arXiv subjects

Bo Wahlberg

Publications and source records attributed to Bo Wahlberg.

At least 19 recordsLinked to original sources

arXiv2026

Bayes Estimators with Performance Comparable to Empirical Bayes Estimators and Improved Local Robustness

Bayes estimation has been extensively studied and widely used in statistics, decision theory, signal processing, machine learning, and system identification. Among its variants, empirical Bayes (EB) estimation has attracted considerable attention due to its favorable estimation performance and computational tractability. However, the direct plug-in dependence of an EB estimator on hyperparameters can make it locally sensitive to hyper-parameter perturbations. This paper considers the linear regression model and focuses on the EB estimator by employing the marginal maximum likelihood hyper-parameter estimator. For conciseness, this estimator is simply referred to as the EB estimator. Given a family of EB weighting functions, a generalized Bayes estimator is constructed with the same excess mean squared error (XMSE) as the corresponding EB estimator. Here, the XMSE is a second-order asymptotic measure of the mean squared error difference between the estimator of interest and the maximum likelihood estimator. Furthermore, the EB estimator is shown to be at most firstorder sensitive to hyper-parameter perturbations, whereas the constructed Bayes estimator is at most second-order sensitive, making it locally more robust. The computational complexities of these two estimators are also analyzed. In some cases, the constructed Bayes estimator can be computationally comparable to, or more efficient than, the EB estimator. These theoretical results are further supported by numerical simulations.

stat.ME↗

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.

math.OC↗

arXiv2026

Stochastic Adaptive Control for Systems with Nonlinear Parameterization: Almost Sure Stability and Tracking

This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of applications, including recurrent neural networks, social dynamics, and signal processing. Despite their importance, adaptive control for these systems remains relatively unexplored in the literature. This gap is primarily due to the inherently nonconvex dependence of the system dynamics on unknown parameters, which significantly complicates both controller design and analysis. To address these challenges, we propose an online nonlinear weighted least-squares (WLS)-based parameter estimation algorithm and establish the global strong consistency of the resulting parameter estimates. In contrast to most existing results, our consistency analysis does not rely on restrictive assumptions such as persistent excitation conditions of the trajectory data, making it applicable to stochastic adaptive control settings. Building on the proposed estimator, we further develop an adaptive control algorithm with an attenuating excitation signal that can effectively combine adaptive estimation and feedback control. Finally, we are able to show that the resulting closed-loop system is globally stable and that the system trajectory can track, in a long-run average sense, the reference trajectory generated with the true system parameters. The proposed methods and theoretical results are finally validated through simulations in two nonlinear interaction network applications.

eess.SY↗

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.

eess.SY↗

arXiv2025

Bayes and Biased Estimators Without Hyper-parameter Estimation: Comparable Performance to the Empirical-Bayes-Based Regularized Estimator

Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator in terms of minimizing mean squared error (MSE). However, regularized estimators often require hyper-parameter estimation. This paper focuses on ridge regression and the regularized estimator by employing the empirical Bayes hyper-parameter estimator. We utilize the excess MSE to quantify the MSE difference between the empirical-Bayes-based regularized estimator and the maximum likelihood estimator for large sample sizes. We then exploit the excess MSE expressions to develop both a family of generalized Bayes estimators and a family of closed-form biased estimators. They have the same excess MSE as the empirical-Bayes-based regularized estimator but eliminate the need for hyper-parameter estimation. Moreover, we conduct numerical simulations to show that the performance of these new estimators is comparable to the empirical-Bayes-based regularized estimator, while computationally, they are more efficient.

