Dirk Reinhardt

Guanru Pan, Dirk Reinhardt, Sebastien Gros et al.

This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.

Erlend Torje Berg Lundby, Adil Rasheed, Ivar Johan Halvorsen et al.

The exploding research interest for neural networks in modeling nonlinear dynamical systems is largely explained by the networks' capacity to model complex input-output relations directly from data. However, they typically need vast training data before they can be put to any good use. The data generation process for dynamical systems can be an expensive endeavor both in terms of time and resources. Active learning addresses this shortcoming by acquiring the most informative data, thereby reducing the need to collect enormous datasets. What makes the current work unique is integrating the deep active learning framework into nonlinear system identification. We formulate a general static deep active learning acquisition problem for nonlinear system identification. This is enabled by exploring system dynamics locally in different regions of the input space to obtain a simulated dataset covering the broader input space. This simulated dataset can be used in a static deep active learning acquisition scheme referred to as global explorations. The global exploration acquires a batch of initial states corresponding to the most informative state-action trajectories according to a batch acquisition function. The local exploration solves an optimal control problem, finding the control trajectory that maximizes some measure of information. After a batch of informative initial states is acquired, a new round of local explorations from the initial states in the batch is conducted to obtain a set of corresponding control trajectories that are to be applied on the system dynamics to get data from the system. Information measures used in the acquisition scheme are derived from the predictive variance of an ensemble of neural networks. The novel method outperforms standard data acquisition methods used for system identification of nonlinear dynamical systems in the case study performed on simulated data.

Shambhuraj Sawant, Akhil S Anand, Dirk Reinhardt et al.

This paper presents an approach for learning Model Predictive Control (MPC) schemes directly from data using Reinforcement Learning (RL) methods. The state-of-the-art learning methods use RL to improve the performance of parameterized MPC schemes. However, these learning algorithms are often gradient-based methods that require frequent evaluations of computationally expensive MPC schemes, thereby restricting their use on big datasets. We propose to tackle this issue by using tools from RL to learn a parameterized MPC scheme directly from data in an offline fashion. Our approach derives an MPC scheme without having to solve it over the collected dataset, thereby eliminating the computational complexity of existing techniques for big data. We evaluate the proposed method on three simulated experiments of varying complexity.

Shambhuraj Sawant, Akhil S Anand, Dirk Reinhardt et al.

Model Predictive Control (MPC) is widely used in industrial and robotic systems for enforcing constraints and embedding domain knowledge through finite-horizon optimization-based planning. However, despite these strengths, an MPC scheme typically does not yield optimal policies for sequential decision-making problems formulated as Markov Decision Processes (MDPs). Recent combinations of MPC with Reinforcement Learning (RL) alleviate this issue by treating MPC as a parameterized model of the optimal policy of an MDP and adjusting its parameters using data. While these approaches typically consider classical MDPs, many real-world problems include future information--such as forecasts, prices, or reference trajectories--at decision time, which must be included in the MDP state for optimal decision-making. Current MPC-RL approaches do not directly account for this augmented-state structure, raising the question of how to incorporate future information into MPC to obtain an optimal policy. This work establishes the structural requirements under which a parameterized MPC can exactly represent the optimal value functions and policy of an MDP with future information. We further demonstrate that such a parameterized MPC can serve as a structured function approximator, with its parameters learned using RL. The approach is illustrated on a point-mass racing task with future reference information.

Akhil S Anand, Shambhuraj Sawant, Dirk Reinhardt et al.

AI models that predict the future behavior of a system (a.k.a. predictive AI models) are central to intelligent decision-making. However, decision-making using predictive AI models often results in suboptimal performance. This is primarily because AI models are typically constructed to best fit the data, and hence to predict the most likely future rather than to enable high-performance decision-making. The hope that such prediction enables high-performance decisions is neither guaranteed in theory nor established in practice. In fact, there is increasing empirical evidence that predictive models must be tailored to decision-making objectives for performance. In this paper, we establish formal (necessary and sufficient) conditions that a predictive model (AI-based or not) must satisfy for a decision-making policy established using that model to be optimal. We then discuss their implications for building predictive AI models for sequential decision-making.

Eivind Bøhn, Erlend M. Coates, Dirk Reinhardt et al.

Attitude control of fixed-wing unmanned aerial vehicles (UAVs) is a difficult control problem in part due to uncertain nonlinear dynamics, actuator constraints, and coupled longitudinal and lateral motions. Current state-of-the-art autopilots are based on linear control and are thus limited in their effectiveness and performance. Deep reinforcement learning (DRL) is a machine learning method to automatically discover optimal control laws through interaction with the controlled system, which can handle complex nonlinear dynamics. We show in this paper that DRL can successfully learn to perform attitude control of a fixed-wing UAV operating directly on the original nonlinear dynamics, requiring as little as three minutes of flight data. We initially train our model in a simulation environment and then deploy the learned controller on the UAV in flight tests, demonstrating comparable performance to the state-of-the-art ArduPlane proportional-integral-derivative (PID) attitude controller with no further online learning required. Learning with significant actuation delay and diversified simulated dynamics were found to be crucial for successful transfer to control of the real UAV. In addition to a qualitative comparison with the ArduPlane autopilot, we present a quantitative assessment based on linear analysis to better understand the learning controller's behavior.