Model predictive control (MPC) achieves stability and constraint satisfaction for general nonlinear systems, but requires computationally expensive online optimization. This paper studies approximations of such MPC controllers via neural networks (NNs) to achieve fast online evaluation. We propose safety augmentation that yields deterministic guarantees for convergence and constraint satisfaction despite approximation inaccuracies. We approximate the entire input sequence of the MPC with NNs, which allows us to verify online if it is a feasible solution to the MPC problem. We replace the NN solution by a safe candidate based on standard MPC techniques whenever it is infeasible or has worse cost. Our method requires a single evaluation of the NN and forward integration of the input sequence online, which is fast to compute on resource-constrained systems. The proposed control framework is illustrated on three non-linear MPC benchmarks of different complexity, demonstrating computational speedups orders of magnitudes higher than online optimization. In the examples, we achieve deterministic safety through the safety-augmented NNs, where naive NN implementation fails.

翻译：模型预测控制（MPC）能够实现一般非线性系统的稳定性和约束满足，但需要计算昂贵的在线优化。本文研究通过神经网络（NN）近似此类MPC控制器以实现快速在线评估的方法。我们提出安全增强机制，即便存在近似误差，仍能为收敛性和约束满足提供确定性保证。通过神经网络近似MPC的整个输入序列，我们能够在线验证该序列是否为MPC问题的可行解。当神经网络解不可行或代价更高时，我们用基于标准MPC技术的安全候选解替代该解。该方法只需在线进行一次神经网络评估和输入序列的前向积分，在资源受限系统上计算速度极快。所提出的控制框架在三个不同复杂度的非线性MPC基准测试中进行了验证，计算加速比在线优化高出数个数量级。在示例中，我们通过安全增强神经网络实现了确定性安全，而朴素神经网络实现则未能满足要求。