arXiv subjects

Sebastien Gros

Publications and source records attributed to Sebastien Gros.

At least 37 records · Page 2Linked to original sources

arXiv2025

MPC4RL -- A Software Package for Reinforcement Learning based on Model Predictive Control

In this paper, we present an early software integrating Reinforcement Learning (RL) with Model Predictive Control (MPC). Our aim is to make recent theoretical contributions from the literature more accessible to both the RL and MPC communities. We combine standard software tools developed by the RL community, such as Gymnasium, stable-baselines3, or CleanRL with the acados toolbox, a widely-used software package for efficient MPC algorithms. Our core contribution is MPC4RL, an open-source Python package that supports learning-enhanced MPC schemes for existing acados implementations. The package is designed to be modular, extensible, and user-friendly, facilitating the tuning of MPC algorithms for a broad range of control problems. It is available on GitHub.

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arXiv2025

All AI Models are Wrong, but Some are Optimal

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.

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arXiv2024

Optimality Conditions for Model Predictive Control: Rethinking Predictive Model Design

Optimality is a critical aspect of Model Predictive Control (MPC), especially in economic MPC. However, achieving optimality in MPC presents significant challenges, and may even be impossible, due to inherent inaccuracies in the predictive models. Predictive models often fail to accurately capture the true system dynamics, such as in the presence of stochasticity, leading to suboptimal MPC policies. In this paper, we establish the necessary and sufficient conditions on the underlying prediction model for an MPC scheme to achieve closed-loop optimality. Interestingly, these conditions are counterintuitive to the traditional approach of building predictive models that best fit the data. These conditions present a mathematical foundation for constructing models that are directly linked to the performance of the resulting MPC scheme.

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arXiv2024

Application of Soft Actor-Critic Algorithms in Optimizing Wastewater Treatment with Time Delays Integration

Wastewater treatment plants face unique challenges for process control due to their complex dynamics, slow time constants, and stochastic delays in observations and actions. These characteristics make conventional control methods, such as Proportional-Integral-Derivative controllers, suboptimal for achieving efficient phosphorus removal, a critical component of wastewater treatment to ensure environmental sustainability. This study addresses these challenges using a novel deep reinforcement learning approach based on the Soft Actor-Critic algorithm, integrated with a custom simulator designed to model the delayed feedback inherent in wastewater treatment plants. The simulator incorporates Long Short-Term Memory networks for accurate multi-step state predictions, enabling realistic training scenarios. To account for the stochastic nature of delays, agents were trained under three delay scenarios: no delay, constant delay, and random delay. The results demonstrate that incorporating random delays into the reinforcement learning framework significantly improves phosphorus removal efficiency while reducing operational costs. Specifically, the delay-aware agent achieved 36% reduction in phosphorus emissions, 55% higher reward, 77% lower target deviation from the regulatory limit, and 9% lower total costs than traditional control methods in the simulated environment. These findings underscore the potential of reinforcement learning to overcome the limitations of conventional control strategies in wastewater treatment, providing an adaptive and cost-effective solution for phosphorus removal.

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arXiv2024

Flipping-based Policy for Chance-Constrained Markov Decision Processes

Safe reinforcement learning (RL) is a promising approach for many real-world decision-making problems where ensuring safety is a critical necessity. In safe RL research, while expected cumulative safety constraints (ECSCs) are typically the first choices, chance constraints are often more pragmatic for incorporating safety under uncertainties. This paper proposes a \textit{flipping-based policy} for Chance-Constrained Markov Decision Processes (CCMDPs). The flipping-based policy selects the next action by tossing a potentially distorted coin between two action candidates. The probability of the flip and the two action candidates vary depending on the state. We establish a Bellman equation for CCMDPs and further prove the existence of a flipping-based policy within the optimal solution sets. Since solving the problem with joint chance constraints is challenging in practice, we then prove that joint chance constraints can be approximated into Expected Cumulative Safety Constraints (ECSCs) and that there exists a flipping-based policy in the optimal solution sets for constrained MDPs with ECSCs. As a specific instance of practical implementations, we present a framework for adapting constrained policy optimization to train a flipping-based policy. This framework can be applied to other safe RL algorithms. We demonstrate that the flipping-based policy can improve the performance of the existing safe RL algorithms under the same limits of safety constraints on Safety Gym benchmarks.

