior-point method for solving the problem. The chordal structure can stem both from the sequential nature of the problem as well as from distributed formulations of the problem related to scenario trees or other formulations. The framework enables efficient parallel computations.

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arXiv2017

Distributed, scalable and gossip-free consensus optimization with application to data analysis

Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence rate. Hence, they can require many iterations or communications among agents to converge. In many cases, however, we do not seek a highly accurate solution for consensus problems. Based on this we propose a controlled relaxation of the coupling in the problem which allows us to compute an approximate solution, where the accuracy of the approximation can be controlled by the level of relaxation. The relaxed problem can be efficiently solved in a distributed way using a combination of primal-dual interior-point methods (PDIPMs) and message-passing. This algorithm purely relies on second-order methods and thus requires far fewer iterations and communications to converge. This is illustrated in numerical experiments, showing its superior performance compared to existing methods.

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arXiv2017

Subspace Identification of Large-Scale 1D Homogeneous Networks

This paper considers the identification of large-scale 1D networks consisting of identical LTI dynamical systems. A new subspace identification method is developed that only uses local input-output information and does not rely on knowledge about the local state interaction. The identification of the local system matrices (up to a similarity transformation) is done via a low dimensional subspace retrieval step that enables the estimation of the Markov parameters of a locally lifted system. Using the estimated Markov parameters, the state-space realization of a single subsystem in the network is determined. The low dimensional subspace retrieval step exploits various key structural properties that are present in the data equation such as a low rank property and a {\em two-layer} Toeplitz structure in the data matrices constructed from products of the system matrices. For the estimation of the system matrices of a single subsystem, it is formulated as a structured low-rank matrix factorization problem. The effectiveness of the proposed identification method is demonstrated by a simulation example.

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arXiv2016

Distributed Localization of Tree-structured Scattered Sensor Networks

Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or communications among computational agents. Furthermore, some of these distributed algorithms put a considerable computational demand on the agents. In this paper, we show that for tree-structured scattered sensor networks, which are networks that their inter-sensor range measurement graphs have few edges (few range measurements among sensors) and can be represented using a tree, it is possible to devise an efficient distributed localization algorithm that solely relies on second-order methods. Particularly, we apply a state-of-the-art primal-dual interior-point method to a semidefinite relaxation of the maximum-likelihood formulation of the localization problem. We then show how it is possible to exploit the tree-structure in the network and use message-passing or dynamic programming over trees, to distribute computations among different computational agents. The resulting algorithm requires far fewer iterations and communications among agents to converge to an accurate estimate. Moreover, the number of required communications among agents, seems to be less sensitive and more robust to the number of sensors in the network, the number of available measurements and the quality of the measurements. This is in stark contrast to distributed algorithms that rely on first-order methods. We illustrate the performance of our algorithm using experiments based on simulated and real data.

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