stat.ML↗

arXiv2025

Excess Mean Squared Error of Empirical Bayes Estimators

Empirical Bayes estimators are based on minimizing the average risk with the hyper-parameters in the weighting function being estimated from observed data. The performance of an empirical Bayes estimator is typically evaluated by its mean squared error (MSE). However, the explicit expression for its MSE is generally unavailable for finite sample sizes. To address this issue, we define a high-order analytical criterion: the excess MSE. It quantifies the performance difference between the maximum likelihood and empirical Bayes estimators. An explicit expression for the excess MSE of an empirical Bayes estimator employing a general data-dependent hyper-parameter estimator is derived. As specific instances, we provide excess MSE expressions for kernel-based regularized estimators using the scaled empirical Bayes, Stein unbiased risk estimation, and generalized cross-validation hyper-parameter estimators. Moreover, we propose a modification to the excess MSE expressions for regularized estimators for moderate sample sizes and show its improvement on accuracy in numerical simulations.

math.ST↗

arXiv2025

A differential game approach to intrinsic encirclement control

This paper investigates the encirclement control problem involving two groups using a non-cooperative differential game approach. The active group seeks to chase and encircle the passive group, while the passive group responds by fleeing cooperatively and simultaneously encircling the active group. Instead of prescribing an expected radius or a predefined path for encirclement, we focus on the whole formation manifold of the desired relative configuration, two concentric circles, by allowing permutation, rotation, and translation of players. The desired relative configurations arise as the steady state resulting from Nash equilibrium strategies and are achieved in an intrinsic way by designing the interaction graphs and weight function of each edge. Furthermore, the asymptotic convergence to the desired manifold is guaranteed. Finally, numerical simulations demonstrate encirclement and counter-encirclement scenarios, verifying the effectiveness of our strategies.

math.OC↗

arXiv2025

Nature-inspired dynamic control for pursuit-evasion of robots

The pursuit-evasion problem is widespread in nature, engineering, and societal applications. It is commonly observed in nature that predators often exhibit faster speeds than their prey but have less agile maneuverability. Over millions of years of evolution, animals have developed effective and efficient strategies for both pursuit and evasion. In this paper, we provide a dynamic framework for the pursuit-evasion problem of unicycle systems, drawing inspiration from nature. First, we address the scenario involving one pursuer and one evader by proposing an Alert-Turn control strategy, which consists of two efficient ingredients: a sudden turning maneuver and an alert condition for starting and maintaining the maneuver. We present and analyze the escape and capture results at two levels: a lower level of a single run and a higher level with respect to parameters' changes. In addition, we provide a theorem with sufficient conditions for capture. The Alert-Turn strategy is then extended to more complex scenarios involving multiple pursuers and evaders by integrating aggregation control laws and a target-changing mechanism. By adjusting a 'selfish parameter', the aggregation control commands produce various escape patterns of evaders: cooperative mode, selfish mode, as well as their combinations. The influence of the selfish parameter is quantified, and the effects of the number of pursuers and the target-changing mechanism are explored from a statistical perspective. Our findings align closely with observations in nature. Finally, the proposed control strategies are validated through numerical simulations that replicate some chasing behaviors of animals in nature.

eess.SY↗

arXiv2024

Meta-Learning Augmented MPC for Disturbance-Aware Motion Planning and Control of Quadrotors

A major challenge in autonomous flights is unknown disturbances, which can jeopardize safety and lead to collisions, especially in obstacle-rich environments. This paper presents a disturbance-aware motion planning and control framework designed for autonomous aerial flights. The framework is composed of two key components: a disturbance-aware motion planner and a tracking controller. The disturbance-aware motion planner consists of a predictive control scheme and a learned model of disturbances that is adapted online. The tracking controller is designed using contraction control methods to provide safety bounds on the quadrotor behaviour in the vicinity of the obstacles with respect to the disturbance-aware motion plan. Finally, the algorithm is tested in simulation scenarios with a quadrotor facing strong crosswind and ground-induced disturbances.

cs.RO↗

arXiv2024

Kinodynamic Motion Planning via Funnel Control for Underactuated Unmanned Surface Vehicles