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arXiv2024

Data-Driven Domestic Flexible Demand: Observations from experiments in cold climate

In this chapter, we report on our experience with domestic flexible electric energy demand based on a regular commercial (HVAC)-based heating system in a house. Our focus is on investigating the predictability of the energy demand of the heating system and of the thermal response when varying the heating system settings. Being able to form such predictions is crucial for most flexible demand algorithms. We will compare several methods for predicting the thermal and energy response, which either gave good results or which are currently promoted in the literature for controlling buildings. We will report that the stochasticity of a house response is -- in our experience -- the main difficulty in providing domestic flexible demand from heating. The experiments were carried out on a regular house in Norway, equipped with four air-to-air Mitsubishi heat pumps and a high-efficiency balanced ventilation system. The house was equipped with multiple IoT-based climate sensors, real-time power measurement, and the possibility to drive the HVAC system via the IoT. The house is operating on the spot market (Nord Pool NO3) and is exposed to a peak energy demand penalty. Over a period of three years, we have collected data on the house (temperatures, humidity, air quality), real-time power and hourly energy consumption, while applying various flexible demand algorithms responding to the local energy costs. This has produced large variations in the settings of the heating system and energy demand, resulting in rich data for investigating the house response. This chapter aims at providing important insights on providing flexible demand from houses in cold climates.

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arXiv2024

Economic Model Predictive Control as a Solution to Markov Decision Processes

Markov Decision Processes (MDPs) offer a fairly generic and powerful framework to discuss the notion of optimal policies for dynamic systems, in particular when the dynamics are stochastic. However, computing the optimal policy of an MDP can be very difficult due to the curse of dimensionality present in solving the underlying Bellman equations. Model Predictive Control (MPC) is a very popular technique for building control policies for complex dynamic systems. Historically, MPC has focused on constraint satisfaction and steering dynamic systems towards a user-defined reference. More recently, Economic MPC was proposed as a computationally tractable way of building optimal policies for dynamic systems. When stochsaticity is present, economic MPC is close to the MDP framework. In that context, Economic MPC can be construed as attractable heuristic to provide approximate solutions to MDPs. However, there is arguably a knowledge gap in the literature regarding these approximate solutions and the conditions for an MPC scheme to achieve closed-loop optimality. This chapter aims to clarify this approximation pedagogically, to provide the conditions for MPC to deliver optimal policies, and to explore some of their consequences.

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arXiv2024

Data-Driven Predictive Control and MPC: Do we achieve optimality?

In this paper, we explore the interplay between Predictive Control and closed-loop optimality, spanning from Model Predictive Control to Data-Driven Predictive Control. Predictive Control in general relies on some form of prediction scheme on the real system trajectories. However, these predictions may not accurately capture the real system dynamics, for e.g., due to stochasticity, resulting in sub-optimal control policies. This lack of optimality is a critical issue in case of problems with economic objectives. We address this by providing sufficient conditions on the underlying prediction scheme such that a Predictive Controller can achieve closed-loop optimality. However, these conditions do not readily extend to Data-Driven Predictive Control. In this context of closed-loop optimality, we conclude that the factor distinguishing the approaches within Data-Driven Predictive Control is if they can be cast as a sequential decision-making process or not, rather than the dichotomy of model-based vs. model-free. Furthermore, we show that the conventional approach of improving the prediction accuracy from data may not guarantee optimality.

