Advances in Control and Optimization of Complex Systems

The field of control and optimization of complex systems is rapidly advancing, with a focus on developing innovative methods that can handle uncertainty, nonlinearity, and stochasticity. Recent developments have seen a significant shift towards the use of neural networks and machine learning techniques to approximate complex dynamics, optimize performance, and certify safety and stability. Notably, researchers are exploring the use of Lyapunov-based approaches, concurrent learning, and generalized Lyapunov functions to improve the accuracy and efficiency of control and optimization algorithms.

The integration of solver sensitivities into end-to-end optimization proxies via Sobolev training has shown promising results, enabling fast and reliable surrogates for safety-critical large-scale optimization workloads. Furthermore, the development of efficient end-to-end learning frameworks, such as meta-optimization approaches, has improved computational efficiency and scalability.

Noteworthy papers in this area include:

  • Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions, which successfully certifies the stability of RL policies trained on Gymnasium and DeepMind Control benchmarks.
  • Certified Neural Approximations of Nonlinear Dynamics, which proposes a novel verification method based on certified first-order models, providing formal error bounds on neural approximations of dynamical systems.

Sources

System Identification and Control Using Lyapunov-Based Deep Neural Networks without Persistent Excitation: A Concurrent Learning Approach

Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions

Sobolev Training of End-to-End Optimization Proxies

Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approach

VeRecycle: Reclaiming Guarantees from Probabilistic Certificates for Stochastic Dynamical Systems after Change

Comparison of Data-Driven Modeling Approaches for Control Optimization of Floating Offshore Wind Turbines

PCA-DDReach: Efficient Statistical Reachability Analysis of Stochastic Dynamical Systems via Principal Component Analysis

Certified Neural Approximations of Nonlinear Dynamics

Neural network based control of unknown nonlinear systems via contraction analysis

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