Author: Denis Avetisyan
A new approach combines system identification with reinforcement learning to achieve efficient and accurate control of complex dynamics.
This review details SINDy-TD3, a method leveraging sparse identification of nonlinear dynamics and twin delayed deep deterministic policy gradients for improved data efficiency in bi-rotor control and model-based planning.
Controlling complex nonlinear systems remains a persistent challenge due to limitations in data efficiency and robustness. This paper introduces a novel approach, ‘Dyna-Style Reinforcement Learning Modeling and Control of Non-linear Dynamics’, which integrates data-driven system identification with reinforcement learning. Specifically, a Sparse Identification of Nonlinear Dynamics (SINDy) model is combined with a Twin Delayed Deep Deterministic Policy Gradient (TD3) agent to enhance learning with limited data. Demonstrated on a bi-rotor system, this SINDy-TD3 framework achieves improved accuracy and robustness compared to conventional reinforcement learning-but could this hybrid modeling and control strategy be extended to even more intricate and unpredictable dynamical systems?
The Challenge of Nonlinearity: A Necessary Refinement
Conventional control systems, meticulously designed around the principle of linearity, often falter when confronted with the unpredictable behavior of inherently nonlinear systems. These limitations stem from the fact that nonlinearities – such as friction, saturation, or complex interactions between system components – invalidate the simplifying assumptions upon which linear control relies. Consequently, performance degrades, stability margins shrink, and the system’s ability to reliably maintain a desired state diminishes. While linear approximations can offer temporary solutions, they frequently introduce inaccuracies and compromise robustness, particularly when operating outside a narrow, predefined range. This struggle highlights the need for control strategies specifically tailored to address the complexities arising from nonlinear dynamics, ensuring consistent and dependable operation across a wider spectrum of conditions.
Many real-world systems, from the intricate movements of robotics and the dynamics of aircraft to the complexities of chemical processes and biological networks, are fundamentally nonlinear. This means their behavior isn’t proportional to the inputs applied – a small change can trigger disproportionately large or unpredictable results. Traditional control strategies, built upon the assumption of linearity, often falter when confronted with these systems, leading to diminished performance, instability, or even failure. Consequently, engineers and scientists are increasingly focused on developing adaptive control techniques that can account for these nonlinearities. These strategies might involve continuously adjusting control parameters based on system behavior, employing intelligent algorithms to learn and predict responses, or utilizing model predictive control to optimize performance over a future time horizon, all to achieve robust and reliable operation in the face of inherent complexity.
From Observation to Insight: Data-Driven Modeling
Data-driven models represent a shift from traditional system modeling, which relies heavily on first-principles equations and assumptions about underlying physics. Instead of explicitly defining system behavior, these models construct representations directly from observed data, typically time series or state measurements. This approach is particularly advantageous when the governing equations are unknown, intractable, or subject to significant uncertainty. By employing techniques like regression, machine learning, or symbolic regression, data-driven models identify patterns and relationships within the data to approximate system dynamics. The accuracy of these models is fundamentally limited by the quantity and quality of the available data, but they offer a powerful means of capturing complex system behavior without requiring detailed a priori knowledge.
Sparse Identification of Nonlinear Dynamics, or SINDy, is a regression-based technique for system identification that aims to discover the underlying governing equations from observed data with limited a priori assumptions. Unlike traditional modeling approaches that require specifying a functional form or library of potential terms, SINDy employs sparse regression-typically using algorithms like LASSO-to identify only the most dynamically relevant terms from a candidate library of functions. This library can include nonlinear functions, derivatives, and other mathematical operations. By enforcing sparsity, SINDy promotes model parsimony, resulting in simpler, more interpretable models that capture the essential dynamics of the system without overfitting to noise or irrelevant features. The process involves representing the time derivative of a state variable as a linear combination of these selected terms, effectively learning the model directly from data.
Sparse Regression, as employed within the SINDy methodology, identifies the most significant terms governing a system’s dynamics by enforcing sparsity in the model’s coefficient vector. This is achieved through regularization techniques, such as L1 regularization ||w||_1 = \sum_i |w_i|, which penalizes non-zero coefficients. By driving many coefficients to zero, Sparse Regression effectively selects a minimal set of active terms, resulting in a parsimonious model. This simplification enhances both interpretability, as the governing equations are expressed with fewer terms, and computational efficiency, reducing the complexity of simulations and predictions. The resulting model focuses on the dominant dynamics, discarding less influential terms without sacrificing accuracy, provided an appropriate threshold for coefficient magnitude is established.
Dyna-Style Reinforcement Learning: Amplifying Experience
Dyna-style Reinforcement Learning enhances agent learning through a cyclical process of real and simulated experience. The agent interacts with the environment, collecting real experiences which are then used to train a forward dynamics model – a learned representation of the environment’s transition function. This model is subsequently used to generate simulated experiences, effectively expanding the dataset available for training the agent’s policy and value functions. By interleaving real and simulated data, the agent leverages the learned model to plan and improve its behavior beyond what is possible with real-world interactions alone, creating a more efficient learning loop.
