We propose a novel Stochastic Nonlinear Model Predictive Control (SNMPC) framework for nonlinear systems with additive noise. Building on recent advances in nonlinear uncertainty propagation, we show that the state distribution of the system can be tractably approximated over time by Gaussian mixture distributions, with formal error bounds in Wasserstein distance. This representation yields closed-form expressions for expected costs and chance constraints, which become exact for affine constraints and exact up to a constant for quadratic costs. Consequently, the resulting control problem can be solved efficiently via nonlinear programming, while providing formal open-loop guarantees of correctness and asymptotic optimality. Experiments on a set of benchmarks demonstrate that the proposed approach compares favorably with existing methods in nonlinear settings with multi-modal disturbances, where standard approaches lead to poorly scaled solutions and unsafe or overly conservative control actions.
Konstantinos Prattis, Luca Laurenti, A. Dabiri· 0 citations
Transportation networks, in particular multi-class transportation networks (i.e., networks with mixed vehicle types), are complex systems that are challenging to control. Recently, Deep Reinforcement Learning (DRL), which learns control policies from interactions with the environment, and Model Predictive Control (MPC), which uses a system model to optimize control inputs, have been increasingly utilized for transportation network control. However, nonlinear system dynamics and high-dimensional state spaces in large-scale networks limit DRL's learning capacity under time-constrained training and increase MPC's computation time, hindering real-time implementation with limited computational resources. Moreover, MPC depends on an accurate network model, which is often unavailable for complex systems such as multi-class transportation networks. This paper proposes a novel DRL-MPC framework for multi-class transportation networks that divides control authority between DRL and MPC, combining DRL's fast online computation and model independence with MPC's built-in optimization and constraint-handling capabilities. In the hierarchical framework, MPC operates at the higher level and determines low-frequency control inputs whose slower update rate accommodates its high computation time, while DRL operates at the lower level and determines high-frequency control inputs using its fast online deployment. The framework is evaluated on a multi-class freeway network against a hierarchical MPC controller and a hybrid state-feedback-MPC controller, including scenarios with model mismatch and noisy traffic demands. Results show that the proposed framework outperforms the hybrid state-feedback-MPC controller, substantially reduces online computation time compared with the hierarchical MPC controller, and provides more effective constraint enforcement under model mismatch.
G. Onur, A. Dabiri, B. D. Schutter· 0 citations
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