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arXiv2024

Personalized Dynamic Pricing Policy for Electric Vehicles: Reinforcement learning approach

With the increasing number of fast-electric vehicle charging stations (fast-EVCSs) and the popularization of information technology, electricity price competition between fast-EVCSs is highly expected, in which the utilization of public and/or privacy-preserved information will play a crucial role. Self-interest electric vehicle (EV) users, on the other hand, try to select a fast-EVCS for charging in a way to maximize their utilities based on electricity price, estimated waiting time, and their state of charge. While existing studies have largely focused on finding equilibrium prices, this study proposes a personalized dynamic pricing policy (PeDP) for a fast-EVCS to maximize revenue using a reinforcement learning (RL) approach. We first propose a multiple fast-EVCSs competing simulation environment to model the selfish behavior of EV users using a game-based charging station selection model with a monetary utility function. In the environment, we propose a Q-learning-based PeDP to maximize fast-EVCS' revenue. Through numerical simulations based on the environment: (1) we identify the importance of waiting time in the EV charging market by comparing the classic Bertrand competition model with the proposed PeDP for fast-EVCSs (from the system perspective); (2) we evaluate the performance of the proposed PeDP and analyze the effects of the information on the policy (from the service provider perspective); and (3) it can be seen that privacy-preserved information sharing can be misused by artificial intelligence-based PeDP in a certain situation in the EV charging market (from the customer perspective).

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arXiv2023

Interpretable Battery Cycle Life Range Prediction Using Early Degradation Data at Cell Level

Battery cycle life prediction using early degradation data has many potential applications throughout the battery product life cycle. For that reason, various data-driven methods have been proposed for point prediction of battery cycle life with minimum knowledge of the battery degradation mechanisms. However, managing the rapidly increasing amounts of batteries at end-of-life with lower economic and technical risk requires prediction of cycle life with quantified uncertainty, which is still lacking. The interpretability (i.e., the reason for high prediction accuracy) of these advanced data-driven methods is also worthy of investigation. Here, a Quantile Regression Forest (QRF) model, having the advantage of not assuming any specific distribution of cycle life, is introduced to make cycle life range prediction with uncertainty quantified as the width of the prediction interval, in addition to point predictions with high accuracy. The hyperparameters of the QRF model are optimized with a proposed alpha-logistic-weighted criterion so that the coverage probabilities associated with the prediction intervals are calibrated. The interpretability of the final QRF model is explored with two global model-agnostic methods, namely permutation importance and partial dependence plot.

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arXiv2023

Once upon a time step: A closed-loop approach to robust MPC design

A novel perspective on the design of robust model predictive control (MPC) methods is presented, whereby closed-loop constraint satisfaction is ensured using recursive feasibility of the MPC optimization. Necessary and sufficient conditions are derived for recursive feasibility, based on the effects of model perturbations and disturbances occurring at one time step. Using these conditions and Farkas' lemma, sufficient conditions suitable for design are formulated. The proposed method is called a closed-loop design, as only the existence of feasible inputs at the next time step is enforced by design. This is in contrast to most existing formulations, which compute control policies that are feasible under the worst-case realizations of all model perturbations and exogenous disturbances in the MPC prediction horizon. The proposed method has an online computational complexity similar to nominal MPC methods while preserving guarantees of constraint satisfaction, recursive feasibility and stability. Numerical simulations demonstrate the efficacy of our proposed approach.

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arXiv2023

Deep active learning for nonlinear system identification

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.

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arXiv2023

Equivalence of Optimality Criteria for Markov Decision Process and Model Predictive Control

This paper shows that the optimal policy and value functions of a Markov Decision Process (MDP), either discounted or not, can be captured by a finite-horizon undiscounted Optimal Control Problem (OCP), even if based on an inexact model. This can be achieved by selecting a proper stage cost and terminal cost for the OCP. A very useful particular case of OCP is a Model Predictive Control (MPC) scheme where a deterministic (possibly nonlinear) model is used to reduce the computational complexity. This observation leads us to parameterize an MPC scheme fully, including the cost function. In practice, Reinforcement Learning algorithms can then be used to tune the parameterized MPC scheme. We verify the developed theorems analytically in an LQR case and we investigate some other nonlinear examples in simulations.