Dyna-style reinforcement learning demonstrates a substantial improvement in data efficiency compared to standard methods. Empirical results indicate that the SINDy-TD3 agent, leveraging simulated experiences, achieved comparable sine wave trajectory tracking performance in 2500 training episodes. In contrast, a standard TD3 agent required approximately 4500 episodes to reach the same level of performance. This nearly 2x reduction in episode count highlights the ability of Dyna-style approaches to accelerate learning and reduce the demand for extensive real-world interactions.
Twin Delayed Deep Deterministic Policy Gradient (TD3) serves as the foundational reinforcement learning algorithm within this framework. TD3 utilizes deep neural networks to approximate both the policy and Q-functions, enabling it to handle complex, continuous action spaces. Experience replay, implemented via a Replay Buffer, stores agent interactions – state, action, reward, and next state – allowing for off-policy learning and breaking temporal correlations in the data. This buffer is sampled randomly during training to update the neural network weights, enhancing stability and sample efficiency. The ‘delayed’ aspect refers to a technique where policy updates are performed less frequently than Q-function updates, further improving stability by reducing the risk of policy overestimation.
A Robust Demonstration: Validation on the Bi-Rotor System
The efficacy of a novel control strategy, integrating Dyna-Style Reinforcement Learning with System Identification without Knowledge of Dynamics (SINDy), was rigorously tested on a Bi-Rotor System – a widely recognized and demanding benchmark in the field of nonlinear control. This complex system, characterized by significant dynamic coupling and inherent instability, presents a substantial challenge for control algorithms. Validation on the Bi-Rotor demonstrates the approach’s ability to learn and adapt to highly nonlinear dynamics without relying on a pre-defined model. The combination of model-free reinforcement learning with data-driven system identification allows the controller to effectively manage the system’s inherent complexities, paving the way for application in other challenging robotic systems where precise and robust control is paramount.
Prior to implementing the control strategy, a thorough understanding of the Bi-Rotor System’s complex dynamics was established through system identification techniques. A Chirp Signal – a signal whose frequency increases or decreases over time – was strategically employed to excite the system across a broad range of operating conditions. The resulting data, capturing the system’s response to this varied excitation, served as the foundation for learning an accurate model of its behavior. This data-driven approach allowed for the creation of a model capable of predicting the system’s responses, which was then integrated into the Dyna-Style Reinforcement Learning framework, ultimately enhancing the agent’s ability to plan and execute precise control actions.
The control strategy’s efficacy was demonstrated through rigorous trajectory tracking tasks on the Bi-Rotor System. The agent consistently and accurately followed a variety of trajectories – including abrupt step changes, smooth sine waves, and oscillating square waves – indicating a high degree of robustness to different dynamic demands. Notably, the agent minimized steady-state error during these maneuvers, suggesting precise control authority. Furthermore, incorporating model-based planning significantly accelerated the learning process; the agent converged on optimal control policies much faster than a comparable system lacking this planning capability, highlighting the benefit of combining data-driven learning with predictive modeling.
The pursuit of efficient control, as demonstrated by SINDy-TD3, echoes a fundamental principle of parsimony. This work elegantly distills complex dynamics into a manageable, data-driven model-a concept remarkably aligned with Epicurus’s belief that “it is not the pursuit of endless desires that brings happiness, but the absence of pain.” The SINDy component, by identifying sparse governing equations, reduces the ‘pain’ of computational burden and improves data efficiency – a direct analogue to Epicurus’s emphasis on minimizing suffering through simplicity. The bi-rotor control validates this streamlined approach, suggesting that optimal performance isn’t achieved through unnecessary complexity, but through a focused understanding of core principles.
What’s Next?
The presented synthesis, while demonstrating improved data efficiency, does not erase the fundamental asymmetry inherent in combining data-driven modeling with control. The SINDy model, for all its elegance, remains a distillation-a reduction of complexity. Future iterations must confront the inevitable information loss and quantify its impact on robustness. A truly parsimonious approach demands not simply more data, but a rigorous interrogation of what data is, in fact, necessary.
The bi-rotor platform, while sufficient for initial validation, represents a constrained landscape. The next logical step is to extend this framework to systems exhibiting higher degrees of freedom and more pronounced nonlinearities. This expansion, however, should not be pursued merely for the sake of complexity. The goal is not to conquer increasingly difficult problems, but to reveal the limitations of the current approach-to expose where simplification breaks down, and where new principles are required.
Ultimately, the pursuit of sample efficiency should not overshadow the question of interpretability. A control policy, however effective, remains opaque if its underlying rationale is hidden within layers of abstraction. The true measure of progress will not be the number of trials avoided, but the degree to which the system’s behavior can be understood, predicted, and, if necessary, corrected with minimal intervention.
Original article: https://arxiv.org/pdf/2512.21081.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2025-12-28 05:02