Feedback systems: Input-output properties

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L2 Gain And Passivity Techniques In Nonlinear Control

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

All you need to know about model predictive control for buildings

Introduction Part I: Preliminaries Linear Algebra and Preliminaries Disctrete-time Linear Systems Stochastic Processes Kalman Filter Part II: Realization Theory Realization of Deterministic Problems Stochastic Realization Theory I Stochastic Realization Theory II Part III: Subspace Identification Subspace Identification I: ORT Subspace Identification II: CCA Identification of Closed-loop System Appendices Least-squares Method Input Signals for System Identification Overlapping Parametrization Matlab(R) Programs Solutions to Problems

Subspace methods for system identification

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.

Learning an Approximate Model Predictive Controller With Guarantees

Robust and optimal predictive control of the COVID-19 outbreak.

In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Due to their relevance in controller design and robustness analysis, we present a novel framework to find and verify dissipativity properties for discrete-time linear time-invariant systems from only one input–output trajectory. Introducing a new data-driven formulation for dissipativity, we obtain necessary and sufficient conditions for dissipativity based only on a definiteness condition on a single data-dependent matrix. Furthermore, we provide a promising relaxation in the case of measurement noise, which, as illustrated in numerous numerical examples, works remarkably well.

Johannes Köhler

Papers

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Learning an Approximate Model Predictive Controller With Guarantees

Robust and optimal predictive control of the COVID-19 outbreak.

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

One-Shot Verification of Dissipativity Properties From Input–Output Data