A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control

Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.Comment: IFAC LPVS 201

Virtual Control Contraction Metrics: Convex Nonlinear Feedback Design via Behavioral Embedding

This paper proposes a novel approach to nonlinear state-feedback control design that has three main advantages: (i) it ensures exponential stability and $\mathcal{L}_2$-gain performance with respect to a user-defined set of reference trajectories, and (ii) it provides constructive conditions based on convex optimization and a path-integral-based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter-varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and $\mathcal{L}_2$-gain performance for all trajectories of the targeted reference behavior. Connections with the linear-parameter-varying (LPV) theory are also explored showing that the proposed methodology is a generalization of LPV state-feedback control in two aspects. First, it is a unified generalization of the two distinct categories of LPV control approaches: global and local methods. Second, it provides rigorous stability and performance guarantees when applied to the true nonlinear system, while such properties are not guaranteed for tracking control using LPV approaches

Nonlinear parameter‐varying state‐feedback design for a gyroscope using virtual control contraction metrics

In this article, we present a virtual control contraction metric (VCCM) based nonlinear parameter-varying approach to design a state-feedback controller for a control moment gyroscope (CMG) to track a user-defined trajectory set. This VCCM based nonlinear (NL) stabilization and performance synthesis approach, which is similar to linear parameter-varying (LPV) control approaches, allows to achieve exact guarantees of exponential stability and (Formula presented.) -gain performance on NL systems with respect to all trajectories from the predetermined set, which is not the case with the conventional LPV methods. Simulation and experimental studies conducted in both fully- and under-actuated operating modes of the CMG show effectiveness of this approach compared with standard LPV control methods

Neural Stochastic Contraction Metrics for Learning-based Control and Estimation

We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable learning-based control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric and its differential Lyapunov function, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The trained NSCM model allows autonomous systems to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic NCM, as shown in simulation results

Analysis and design of model predictive control frameworks for dynamic operation -- An overview

This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference signals to the general economic operation of a plant under online changing time-varying operating conditions. We focus on the particular challenges that arise when dealing with such more general control goals and present methods that have emerged in the literature to address these issues. The goal of this article is to present an overview of the state-of-the-art techniques, providing a diverse toolkit to apply and further develop MPC formulations that can handle the challenges intrinsic to dynamic operation. We also critically assess the applicability of the different research directions, discussing limitations and opportunities for further researc