Learning an Approximate Model Predictive Controller with Guarantees

A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter

Learning an approximate model predictive controller with guarantees

In this thesis, a supervised learning framework to approximate a model predictive controller (MPC) with guarantees on stability and constraint satisfaction is proposed. The approximate controller has a reduced computational complexity in comparison to standard MPC which makes it possible to implement the resulting controller for systems with a high sampling rate on a cheap hardware. The framework can be used for a wide class of nonlinear systems. In order to obtain closed-loop guarantees for the approximate MPC, a robust MPC (RMPC) with robustness to bounded input disturbances is used which guarantees stability and constraint satisfaction if the input is approximated with a bound on the approximation error. The RMPC can be sampled offline and hence, any standard supervised learning technique can be used to approximate the MPC from samples. Neural networks (NN) are discussed in this thesis as one suitable approximation method. To guarantee a bound on the approximation error, statistical learning bounds are used. A method based on Hoeffding’s Inequality is proposed to validate that the approximate MPC satisfies these bounds with high confidence. This validation method is suited for any approximation method. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the approximated MPC. Within this thesis, an algorithm to obtain automatically an approximate controller is proposed. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem for which we learn a neural network controller that guarantees stability and constraint satisfaction. The combination of robust control and statistical validation can also be used for other learning based control methods to obtain guarantees on stability and constraint satisfaction

Data-driven estimation of the maximum sampling interval: analysis and controller design for discrete-time systems

This article is concerned with data-driven analysis of discrete-time systems under aperiodic sampling, and in particular with a data-driven estimation of the maximum sampling interval (MSI). The MSI is relevant for analysis of and controller design for cyber-physical, embedded and networked systems, since it gives a limit on the time span between sampling instants such that stability is guaranteed. We propose tools to compute the MSI for a given controller and to design a controller with a preferably large MSI, both directly from a finite-length, noise-corrupted state-input trajectory of the system. We follow two distinct approaches for stability analysis, one taking a robust control perspective and the other a switched systems perspective on the aperiodically sampled system. In a numerical example and a subsequent discussion, we demonstrate the efficacy of our developed tools and compare the two approaches.Comment: 16 pages, 4 figure, 1 table. Now contains 1) a disturbance description via multipliers, 2) extended proofs and 3) an extensive numerical case study, including a comparison of different data lengths, a discussion of complexity and a comparison with set membership estimatio