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Robust Model Predictive Control with a Reactive Safety Mode.

机译：具有无功安全模式的鲁棒模型预测控制。

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摘要

Control algorithms suitable for online implementation in engineering applications, such as aerospace and mechanical vehicles, often require adherence to physical state and control constraints. Additionally, the chosen algorithms must provide robustness to uncertainty affecting both the system dynamics and the constraints. As further autonomy is built into these systems, the algorithms must be capable of blending multiple operational modes without violating the intrinsic constraints. Further, for real-time applications, the implemented control algorithms must be computationally efficient and reliable. The research in this thesis approaches these application needs by building upon the framework of MPC (Model Predictive Control).;The MPC algorithm makes use of a nominal dynamics model to predict and optimize the response of a system under the application of a feedforward control policy, which is computed online in a finite-horizon optimization problem. The MPC algorithm is quite general and can be applied to linear and nonlinear systems and include explicit state and control constraints. The finite-horizon optimization is advantageous given the finite online computational capabilities in practical applications. Further, recursively re-solving the finite-horizon optimization in a compressing- or receding-horizon manner provides a form of closed-loop control that updates the feedforward control policy by setting the nominal state at re-solve to the current actual state. However, uncertainty between the nominal model and the actual system dynamics, along with constraint uncertainty can cause feasibility, and hence, robustness issues with the traditional MPC algorithm.;In this thesis, an R-MPC (Robust and re-solvable MPC) algorithm is developed for uncertain nonlinear systems to address uncertainty affecting the dynamics. The R-MPC control policy consists of two components: the feedforward component that is solved online as in traditional MPC; and a separate feedback component that is determined offline, based on a characterization of the uncertainty between the nominal model and actual system. The addition of the feedback policy generates an invariant tube that ensures the actual system trajectories remain in the proximity of the nominal feedforward trajectory for all time. Further, this tube provides a means to theoretically guarantee continued feasibility and thus re-solvability of the R-MPC algorithm, both of which are required to guarantee asymptotic stability.;To address uncertainty affecting the state constraints, an SR-MPC (Safety-mode augmented R-MPC) algorithm is developed that blends a reactive safety mode with the R-MPC algorithm for uncertain nonlinear systems. The SR-MPC algorithm has two separate operational modes: standard mode implements a modified version of the R-MPC algorithm to ensure asymptotic convergence to the origin; safety mode, if activated, guarantees containment within an invariant set about a safety reference for all time. The standard mode modifies the R-MPC algorithm with a special constraint to ensure safety-mode availability at any time. The safety-mode control is provided by an offline designed control policy that can be activated at any time during standard mode. The separate, reactive safety mode provides robustness to unexpected state-constraint changes; e.g., other vehicles crossing/stopping in the feasible path, or unexpected ground proximity in landing scenarios.;Explicit design methods are provided for implementation of the R-MPC and SR-MPC algorithms on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives. Further, a discrete SR-MPC algorithm is developed that is more broadly applicable to real engineering systems. The discrete algorithm is formulated as a second-order cone program that can be solved online in a computationally efficient manner by using interior-point algorithms, which provide convergence guarantees in finite time to a prescribed level of accuracy. This discrete SR-MPC algorithm is demonstrated in simulation of a spacecraft descent toward a small asteroid where there is an uncertain gravity model, as well as errors in the expected surface altitude. Further, realistic effects such as control-input uncertainty, sensor noise, and unknown disturbances are included to further demonstrate the applicability of the discrete SR-MPC algorithm in a realistic implementation.
机译：适用于在线应用在航空航天和机械车辆等工程应用中的控制算法通常需要遵守物理状态和控制约束条件。此外，所选算法必须对影响系统动力学和约束的不确定性提供鲁棒性。随着这些系统内置更多自治功能，这些算法必须能够混合多种操作模式，而不会违反固有约束。此外，对于实时应用，所实现的控制算法必须在计算上高效且可靠。本文的研究通过建立在模型预测控制（MPC）框架上来满足这些应用需求。MPC算法利用名义动力学模型来预测和优化应用前馈控制策略的系统响应。 ，它是在有限水平优化问题中在线计算的。 MPC算法非常通用，可以应用于线性和非线性系统，并且包含显式状态和控制约束。鉴于在实际应用中有限的在线计算能力，有限水平优化是有优势的。此外，以压缩或后退水平方式递归地解决有限水平优化问题，提供了一种闭环控制形式，它通过将重新确定的标称状态设置为当前实际状态来更新前馈控制策略。然而，名义模型与实际系统动力学之间的不确定性以及约束条件的不确定性可能会导致可行性，并因此导致传统MPC算法的鲁棒性问题。本文采用R-MPC（鲁棒和可解MPC）算法针对不确定的非线性系统而开发，以解决影响动力学的不确定性。 R-MPC控制策略包括两个组件：前馈组件，可以像传统MPC一样在线解决；以及根据名义模型与实际系统之间不确定性的特征，离线确定独立的反馈组件。反馈策略的添加会生成一个不变管，以确保实际系统轨迹始终保持在标称前馈轨迹的附近。此外，该管还提供了一种从理论上保证R-MPC算法的连续可行性和可再求解性的方法，这两者都需要保证渐近稳定性。为了解决影响状态约束的不确定性，SR-MPC（安全性开发了一种模式增强R-MPC算法，该算法将反应性安全模式与R-MPC算法融合在一起，用于不确定的非线性系统。 SR-MPC算法具有两种独立的操作模式：标准模式实现R-MPC算法的修改版本，以确保与原点的渐近收敛；如果激活了安全模式，则始终确保将其包含在关于安全参考的不变集合内。标准模式对R-MPC算法进行了特殊的约束，以确保在任何时候都可以使用安全模式。安全模式控制由脱机设计的控制策略提供，该策略可以在标准模式下随时激活。单独的无功安全模式可为意外的状态约束更改提供鲁棒性。例如，其他车辆在可行路径上越过/停车，或在着陆情况下意外地接近地面。；提供了明确的设计方法，用于在一类具有规范的不确定非线性项的系统上实施R-MPC和SR-MPC算法有界衍生物。此外，开发了一种离散SR-MPC算法，该算法更广泛地适用于实际工程系统。离散算法被公式化为二阶锥程序，可以通过使用内点算法以计算有效的方式在线求解，该内点算法可在有限时间内提供收敛保证，达到规定的准确性。这种离散SR-MPC算法在航天器向小型小行星下降的仿真中得到了证明，该小行星存在引力模型不确定以及预期表面高度存在误差的情况。此外，还包括诸如控制输入不确定性，传感器噪声和未知干扰之类的现实效果，以进一步证明离散SR-MPC算法在实际实现中的适用性。

著录项

  • 作者

    Carson, John M., III.;

  • 作者单位

    California Institute of Technology.;

  • 授予单位 California Institute of Technology.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 125 p.
  • 总页数 125
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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