arXiv subjects

Erik-Jan van Kampen

Publications and source records attributed to Erik-Jan van Kampen.

12 recordsLinked to original sources

arXiv2026

Critical slowing down for predicting controller induced loss of control in quadrotors

We develop a novel forecasting scheme to anticipate controller induced loss of control (LOC) in quadrotors and evaluate it on real LOC flight data from four different quadrotors. For this, early warning signals of LOC are derived using critical slowing down (CSD), a generic phenomenon shown to precede critical transitions across various complex ecological and biological systems. As such, our early warning indicators are generic in the sense that no system models are needed to facilitate forecasts of LOC. The approach is evaluated on real quadrotor flight data wherein LOC occurs due to unstable controller behavior arising from input-output delays. Our approach achieves a time-to-LOC forecast of up to 0.9 seconds before LOC occurs, outperforming state-of-the-art recurrent neural network quadrotor LOC forecasters in terms of detection accuracy and LOC data reliance. In particular, we leverage insights from CSD to accurately predict LOC without using data of the LOC event itself. Going further, we apply our forecasters without any re-parameterization to anticipate a different LOC scenario, quadrotor flyways, that occur on other quadrotors flying both indoors and outdoors. Despite these differences, our approach successfully detects LOC, demonstrating that it can generalize across controller architectures, quadrotors, and LOC scenarios.

eess.SY↗

arXiv2026

Temporally smoothed incremental model-based heuristic dynamic programming for command-filtered cascaded online learning flight control

Approximate Dynamic Programming (ADP) enables online adaptation of control laws through adaptive critic methods. However, its application to online learning Angle-of-Attack (AoA) tracking control remains challenging due to oscillatory control actions under nonlinear dynamics, which may induce system oscillations, degrade tracking performance, and increase actuator effort. To address this challenge, this paper proposes two innovations for online learning flight control: (1) incorporating temporal-scale policy smoothness regularization into the Incremental Model-based Heuristic Dynamic Programming (IHDP) framework; and (2) employing a low-pass filter to attenuate high-frequency pitch-rate commands. Furthermore, a primal-dual approach is developed to adaptively adjust the smoothness penalty weight in the policy objective according to a prescribed smoothness criterion. Tracking control simulations demonstrate that the proposed methods reduce control system oscillations, improve tracking performance, and exhibit post-training policy robustness to model uncertainties.

eess.SY↗

arXiv2026

Reachability-Preserving Bellman Operator for the Discounted Reach-Cost Value Function: Uniting Hamilton-Jacobi Reachability and Reinforcement Learning

Hamilton-Jacobi (HJ) reachability provides rigorous safety and reachability guarantees for continuous-time dynamical systems, but its numerical solution suffers from the curse of dimensionality. Deep reinforcement learning (DRL), by contrast, offers scalable sample-based methods. However, RL is typically built around additive cumulative rewards; whereas, reachability objectives are inherently non-additive. This mismatch makes a direct bridge between HJ reachability and RL nontrivial. Recent discounted formulations have either introduced contraction by altering the original reachability semantics, or preserved exact semantics on the HJ side without a corresponding Bellman fixed-point characterization. In this paper, we close this gap by building on a semantics-preserving discounted reach-based value function and deriving a non-additive Bellman operator whose unique fixed point exactly matches the value function in the HJ formulation. We prove that discounting makes this operator contractive, yielding existence, uniqueness, and convergence of value iteration. Furthermore, we establish the equivalence between the HJ and Bellman characterizations, and show that RL can be interpreted as a sample-based approximation scheme for the same fixed-point equation. This yields a principled and semantically exact connection between HJ reachability and RL, enabling learning-based methods to approximate reachability value functions while preserving their safety-critical meaning. As a result, the proposed framework opens the door to scalable, data-driven computation of reachable sets and safety certificates in high-dimensional systems. Numerical experiments demonstrate close agreement with HJ solutions, confirm preservation of reachability semantics via alignment of zero level sets, and support the interpretation of reinforcement learning as a sample-based solver of the proposed Bellman operator.

eess.SY↗

arXiv2026

Unifying Hamilton-Jacobi Reachability and Reinforcement Learning

We unify Hamilton-Jacobi (HJ) reachability and Reinforcement Learning (RL) through a proposed running cost formulation. We prove that the resultant travel-cost value function is the unique bounded viscosity solution of a time-dependent Hamilton-Jacobi Bellman (HJB) Partial Differential Equation (PDE) with zero terminal data, whose negative sublevel set equals the strict backward-reachable tube. Using a forward reparameterization and a contraction inducing Bellman update, we show that fixed points of small-step RL value iteration converge to the viscosity solution of the forward discounted HJB. Experiments on a classical benchmark validate this connection by demonstrating convergence of learned value functions toward semi-Lagrangian HJB solutions and by quantifying approximation error across the state space. These results empirically support the theoretical analysis, showing that the proposed framework preserves reachability-based safety semantics while remaining compatible with deep RL implementations.

eess.SY↗

arXiv2026

Deep deterministic policy gradient with symmetric data augmentation for lateral attitude tracking control of a fixed-wing aircraft

The symmetry of dynamical systems can be exploited for state-transition prediction and to facilitate control policy optimization. This paper leverages system symmetry to develop sample-efficient offline reinforcement learning (RL) approaches. Under the symmetry assumption for a Markov Decision Process (MDP), a symmetric data augmentation method is proposed. The augmented samples are integrated into the dataset of Deep Deterministic Policy Gradient (DDPG) to enhance its coverage rate of the state-action space. Furthermore, sample utilization efficiency is improved by introducing a second critic trained on the augmented samples, resulting in a dual-critic structure. The aircraft's model is verified to be symmetric, and flight control simulations demonstrate accelerated policy convergence when augmented samples are employed.

