Pareto iterative learning control: Optimized control for multiple performance objectives $ Ingyu Lim, Kira L. Barton n Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA article info Article history: Received 30 April 2013 Accepted 10 January 2014 Available online 11 February 2014 Keywords: Learning control Pareto optimization Multi-objective control abstract 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. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction 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, Tharayil, & Alleyne, 2006; Moore, Dahley, & Bhattacharyya, 1992). ILC has been success- fully applied to repetitive applications in robotics (Arimoto, Kawamura, & Miyazaki, 1984; Tayebi & Islam, 2006), manufacturing (Barton & Alleyne, 2011; Kim & Kim, 1993; Rotariu, Steinbuch, & Ellenbroek, 2008), and chemical processing (Lee & Lee, 2007; 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 ðn i Þ Dy d ðkÞ, where n i are the selected points for all i ¼ 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 ðn i Þ. By removing the unnecessary con- straint 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 under- utilized 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, vibra- tion isolation); and unmanned air/ground vehicles (metrics: path following, patrol efficiency, energy consumption, sensor transmis- sion 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 perfor- mance and robustness (Boulet & Duan, 2007; Jin & 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 repeti- tive tasks. This initial work presented the basic framework, but did not provide a tradeoff analysis or experimental validation (Lim & Barton, 2013). Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice 0967-0661/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conengprac.2014.01.011 ☆ This work was supported by start-up funds from the University of Michigan. n Corresponding author. E-mail addresses: ingyulim@umich.edu (I. Lim), bartonkl@umich.edu (K.L. Barton). Control Engineering Practice 26 (2014) 125–135