Differentially Flat Learning-based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter

• URL: http://arxiv.org/abs/2307.10541v1
• Date: Thu, 20 Jul 2023 02:42:23 GMT
• Title: Differentially Flat Learning-based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter
• Authors: Adam W. Hall and Melissa Greeff and Angela P. Schoellig
• Abstract summary: Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. We present a novel nonlinear controller that exploits differential flatness to achieve similar performance to state-of-the-art learning-based controllers.
• Score: 10.52705437098686
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for faster computation, or nonlinear optimization methods, which typically perform better but can limit real-time applicability. In this work, we present a novel nonlinear controller that exploits differential flatness to achieve similar performance to state-of-the-art learning-based controllers but with significantly less computational effort. Differential flatness is a property of dynamical systems whereby nonlinear systems can be exactly linearized through a nonlinear input mapping. Here, the nonlinear transformation is learned as a Gaussian process and is used in a safety filter that guarantees, with high probability, stability as well as input and flat state constraint satisfaction. This safety filter is then used to refine inputs from a flat model predictive controller to perform constrained nonlinear learning-based optimal control through two successive convex optimizations. We compare our method to state-of-the-art learning-based control strategies and achieve similar performance, but with significantly better computational efficiency, while also respecting flat state and input constraints, and guaranteeing stability.

Related papers

• Learning to Boost the Performance of Stable Nonlinear Systems [0.0]
  We tackle the performance-boosting problem with closed-loop stability guarantees. Our methods enable learning over arbitrarily deep neural network classes of performance-boosting controllers for stable nonlinear systems.
  arXiv  Detail & Related papers  (2024-05-01T21:11:29Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System [4.3012765978447565]
  We propose a parameterization of nonlinear output feedback controllers for linear dynamical systems. Our approach guarantees the closed-loop stability of partially observable linear dynamical systems without requiring any constraints to be satisfied.
  arXiv  Detail & Related papers  (2021-12-08T10:43:47Z)
• Imitation Learning of Stabilizing Policies for Nonlinear Systems [1.52292571922932]
  It is shown that the methods developed for linear systems and controllers can be readily extended to controllers using sum of squares. A projected gradient descent algorithm and an alternating direction method of algorithm are proposed ass for the stabilizing imitation learning problem.
  arXiv  Detail & Related papers  (2021-09-22T17:27:19Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Closing the Closed-Loop Distribution Shift in Safe Imitation Learning [80.05727171757454]
  We treat safe optimization-based control strategies as experts in an imitation learning problem. We train a learned policy that can be cheaply evaluated at run-time and that provably satisfies the same safety guarantees as the expert.
  arXiv  Detail & Related papers  (2021-02-18T05:11:41Z)
• Reinforcement Learning Control of Constrained Dynamic Systems with Uniformly Ultimate Boundedness Stability Guarantee [12.368097742148128]
  Reinforcement learning (RL) is promising for complicated nonlinear control problems. The data-based learning approach is notorious for not guaranteeing stability, which is the most fundamental property for any control system. In this paper, the classic Lyapunov's method is explored to analyze the uniformly ultimate boundedness stability (UUB) solely based on data.
  arXiv  Detail & Related papers  (2020-11-13T12:41:56Z)
• Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems [81.7983463275447]
  Learning-based control algorithms require data collection with abundant supervision for training. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained optimal control with dynamics learning and feedback control.
  arXiv  Detail & Related papers  (2020-05-09T05:57:43Z)
• Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees [1.1086440815804224]
  We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems. We employ automatic differentiation to obtain direct policy gradients by backpropagating the model predictive control (MPC) loss function and constraints penalties through a differentiable closed-loop system dynamics model.
  arXiv  Detail & Related papers  (2020-04-23T14:24:44Z)
• Tracking Performance of Online Stochastic Learners [57.14673504239551]
  Online algorithms are popular in large-scale learning settings due to their ability to compute updates on the fly, without the need to store and process data in large batches. When a constant step-size is used, these algorithms also have the ability to adapt to drifts in problem parameters, such as data or model properties, and track the optimal solution with reasonable accuracy. We establish a link between steady-state performance derived under stationarity assumptions and the tracking performance of online learners under random walk models.
  arXiv  Detail & Related papers  (2020-04-04T14:16:27Z)
• Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems [91.43582419264763]
  We study the problem of system identification and adaptive control in partially observable linear dynamical systems. We present the first model estimation method with finite-time guarantees in both open and closed-loop system identification. We show that AdaptOn is the first algorithm that achieves $textpolylogleft(Tright)$ regret in adaptive control of unknown partially observable linear dynamical systems.
  arXiv  Detail & Related papers  (2020-03-25T06:00:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.