We develop an algorithm to control an underactuated unmanned surface vehicle (USV) using kinodynamic motion planning with funnel control (KDF). KDF has two key components: motion planning used to generate trajectories with respect to kinodynamic constraints, and funnel control, also referred to as prescribed performance control, which enables trajectory tracking in the presence of uncertain dynamics and disturbances. We extend prescribed performance control to address the challenges posed by underactuation and control-input saturation present on the USV. The proposed scheme guarantees stability under user-defined prescribed performance functions where model parameters and exogenous disturbances are unknown. Furthermore, we present an optimization problem to obtain smooth, collision-free trajectories while respecting kinodynamic constraints. We deploy the algorithm on a USV and verify its efficiency in real-world open-water experiments.

cs.RO↗

arXiv2023

A Biologically-Inspired Computational Model of Time Perception

Time perception - how humans and animals perceive the passage of time - forms the basis for important cognitive skills such as decision-making, planning, and communication. In this work, we propose a framework for examining the mechanisms responsible for time perception. We first model neural time perception as a combination of two known timing sources: internal neuronal mechanisms and external (environmental) stimuli, and design a decision-making framework to replicate them. We then implement this framework in a simulated robot. We measure the agent's success on a temporal discrimination task originally conducted by mice to evaluate its capacity to exploit temporal knowledge. We conclude that the agent is able to perceive time similarly to animals when it comes to their intrinsic mechanisms of interpreting time and performing time-aware actions. Next, by analysing the behaviour of agents equipped with the framework, we propose an estimator to infer characteristics of the timing mechanisms intrinsic to the agents. In particular, we show that from their empirical action probability distribution we are able to estimate parameters used for perceiving time. Overall, our work shows promising results when it comes to drawing conclusions regarding some of the characteristics present in biological timing mechanisms.

eess.SY↗

arXiv2023

Diagnosing and Augmenting Feature Representations in Correctional Inverse Reinforcement Learning

Robots have been increasingly better at doing tasks for humans by learning from their feedback, but still often suffer from model misalignment due to missing or incorrectly learned features. When the features the robot needs to learn to perform its task are missing or do not generalize well to new settings, the robot will not be able to learn the task the human wants and, even worse, may learn a completely different and undesired behavior. Prior work shows how the robot can detect when its representation is missing some feature and can, thus, ask the human to be taught about the new feature; however, these works do not differentiate between features that are completely missing and those that exist but do not generalize to new environments. In the latter case, the robot would detect misalignment and simply learn a new feature, leading to an arbitrarily growing feature representation that can, in turn, lead to spurious correlations and incorrect learning down the line. In this work, we propose separating the two sources of misalignment: we propose a framework for determining whether a feature the robot needs is incorrectly learned and does not generalize to new environment setups vs. is entirely missing from the robot's representation. Once we detect the source of error, we show how the human can initiate the realignment process for the model: if the feature is missing, we follow prior work for learning new features; however, if the feature exists but does not generalize, we use data augmentation to expand its training and, thus, complete the correction. We demonstrate the proposed approach in experiments with a simulated 7DoF robot manipulator and physical human corrections.

cs.RO↗

arXiv2023

Optimal Transport for Correctional Learning

The contribution of this paper is a generalized formulation of correctional learning using optimal transport, which is about how to optimally transport one mass distribution to another. Correctional learning is a framework developed to enhance the accuracy of parameter estimation processes by means of a teacher-student approach. In this framework, an expert agent, referred to as the teacher, modifies the data used by a learning agent, known as the student, to improve its estimation process. The objective of the teacher is to alter the data such that the student's estimation error is minimized, subject to a fixed intervention budget. Compared to existing formulations of correctional learning, our novel optimal transport approach provides several benefits. It allows for the estimation of more complex characteristics as well as the consideration of multiple intervention policies for the teacher. We evaluate our approach on two theoretical examples, and on a human-robot interaction application in which the teacher's role is to improve the robots performance in an inverse reinforcement learning setting.

cs.LG↗

arXiv2023

Prediction-Based Leader-Follower Rendezvous Model Predictive Control with Robustness to Communication Losses

