DEVELOPMENT OF ALGORITHMS FOR ROBUST ONLINE OPTIMAL PERIODIC CONTROL IN THE PRESENCE OF PLANT PARAMETER UNCERTAINTY

Open Access
Author:
Ghanaatpishe, Mohammad
Graduate Program:
Mechanical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 18, 2017
Committee Members:
  • Hosam Kadry Fathy, Dissertation Advisor
  • Karen Ann Thole, Committee Chair
  • Christopher Rahn, Committee Member
  • Bo Cheng, Committee Member
  • Constantino Manuel Lagoa, Outside Member
Keywords:
  • Adaptive Control
  • Drug Delivery
  • Insect Flight
  • Optimal Periodic Control
  • Optimization
  • Estimation
  • Tracking
Abstract:
This dissertation furnishes a framework addressing the challenges of designing online algorithms for optimal periodic control (OPC). The proposed framework aims to expand the use of the OPC discipline, moving beyond the traditional offline optimization of periodic control trajectories for plants with known dynamics, and instead focusing on the online and stable periodic optimal control of plants whose dynamics are not fully known a priori. More specifically, the design objective of this online framework is to discover, achieve, and maintain the best cyclic performance level of a given engineering system, despite the potential open-loop instabilities of the underlying dynamics and unknown plant model parameters. This dissertation is motivated by the exciting applications of the OPC theory in nature and engineering. This research area has been studied for nearly 6 decades. The literature has developed mathematical tests for properness: a condition under which there is a periodic trajectory that in average outperforms the best equilibrium point of a given dynamic system. Necessary and sufficient conditions have also been developed to analyze the optimality of a candidate periodic trajectory. Furthermore, researchers have proposed direct and indirect algorithms for the numerical computation of the OPC problem solutions. However, a common limitation of the existing OPC research lies in the fact that traditional OPC has been applied to the offline optimization of trajectories for systems with known dynamics. This stands in contrast both to the goal of this dissertation and to several examples of OPC practices that are observed in nature. This dissertation seeks to address the above limitations by proposing an adaptive framework that enables engineering systems to achieve robust online periodic optimal control. The steps leading to the development of the online framework are illustrated/validated on an insect flight model, a benchmark drug delivery application problem from the OPC literature, and a vehicle suspension example. The first two of these application problems are known to benefit from OPC, while the oscillatory behavior is enforced on the last application through a periodic road roughness profile. The work of this dissertation builds on established techniques in control theory including variational calculus methods, direct optimal control, indirect adaptive control, Floquet stability, Lyapunov stability, and feedback linearization. However, it combines these tools in a manner that will result in a novel framework for achieving robust online periodic optimality. The development of algorithms in this dissertation follows a progressive trend towards the end framework. This is also reflected through the organization of the dissertation as explained below. Chapter 2 introduces a properness test from the OPC literature to determine whether periodic operations can offer any advantage over the best steady-state performance. The application of this tool is demonstrated on a flapping flight model of the fruit fly. Chapter 3 incorporates variational calculus methods to discover the structure of the solution trajectory of the periodic drug delivery application, once OPC properness is established. Also, a discretization approach based on the discovered structure is shown to reduce the computational requirements of solving the OPC problem offline. Chapter 4 develops an adaptive controller to achieve online OPC for the drug delivery application in the presence of unknown plant parameters. This controller is dependent on the innate open-loop stability of the drug absorption dynamics and the local convergence of the closed loop scheme is shown using Floquet analysis. Chapter 5 designs a novel adaptive tracking algorithm grounded in principles of feedback linearization theory. A Lyapunov stability analysis establishes global convergence to a target trajectory dependent on unknown plant parameters. A numerical active vehicle suspension example is employed to showcase the performance of the algorithm. Chapter 6 finally presents the online OPC framework of this dissertation with the adaptive tracking controller of Chapter 5 incorporated at its heart. The performance of the closed-loop scheme is demonstrated on the benchmark drug delivery application. The proposed online OPC framework (i) provides an online estimate of the uncertain plant parameters, (ii) efficiently solves for and employs a family of precalculated optimal periodic solutions indexed by the plant parameter estimates, and (iii) offers an input adaptation mechanism which enables asymptotic and stable tracking of a dynamically-changing target trajectory constructed from this family of optimal solutions. These tasks collectively are shown to enable stable and global convergence of the closed loop system towards its optimal periodic path.