Estimation and Control of Nonlinear Dynamical Systems

非线性动力系统的估计和控制

• 批准号: RGPIN-2020-04796
• 负责人: Michalska, Hannah
• 金额: $ 2.04万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=740222
• 关键词: Estimation; Control; Nonlinear; Dynamical; Systems

The General Objectives of the Proposed Research Program are : (i) Development and analysis of algebraic and recursive state and parameter estimation methods for linear and nonlinear systems capable of exploiting the power of differential invariance. Algebraic estimation refers to the situation when the estimates must be produced using observations within a finite time interval. The idea of making use of any known differential invariants of the system is attractive because invariants carry additional information that is independent of system output measurement noise. The methods developed and evaluated will include: (a) novel versions of adaptive kernel Kalman filters in which the recursive estimates will be constrained to conserve the existing differential invariance; (b) design of invariance -based moving- horizon minimum- energy adaptive filters that exhibit accelerated and more reliable convergence properties than the extended Kalman filter; (c) design of trajectory trackers that are robust with respect to unknown additive coloured measurement noise. (ii) Development of novel on-line nonlinear globally stabilizing controllers for spatial kinematic chain mechanical systems that are subject to gravity. Examples of such systems are robotic models of the human posture and multi-link vertical robotic arms. Research Approach and Originality : The proposed estimators will exploit a forward--backward- kernel integral representation of system differential invariance originally proposed by the author. Explicit formulae for the integral kernels have been derived for homogeneous linear time invariant systems as well as time--varying and parameter--varying systems of arbitrary orders where the differential invariance was represented by the system characteristic equation. Explicit expressions of kernels are also available for systems forced by exogenous inputs. Most importantly, the kernels of the integral system representation give rise to time-domain integral transforms that can serve as exact system-output differentiators. Existing algebraic estimation methods reported in the literature are noise- sensitive and require re--initialization when used on long time intervals. Long Term Research Goals Include: (a) A systematic approach to the construction of integral representations of nonlinear differential invariants arising in polynomial and rational systems which are affine in control and which are equipped with flat outputs whose differentials generate the state space and parameters of the system; (b) Construction of approximate differential invariants in general nonlinear systems that can be computed and employed in on-line estimation and filtering algorithms; in depth analysis of the computational efficiency of the proposed estimation methods. The Importance for Applications: The proposed highly adaptive nonlinear estimation methods are expected to benefit many applications including those related to target tracking & surveillance systems.

提出的研究计划的总体目标是：(i)开发和分析能够利用微分不变性的线性和非线性系统的代数和递归状态和参数估计方法。代数估计是指必须在有限时间间隔内使用观测值进行估计的情况。利用系统中任何已知的微分不变量的想法是有吸引力的，因为不变量携带了与系统输出测量噪声无关的附加信息。开发和评估的方法将包括：(a)自适应核卡尔曼滤波器的新版本，其中递归估计将被约束以保持现有的微分不变性；(b)设计了基于不变性的移动视界最小能量自适应滤波器，该滤波器比扩展卡尔曼滤波器具有更快和更可靠的收敛特性；(c)设计对未知加性彩色测量噪声具有鲁棒性的轨迹跟踪器。（二）针对重力作用下空间运动链机械系统的新型在线非线性全局稳定控制器的开发。这种系统的例子是人体姿势的机器人模型和多连杆垂直机器人手臂。研究方法和独创性：所提出的估计量将利用作者最初提出的系统微分不变性的前向-后向核积分表示。对于齐次线性时不变系统以及任意阶的时变系统和参数变系统，导出了积分核的显式表达式，其中微分不变性用系统特征方程表示。对于受外源输入强迫的系统，核的显式表达式也可用。最重要的是，积分系统表示的核产生时域积分变换，可以作为精确的系统输出微分。现有的代数估计方法是噪声敏感的，并且在较长的时间间隔上使用时需要重新初始化。长期研究目标包括：(a)系统地构建非线性微分不变量的积分表示，这些非线性微分不变量出现在控制仿射的多项式和有理系统中，这些系统具有平面输出，其微分产生系统的状态空间和参数；(b)一般非线性系统中近似微分不变量的构造，可计算并用于联机估计和滤波算法；深入分析了所提出的估计方法的计算效率。应用的重要性：所提出的高度自适应非线性估计方法有望使许多应用受益，包括与目标跟踪和监视系统相关的应用。