In this paper we propose a novel distributed model predictive control (DMPC) based algorithm with a trajectory predictor for a scenario of landing of unmanned aerial vehicles (UAVs) on a moving unmanned surface vehicle (USV). The algorithm is executing DMPC with exchange of trajectories between the agents at a sufficient rate. In the case of loss of communication, and given the sensor setup, agents are predicting the trajectories of other agents based on the available measurements and prior information. The predictions are then used as the reference inputs to DMPC. During the landing, the followers are tasked with avoidance of USV-dependent obstacles and inter-agent collisions. In the proposed distributed algorithm, all agents solve their local optimization problem in parallel and we prove the convergence of the proposed algorithm. Finally, the simulation results support the theoretical findings.

eess.SY↗

arXiv2023

Interaction and Decision Making-aware Motion Planning using Branch Model Predictive Control

Motion planning for autonomous vehicles sharing the road with human drivers remains challenging. The difficulty arises from three challenging aspects: human drivers are 1) multi-modal, 2) interacting with the autonomous vehicle, and 3) actively making decisions based on the current state of the traffic scene. We propose a motion planning framework based on Branch Model Predictive Control to deal with these challenges. The multi-modality is addressed by considering multiple future outcomes associated with different decisions taken by the human driver. The interactive nature of humans is considered by modeling them as reactive agents impacted by the actions of the autonomous vehicle. Finally, we consider a model developed in human neuroscience studies as a possible way of encoding the decision making process of human drivers. We present simulation results in various scenarios, showing the advantages of the proposed method and its ability to plan assertive maneuvers that convey intent to humans.

cs.RO↗

arXiv2022

Robust Trajectory Tracking for Underactuated Quadrotors with Prescribed Performance

We propose a control protocol based on the prescribed performance control (PPC) methodology for a quadrotor unmanned aerial vehicle (UAV). Quadrotor systems belong to the class of underactuated systems for which the original PPC methodology cannot be directly applied. We introduce the necessary design modifications to stabilize the considered system with prescribed performance. The proposed control protocol does not use any information of dynamic model parameters or exogenous disturbances. Furthermore, the stability analysis guarantees that the tracking errors remain inside of designer-specified time-varying functions, achieving prescribed performance independent from the control gains' selection. Finally, simulation results verify the theoretical results.

eess.SY↗

arXiv2022

Aperiodic Communication for MPC in Autonomous Cooperative Landing

This paper investigates the rendezvous problem for the autonomous cooperative landing of an unmanned aerial vehicle (UAV) on an unmanned surface vehicle (USV). Such heterogeneous agents, with nonlinear dynamics, are dynamically decoupled but share a common cooperative rendezvous task. The underlying control scheme is based on distributed Model Predictive Control (MPC). The main contribution is a rendezvous algorithm with an online update rule of the rendezvous location. The algorithm only requires the agents to exchange information when they can not guarantee to rendezvous. Hence, the exchange of information occurs aperiodically, which reduces the necessary communication between the agents. Furthermore, we prove that the algorithm guarantees recursive feasibility. The simulation results illustrate the effectiveness of the proposed algorithm applied to the problem of autonomous cooperative landing.

eess.SY↗

arXiv2022

A Teacher-Student Markov Decision Process-based Framework for Online Correctional Learning

A classical learning setting typically concerns an agent/student who collects data, or observations, from a system in order to estimate a certain property of interest. Correctional learning is a type of cooperative teacher-student framework where a teacher, who has partial knowledge about the system, has the ability to observe and alter (correct) the observations received by the student in order to improve the accuracy of its estimate. In this paper, we show how the variance of the estimate of the student can be reduced with the help of the teacher. We formulate the corresponding online problem - where the teacher has to decide, at each time instant, whether or not to change the observations due to a limited budget - as a Markov decision process, from which the optimal policy is derived using dynamic programming. We validate the framework in numerical experiments, and compare the optimal online policy with the one from the batch setting.

cs.LG↗