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.

拟议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。代数估计是指估计必须是的情况。利用有限时间间隔内的观测值产生的想法很有吸引力，因为不变量携带独立于系统输出测量噪声的附加信息。 (a) 自适应核卡尔曼滤波器的新版本，其中递归估计将受到限制以保留现有的微分不变性；(b) 基于不变性的移动水平最小能量自适应滤波器的设计，其表现出比传统滤波器更快且更可靠的收敛特性。扩展卡尔曼滤波器；（c）设计对未知加性有色测量噪声具有鲁棒性的轨迹跟踪器；（ii）开发用于空间运动链机械系统的新型在线非线性全局稳定控制器。此类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臂。研究方法和独创性：所提出的估计器将利用最初提出的系统微分不变性的前向-后向核积分表示。作者导出了齐次线性时不变系统以及任意阶的时变和参数变化系统的积分核的显式公式，其中微分不变性由系统特征方程的显式表达式表示。内核也可用于受外生输入强制的系统。最重要的是，积分系统表示的内核产生时域积分变换，可以作为精确的系统输出微分器。文献中报告的现有代数估计方法是噪声的。敏感，并且在长时间间隔使用时需要重新初始化 长期研究目标包括： (a) 构造多项式和中出现的非线性微分不变量的积分表示的系统方法。控制仿射且配备平坦输出的理性系统，其微分生成系统的状态空间和参数；滤波算法；深入分析所提出的估计方法的计算效率：所提出的高度自适应非线性估计方法预计将有利于许多应用，包括与目标跟踪和监视系统相关的应用。