Learning control for uncertain nonholonomic mechanical systems

We employ two adaptive strategies for motion control of uncertain nonholonomic mechanical systems with chained form kinematics. Chained form systems possess sufficient structure to permit very effective control strategies to be developed for them. For example, these systems are differentially flat, which can be shown to be quite useful for motion control, and they are also easier to stabilize than some other classes of nonholonomic systems; both of these properties are exploited in the paper. As a consequence of the adaptive nature of the control laws and the properties of chained form systems, the employed schemes are simple and modular, are easily implemented with a wide range of mechanical systems, and provide a reasonable starting point for addressing such practical problems as collision avoidance and sensor-based planning and control. The first controller combines an efficient trajectory generation algorithm with an adaptive tracking strategy to obtain the desired motion control, while the second scheme achieves this control objective through the use of a stabilizing control law developed utilizing adaptation and homogeneous system theory. Each of the control strategies is computationally efficient, ensures accurate motion control, and is implementable in the presence of considerable uncertainty concerning the mechanical system model. The efficacy of the approach is illustrated through computer simulations with a single chain nonholonomic system.

168 Impact of Connecticut’s Good Samaritan Laws in Preventing Opioid Overdose Deaths – An Applied System Dynamics Approach

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection and adapted frame fields, we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affine constraints. In the second part of the paper, we show that the Kaluza–Klein theory is best presented and explained by using the framework of nonholonomic mechanical systems. We show that the geodesics of the Kaluza–Klein space, which are tangent to the electromagnetic distribution, coincide with the solutions of Lagrange–d’Alembert equations for a nonholonomic mechanical system with linear constraints, and their projections on the spacetime are the geodesics from general relativity. Any other geodesic of the Kaluza–Klein space that is not tangent to the electromagnetic distribution is also a solution of Lagrange–d’Alembert equations, but for affine constraints. In particular, some of these geodesics project exactly on the solutions of the Lorentz force equations of the spacetime.

This paper describes a multi-level system dynamics (SD) / discrete event simulation (DES) approach for assessing planning and scheduling problems within an aviation training continuum. The aviation training continuum is a complex system, consisting of multiple aviation schools interacting through interschool student and instructor flows that are affected by external triggers such as resource availability and the weather. SD was used to model the overall training continuum at a macro level to ascertain relationships between system entities. SD also assisted in developing a shared understanding of the training continuum, which involves constructing the definitions of the training requirements, resources and policy objectives. An end-to-end model of the continuum is easy to relate to, while dynamic visualisation of system behaviour provides a method for exploration of the model. DES was used for micro level exploration of an individual school within the training continuum to capture the physical aspects of the system including resource capacity requirements, bottlenecks and student waiting times. It was also used to model stochastic events such as weather and student availability. DES has the advantage of being able to represent system variability and accurately reflect the limitations imposed on a system by resource constraints. Through sharing results between the models, we demonstrate a multi-level approach to the analysis of the overall continuum. The SD model provides the school’s targeted demand to the DES model. The detailed DES model is able to assess schedules in the presence of resource constraints and variability and provide the expected capacity of a school to the high level SD model, subjected to constraints such as instructor availability or budgeted number of training systems. The SD model allows stakeholders to assess how policy and planning affect the continuum, both in the short and the long term. The development of this approach permits moving the analysis of the continuum between SD and DES models as appropriate for given system entities, scales and tasks. The resultant model outcomes are propagated between the continuum and the detailed DES model, iteratively generating an assessment of the entire set of plans and schedule across the continuum. Combining data and information between SD and DES models and techniques assures relevance to the stakeholder needs and effective problem scoping and scaling that can also evolve with dynamic architecture and policy requirements. An example case study shows the combined use of the two models and how they are used to evaluate a typical scenario where increased demand is placed on the training continuum. The multi-level approach provides a high level indication of training requirements to the model of the new training school, where the detailed model indicates the resources required to achieve those particular student levels.

Many problematic outcomes in agricultural and food systems have important dynamic dimensions and arise due to underlying system structure. Thus, understanding the linkages between system structure and dynamic behavior often is important for the design and implementation of interventions to achieve sustained improvements. System Dynamics (SD) modeling represents system structure using stock-flow-feedback structures expressed as systems of differential equations solved by numerical integration methods. SD methods also encompass a broader methodological approach that emphasizes model structural development and data inputs to replicate one of a limited number of problematic behavioral modes, anticipates dynamic complexity and focuses on feedback processes arising from endogenous system elements. A variety of data sources may be used in SD model development, and parametric sensitivity analysis with SD models can determine priority information needs in feedback-rich systems when data are lacking. Although numerous applications of SD modeling to agriculture exist, the approach is underutilized as a useful tool for research, instruction and programmatic development. This presentation highlights key elements of SD modeling using two examples from animal agriculture at different scales. A dynamic version of the Cornell Net Carbohydrate and Protein System (CNCPS) that represents outcomes for an individual dairy cow is formulated as an SD model, and illustrates the benefits of the SD approach in animal nutrition research and for farm-level nutritional management decisions. At a very different scale, an SD model of the Brazilian dairy supply chain (farms, processing and consumers) illustrates the country-level impacts of efforts to improve cow productivity and how impacts differ if productivity improvement occurs on small farms rather than large farms. The presentation concludes with recommendations to increase awareness and training is SD methods to enhance its appropriate use in research and instruction.

Deterministic learning-based neural control for output-constrained strict-feedback nonlinear systems

In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations.

