کنترل یادگیری تکراری پارتو : کنترل بهینه شده برای اهداف عملکرد چندگانه

Iterative learning control (ILC) is a 2-degree-of-freedom technique that seeks to improve system performance along the time and iteration domains. Traditionally, ILC has been implemented to minimize trajectory-tracking errors across an entire cycle period. However, there are applications in which the necessity for improved tracking performance can be limited to a few specific locations. For such systems, a modified learning controller focused on improved tracking at the selected points can be leveraged to address multiple performance metrics, resulting in systems that exhibit significantly improved behaviors across a wide variety of performance metrics. This paper presents a pareto learning control framework that incorporates multiple objectives into a single design architecture.

Iterative learning control (ILC) is an adaptive control approach in which the adaptation occurs at the input signal rather than as a system or control parameter update (Bristow et al., 2006 and Moore et al., 1992). ILC has been successfully applied to repetitive applications in robotics (Arimoto et al., 1984 and Tayebi and Islam, 2006), manufacturing (Barton and Alleyne, 2011, Kim and Kim, 1993 and Rotariu et al., 2008), and chemical processing (Lee and Lee, 2007 and Mezghani et al., 2002). In these applications, ILC was implemented to improve the trajectory tracking performance of the system through iterative updates to the control signal. Conventional ILC approaches use the complete error signal from previous iterations to generate an updated control signal for improved system performance (Bristow et al., 2006). As an alternative to using the complete error signal, a point-based controller focuses on improving the error at discrete locations or times for performance enhancements in applications such as robotic pick n׳ place tasks (Dijkstra et al., 2001), patient stroke rehabilitation (Freeman et al., 2009), and reconnaissance missions with UAVs (Lim & Bang, 2010). In these application examples, specific locations (e.g. the start and end positions for pick n׳ place robots) are critical to the success of the task, while the motion profile between the locations is irrelevant. Recent work by Freeman, Cai, Rogers, and Lewin (2011) has resulted in an ILC algorithm termed point-to-point learning control that focuses on specific times or locations of a predetermined motion profile. In point-to-point ILC, the selected points define a subset of the motion profile, χ(ni)⊆yd(k)χ(ni)⊆yd(k), where n i are the selected points for all i =1,…,M , y d(k ) defines the motion profile, and k is the time index. The learning controller only applies a feedforward update to these specified points, χ(ni)χ(ni). By removing the unnecessary constraint of a predefined path between the points, additional control freedom can be obtained and redirected towards achieving multiple performance objectives ( Fig. 1).The introduction of multiple performance objectives into a learning framework provides an opportunity to leverage underutilized control actuation to improve system performance, in addition to using learning as a means of improving the system performance. Examples of applications that perform repetitive tasks with multiple performance metrics can be found in manufacturing (metrics: throughput, part quality, material waste); robotics (metrics: speed, precision motion control, power utilization, vibration isolation); and unmanned air/ground vehicles (metrics: path following, patrol efficiency, energy consumption, sensor transmission strength). Pareto optimization is a commonly employed multi-objective approach in which two or more conflicting objectives are weighted (Yang & Catthoor, 2003) within a single framework. Solutions to this class of problems require a tradeoff in the performance objectives based on the desired design criteria. Tradeoff within a control design is frequently made as a tradeoff between performance and robustness (Boulet and Duan, 2007 and Jin and Sendhoff, 2003), or as a single performance objective optimization within a constrained system (Mishra, Topcu, & Tomizuka, 2011). Recent work by the authors presented a pareto learning controller for addressing multiple objectives with systems that perform repetitive tasks. This initial work presented the basic framework, but did not provide a tradeoff analysis or experimental validation (Lim & Barton, 2013). Recently published papers presented a dual optimization approach to multi-objective learning (Freeman and Tan, 2013, Freeman, 2012 and Owens et al., 2013). These papers utilize a two-step approach to optimizing the overall performance as close to zero steady-state tracking as possible. In step 1, the framework obtains an optimal control solution for zero steady-state trajectory tracking. In step 2, the framework seeks to optimize the performance of an additional objective through the use of a cost function that considers the additional objective while simultaneously minimizing the difference between a new control input and the optimal control signal determined in step 1. This iterative learning sequence involves multiple steps, while bounding the range of the new solution to be arbitrarily close to the initial optimal input. In this paper, we present a generalized multi-objective learning control framework for systems that require the optimization of multiple performance objectives simultaneously. To address the performance requirements for these types of systems, the control objectives are posed as a pareto optimization-based learning problem where the controller seeks to optimize a cost function containing multiple performance objectives. As a result of our one-step optimization approach, tradeoffs between trajectory tracking and additional objectives can be clearly observed. Additionally, the optimization search is implemented over a broad set of potential solutions, thus enabling a greater variety of possible outcomes. This research extends the work provided in Lim and Barton (2013) through several notable modifications: (1) the modified learning controller with cost function convergence and bounded system outputs is provided, (2) a performance tradeoff analysis is included to evaluate potential design choices for energy reduction, (3) a detailed design methodology has been provided, and (4) simulation and experimental results validate the controller performance and provide a means for verifying trends in the system behavior.

This paper presents a generalized multi-objective learning control framework. Utilizing a point-to-point ILC scheme, the tracking performance at selected points can be maintained, while relaxing the control constraints between points. Leveraging this extra control freedom, a pareto optimization-based learning algorithm introduces additional performance metrics into a single design framework for improved system performance of multiple competing objectives. The specific contributions of this work include (1) the development of a generalized multi-performance objective learning framework across n-objectives, (2) output stability analysis and cost function convergence validation for the modified learning algorithm with new learning filters and update law, (3) an analytical discussion of the tradeoff benefits of the pareto optimization-based learning approach for a specific set of performance objectives resulting in a generalizable set of control design guidelines, and (4) experimental validation of the new control approach on a robotic test platform. The experimental testing demonstrated the tradeoff benefits of the pareto learning approach with a 26% reduction in energy usage over point-to-point ILC methods, while maintaining over 90% reduction in the tracking errors over nominal feedback without learning. As illustrated by the experimental example, the flexibility in the proposed framework enables the user to personalize the control design to specific cases, a necessary requirement for generalizing the framework across various applications. While these performance tradeoffs are demonstrated with a simple robotic platform, they indicate the potential for this framework to achieve substantial cost, time, or energy usage savings by leveraging the additional control freedom available in point-based learning problems.