cs.LG↗

arXiv2026

Certifying Hamilton-Jacobi Reachability Learned via Reinforcement Learning

We present a framework to \emph{certify} Hamilton--Jacobi (HJ) reachability learned by reinforcement learning (RL). Building on a discounted initial time \emph{travel-cost} formulation that makes small-step RL value iteration provably equivalent to a forward Hamilton--Jacobi (HJ) equation with damping, we convert certified learning errors into calibrated inner/outer enclosures of strict backward reachable tube. The core device is an additive-offset identity: if $W_λ$ solves the discounted travel-cost Hamilton--Jacobi--Bellman (HJB) equation, then $W_\varepsilon:=W_λ+ \varepsilon$ solves the same PDE with a constant offset $λ\varepsilon$. This means that a uniform value error is \emph{exactly} equal to a constant HJB offset. We establish this uniform value error via two routes: (A) a Bellman operator-residual bound, and (B) a HJB PDE-slack bound. Our framework preserves HJ-level safety semantics and is compatible with deep RL. We demonstrate the approach on a double-integrator system by formally certifying, via satisfiability modulo theories (SMT), a value function learned through reinforcement learning to induce provably correct inner and outer backward-reachable set enclosures over a compact region of interest.

eess.SY↗

arXiv2025

Lyapunov Function-guided Reinforcement Learning for Flight Control

A cascaded online learning flight control system has been developed and enhanced with respect to action smoothness. In this paper, we investigate the convergence performance of the control system, characterized by the increment of a Lyapunov function candidate. The derivation of this metric accounts for discretization errors and state prediction errors introduced by the incremental model. Comparative results are presented through flight control simulations.

cs.AI↗

arXiv2022

Adaptive Risk-Tendency: Nano Drone Navigation in Cluttered Environments with Distributional Reinforcement Learning

Enabling the capability of assessing risk and making risk-aware decisions is essential to applying reinforcement learning to safety-critical robots like drones. In this paper, we investigate a specific case where a nano quadcopter robot learns to navigate an apriori-unknown cluttered environment under partial observability. We present a distributional reinforcement learning framework to generate adaptive risk-tendency policies. Specifically, we propose to use lower tail conditional variance of the learnt return distribution as intrinsic uncertainty estimation, and use exponentially weighted average forecasting (EWAF) to adapt the risk-tendency in accordance with the estimated uncertainty. In simulation and real-world empirical results, we show that (1) the most effective risk-tendency vary across states, (2) the agent with adaptive risk-tendency achieves superior performance compared to risk-neutral policy or risk-averse policy baselines.

cs.RO↗

arXiv2022

Soft Actor-Critic Deep Reinforcement Learning for Fault Tolerant Flight Control

Fault-tolerant flight control faces challenges, as developing a model-based controller for each unexpected failure is unrealistic, and online learning methods can handle limited system complexity due to their low sample efficiency. In this research, a model-free coupled-dynamics flight controller for a jet aircraft able to withstand multiple failure types is proposed. An offline trained cascaded Soft Actor-Critic Deep Reinforcement Learning controller is successful on highly coupled maneuvers, including a coordinated 40 degree bank climbing turn with a normalized Mean Absolute Error of 2.64%. The controller is robust to six failure cases, including the rudder jammed at -15 deg, the aileron effectiveness reduced by 70%, a structural failure, icing and a backward c.g. shift as the response is stable and the climbing turn is completed successfully. Robustness to biased sensor noise, atmospheric disturbances, and to varying initial flight conditions and reference signal shapes is also demonstrated.

eess.SY↗

arXiv2016

On Approximate Dynamic Programming with Multivariate Splines for Adaptive Control

We define a SDP framework based on the RLSTD algorithm and multivariate simplex B-splines. We introduce a local forget factor capable of preserving the continuity of the simplex splines. This local forget factor is integrated with the RLSTD algorithm, resulting in a modified RLSTD algorithm that is capable of tracking time-varying systems. We present the results of two numerical experiments, one validating SDP and comparing it with NDP and another to show the advantages of the modified RLSTD algorithm over the original. While SDP requires more computations per time-step, the experiment shows that for the same amount of function approximator parameters, there is an increase in performance in terms of stability and learning rate compared to NDP. The second experiment shows that SDP in combination with the modified RLSTD algorithm allows for faster recovery compared to the original RLSTD algorithm when system parameters are altered, paving the way for an adaptive high-performance non-linear control method.

cs.LG↗

arXiv2016

Framework for state and unknown input estimation of linear time-varying systems

The design of unknown-input decoupled observers and filters requires the assumption of an existence condition in the literature. This paper addresses an unknown input filtering problem where the existence condition is not satisfied. Instead of designing a traditional unknown input decoupled filter, a Double-Model Adaptive Estimation approach is extended to solve the unknown input filtering problem. It is proved that the state and the unknown inputs can be estimated and decoupled using the extended Double-Model Adaptive Estimation approach without satisfying the existence condition. Numerical examples are presented in which the performance of the proposed approach is compared to methods from literature.

eess.SY↗

arXiv2016

Towards the multivariate simplotope spline: continuity conditions in a class of mixed simplotopic grids

Smooth joins of simplex Bernstein-Bézier polynomials have been studied extensively in the past. In this paper a new method is proposed to define continuity conditions for tensor-product Bernstein polynomials on a class of mixed grids that meets certain out-of-facet parallelism criteria. The conditions are derived by first defining a simplex around the simplotopic bases of the tensor-product polynomials. Then the continuity conditions in the multivariate simplex spline defined on the resulting simplices, are adapted to hold for the tensor-product polynomials. The two- and three-dimensional results agree with the results found in the literature. It is expected that the method can be employed in more general grids.

math.NA↗