The multi-degree-freedom nonholonomic constraint systems were analyzed using method of canonical coordinates. The theorem and characteristic equations of the canonical coordinate’s equations for multi-degree-freedom nonholonomic systems are obtained. The conserved quantities and general solutions of the systems are deduced directly by choosing appropriate canonical coordinates. An example is given to illustrate application of the results.

In this paper, variational techniques are used to analyze the dynamics of nonholonomic mechanical systems with impacts. Implicit nonholonomic smooth Lagrangian and Hamiltonian systems are extended to a nonsmooth context appropriate for collisions. In particular, we provide a variational formulation for implicit nonholonomic mechanical systems with collisions, for those collisions that preserve energy and momentum at the impact. Lastly, the theoretical results are illustrated by examining the example of a rolling disk hitting a wall.

This thesis studies geometric formulations of a slow-fast realization of nonholonomic mechanical control systems mediated by strong friction forces. Such realization is motivated by wheeled mobile robotic systems and viewed as a singular perturbation of nonholonomic dynamics. For sufficiently strong friction forces, the dynamics emit an attractive invariant manifold interpreted as the perturbation of the constraints. This invariant manifold describes small slip velocities at the wheel contact points. We propose a systematic decomposition of the control system into slow and fast directions. The invariant manifold is approximated with a power series, which can be recursively computed. Accordingly, we develop a novel recursive procedure to input-output linearize the slow subsystem by dynamic-state feedback transformations. Using this procedure, design a trajectory-tracking PD controller to compensate for the violations of constraints and closed-loop stability analysis is performed. Our approach is illustrated through a numerical case study.

Underactuated mechanical systems are frequently encountered in several industrial and real-world applications such as robotic manipulators with elastic components, aerospace vehicles, marine vessels, and overhead container cranes. The design of accurate controllers for this kind of mechanical system can become very challenging, especially if a high level of uncertainty is involved. In this paper, an adaptive fuzzy inference system is combined with a sliding mode controller in order to enhance the control performance of uncertain underactuated mechanical systems. The proposed scheme can deal with a large class of multiple-input–multiple-output underactuated systems subject to parameter uncertainties, unmodeled dynamics, and external disturbances. The convergence properties of the resulting intelligent controller are proved by means of a Lyapunov-like stability analysis. Experimental results obtained with an overhead container crane demonstrate not only the feasibility of the proposed scheme, but also its improved efficacy for both stabilization and trajectory tracking problems.

PurposeThe purpose of this research is to investigate sustainable strategies for skills development that is specific to the youth of South Africa. International and South African data are statistically analysed and quantified to provide inputs for the systems dynamics (SD)-based predictive skills model. The skills model simulates the impact of barriers and drivers on youth skills development towards identification of focus areas for improvement.Design/methodology/approachThe research adopts a mixed-methods approach. The study begins with an explorative literature study on skills development, with the findings applied in developing (1) South African specific research instruments for small, medium and micro enterprises (SMMEs) and skills programme grant recipients and (2) a conceptual framework of the SD predictive skills model. The responses to the South African specific instruments are analysed via confirmatory factor analysis (CFA), which quantifies the input coefficients to the system dynamics model. To quantify the global inputs for the SD model, an in-depth literature review of the global skills development initiatives is conducted. The SD model output on skills, for the South African inputs, is comparatively evaluated against global inputs.FindingsThe paper details the results of the literature analysis, instrument analyses, CFA and SD model. The instrument results rank experience, skills and interactions with experts and work-based learning as most important. South African and global learners identify networking as the primary medium for identifying training and employment opportunities. South African and global learners also identify qualifications and work-based experience as key to finding employment. The quantified results of the SA and global analysis are used as inputs in the SD model to deliver a forecasting tool. The SD model finds that the global data provide for better development of the skills base than the South African inputs. The key focus areas identified for improvement in South Africa include networking, work-based experience and a reduction in administrative requirements.Originality/valueThe research's originality resides in the ability to predict the impact of drivers and barriers on skills development. This research sought to transform qualitative global and South African inputs into a consolidated, predictive systems-based model. The SD model can be adopted as an indicator of drivers and barriers focused towards the optimisation of skills development.

System Dynamics (SD) modelling is a highly complex process. Although the SD methodology has been discussed extensively in most breakthroughs and present literature, discussions on data collection methods for SD modelling are not explained in details in most studies. To date, comprehensive descriptions of knowledge extraction for SD modelling is still scarce in the literature either. In an attempt to fill in the gap, three primary groups of data sources proposed by Forrester: (1) mental database, (2) written database and (3) numerical database, were reviewed, including the potential data collections methods for each database by taking into account the advancement of current computer and information technology. The contributions of this paper come in threefolds. First, this paper highlights the potential data sources that deserved to be acknowledged and reflected in the SD domain. Second, this paper provides insights into the appropriate mix and match of data collection methods for SD development. Third, this paper provides a practical synthesis of potential data sources and their suitability according to the SD modelling stage, which can serve as modelling practice guidelines.

Dynamic hybrid modelling: Switching between AB and SD designs of a predator-prey model

In the convolutional learning control design, a desired output trajectory is specified and an iterative algorithm is implemented to improve the tracking performance as the action is repeated. This limits the applications of the learning controller because in some important tasks like impedance control of a robotic manipulator, a desired model is given rather than the trajectories. In this paper, a model reaching learning control scheme (MRLC) is proposed for a class of nonlinear systems. A desired model specifying the desired output is given and an iterative algorithm is designed so that the learning system will eventually follow the desired response specified by the desired model as the action is repeated. This allows extra freedom in learning controller design and represents many important applications. The proposed learning controller is applied to impedance control of robotic manipulators. Simulation results of a cylindrical robot are presented to illustrate the performances of the learning controllers.