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.

拟议的研究计划的一般目标是：（i）能够利用差异不变性功能的线性和非线性系统的代数和递归状态和参数估计方法的开发和分析。代数估计是指必须在有限的时间间隔内使用观测值产生估计的情况。使用该系统的任何已知差异不变的想法很有吸引力，因为不变式带有与系统输出测量噪声无关的其他信息。开发和评估的方法将包括：（a）自适应核Kalman过滤器的新型版本，其中递归估计值将受到约束以保护现有的差异不变性； （b）与扩展的卡尔曼滤波器相比，基于不变性的最小能量自适应过滤器的设计最小能量自适应过滤器； （c）与未知的其他彩色测量噪声相对于未知的轨迹跟踪器的设计。 （ii）开发新型的在线非线性全球稳定控制器，用于可能会受到重力的空间运动链机械系统。此类系统的示例是人类姿势和多连锁垂直机器人臂的机器人模型。研究方法和原创性：拟议的估计器将利用系统差异不变性的前向内核的积分表示，用于整体内核的显式公式，用于均质的线性不变性系统以及时间 - 变化和参数系统的均质线性时间不变性系统，并以差异不差为代表的差异范围代表系统特征。外源输入强迫的系统也可以使用明确的内核表达式。最重要的是，积分系统表示的内核会产生时间域的积分变换，可以用作精确的系统输出区分。文献中报道的现有代数估计方法是噪声敏感的，需要长时间间隔使用时需要进行重新启动。长期研究目标包括：（a）在多项式和理性系统中产生的非线性差异不变性的积分表示的系统方法，这些系统具有控制，并且配备了平面输出，其差异可以生成系统的状态空间和系统的参数； （b）在一般的非线性系统中构建近似差异不变的，可以在线估计和过滤算法中计算和执行；深入分析提出的估计方法的计算效率。对应用的重要性：预计所提出的高度自适应非线性估计方法将使许多应用程序受益，包括与目标跟踪和监视系统有关的应用程序。