Efficient model predictive control for nonlinear systems modelled by deep neural networks

This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex nonlinearity of the system state and control input, the MPC problem is nonlinear and challenging to solve for real-time control. This paper proposes two types of methods for solving the MPC problem: the mixed integer programming (MIP) method which produces an exact solution to the nonlinear MPC, and linear relaxation (LR) methods which generally give suboptimal solutions but are much computationally cheaper. Extensive numerical simulation for an inverted pendulum system modelled by ReLU NNs of various sizes is used to demonstrate and compare performance of the MIP and LR methods.

Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximation

Safe control of neural network dynamic models (NNDMs) is important to robotics and many applications. However, it remains challenging to compute an optimal safe control in real time for NNDM. To enable real-time computation, we propose to use a sound approximation of the NNDM in the control synthesis. In particular, we propose Bernstein over-approximated neural dynamics (BOND) based on the Bernstein polynomial over-approximation (BPO) of ReLU activation functions in NNDM. To mitigate the errors introduced by the approximation and to ensure persistent feasibility of the safe control problems, we synthesize a worst-case safety index using the most unsafe approximated state within the BPO relaxation of NNDM offline. For the online real-time optimization, we formulate the first-order Taylor approximation of the nonlinear worst-case safety constraint as an additional linear layer of NNDM with the l2 bounded bias term for the higher-order remainder. Comprehensive experiments with different neural dynamics and safety constraints show that with safety guaranteed, our NNDMs with sound approximation are 10-100 times faster than the safe control baseline that uses mixed integer programming (MIP), validating the effectiveness of the worst-case safety index and scalability of the proposed BOND in real-time large-scale settings.

Runtime Monitoring and Fault Detection for Neural Network-Controlled Systems

There is an emerging trend in applying deep learning methods to control complex nonlinear systems. This paper considers enhancing the runtime safety of nonlinear systems controlled by neural networks in the presence of disturbance and measurement noise. A robustly stable interval observer is designed to generate sound and precise lower and upper bounds for the neural network, nonlinear function, and system state. The obtained interval is utilised to monitor the real-time system safety and detect faults in the system outputs or actuators. An adaptive cruise control vehicular system is simulated to demonstrate effectiveness of the proposed design.

Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation

Counterfactual Explanations (CEs) have received increasing interest as a major methodology for explaining neural network classifiers. Usually, CEs for an input-output pair are defined as data points with minimum distance to the input that are classified with a different label than the output. To tackle the established problem that CEs are easily invalidated when model parameters are updated (e.g. retrained), studies have proposed ways to certify the robustness of CEs under model parameter changes bounded by a norm ball. However, existing methods targeting this form of robustness are not sound or complete, and they may generate implausible CEs, i.e., outliers wrt the training dataset. In fact, no existing method simultaneously optimises for proximity and plausibility while preserving robustness guarantees. In this work, we propose Provably RObust and PLAusible Counterfactual Explanations (PROPLACE), a method leveraging on robust optimisation techniques to address the aforementioned limitations in the literature. We formulate an iterative algorithm to compute provably robust CEs and prove its convergence, soundness and completeness. Through a comparative experiment involving six baselines, five of which target robustness, we show that PROPLACE achieves state-of-the-art performances against metrics on three evaluation aspects.

Data-Driven Cooperative Adaptive Cruise Control for Unknown Nonlinear Vehicle Platoons

This paper studies cooperative adaptive cruise control (CACC) for vehicle platoons with consideration of the unknown nonlinear vehicle dynamics that are normally ignored in the literature. A unified data-driven CACC design is proposed for platoons of pure automated vehicles (AVs) or of mixed AVs and human-driven vehicles (HVs). The CACC leverages online-collected sufficient data samples of vehicle accelerations, spacing and relative velocities. The data-driven control design is formulated as a semidefinite program (SDP) that can be solved efficiently using off-the-shelf solvers. The efficacy and advantage of the proposed CACC are demonstrated through a comparison with the classic adaptive cruise control (ACC) method on a platoon of pure AVs and a mixed platoon under a representative aggressive driving profile.

Data-driven dual-loop control for platooning mixed human-driven and automated vehicles

This paper considers controlling automated vehicles (AVs) to form a platoon with human-driven vehicles (HVs) under consideration of unknown HV model parameters and propulsion time constants. The proposed design is a data-driven dual-loop control strategy for the ego AVs, where the inner loop controller ensures platoon stability and the outer loop controller keeps a safe inter-vehicular spacing under control input limits. The inner loop controller is a constant-gain state feedback controller solved from a semidefinite program (SDP) using the online collected data of platooning errors. The outer loop is a model predictive control (MPC) that embeds a data-driven internal model to predict the future platooning error evolution. The proposed design is evaluated on a mixed platoon with a representative aggressive reference velocity profile, the SFTP-US06 Drive Cycle. The results confirm efficacy of the design and its advantages over the existing single loop data-driven MPC in terms of platoon stability and computational cost.