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arXiv2023

Learning-based MPC from Big Data Using Reinforcement Learning

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.

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arXiv2022

Recursive Feasibility of Stochastic Model Predictive Control with Mission-Wide Probabilistic Constraints

This paper is concerned with solving chance-constrained finite-horizon optimal control problems, with a particular focus on the recursive feasibility issue of stochastic model predictive control (SMPC) in terms of mission-wide probability of safety (MWPS). MWPS assesses the probability that the entire state trajectory lies within the constraint set, and the objective of the SMPC controller is to ensure that it is no less than a threshold value. This differs from classic SMPC where the probability that the state lies in the constraint set is enforced independently at each time instant. Unlike robust MPC, where strict recursive feasibility is satisfied by assuming that the uncertainty is supported by a compact set, the proposed concept of recursive feasibility for MWPS is based on the notion of remaining MWPSs, which is conserved in the expected value sense. We demonstrate the idea of mission-wide SMPC in the linear SMPC case by deploying a scenario-based algorithm.

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arXiv2022

Solving Mission-Wide Chance-Constrained Optimal Control Using Dynamic Programming

This paper aims to provide a Dynamic Programming (DP) approach to solve the Mission-Wide Chance-Constrained Optimal Control Problems (MWCC-OCP). The mission-wide chance constraint guarantees that the probability that the entire state trajectory lies within a constraint/safe region is higher than a prescribed level, and is different from the stage-wise chance constraints imposed at individual time steps. The control objective is to find an optimal policy sequence that achieves both (i) satisfaction of a mission-wide chance constraint, and (ii) minimization of a cost function. By transforming the stage-wise chance-constrained problem into an unconstrained counterpart via Lagrangian method, standard DP can then be deployed. Yet, for MWCC-OCP, this methods fails to apply, because the mission-wide chance constraint cannot be easily formulated using stage-wise chance constraints due to the time-correlation between the latter (individual states are coupled through the system dynamics). To fill this gap, firstly, we detail the conditions required for a classical DP solution to exist for this type of problem; secondly, we propose a DP solution to the MWCC-OCP through state augmentation by introducing an additional functional state variable.

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arXiv2022

Policy Gradient Reinforcement Learning for Uncertain Polytopic LPV Systems based on MHE-MPC

In this paper, we propose a learning-based Model Predictive Control (MPC) approach for the polytopic Linear Parameter-Varying (LPV) systems with inexact scheduling parameters (as exogenous signals with inexact bounds), where the Linear Time Invariant (LTI) models (vertices) captured by combinations of the scheduling parameters becomes wrong. We first propose to adopt a Moving Horizon Estimation (MHE) scheme to simultaneously estimate the convex combination vector and unmeasured states based on the observations and model matching error. To tackle the wrong LTI models used in both the MPC and MHE schemes, we then adopt a Policy Gradient (PG) Reinforcement Learning (RL) to learn both the estimator (MHE) and controller (MPC) so that the best closed-loop performance is achieved. The effectiveness of the proposed RL-based MHE/MPC design is demonstrated using an illustrative example.

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arXiv2022

Bridging the gap between QP-based and MPC-based RL

Reinforcement learning methods typically use Deep Neural Networks to approximate the value functions and policies underlying a Markov Decision Process. Unfortunately, DNN-based RL suffers from a lack of explainability of the resulting policy. In this paper, we instead approximate the policy and value functions using an optimization problem, taking the form of Quadratic Programs (QPs). We propose simple tools to promote structures in the QP, pushing it to resemble a linear MPC scheme. A generic unstructured QP offers high flexibility for learning, while a QP having the structure of an MPC scheme promotes the explainability of the resulting policy, additionally provides ways for its analysis. The tools we propose allow for continuously adjusting the trade-off between the former and the latter during learning. We illustrate the workings of our proposed method with the resulting structure using a point-mass task.

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