DARPA, managed by the U.S. Air Force Research Laboratory:
An Integrated, Multi-Layer Approach to Software-Enabled Control:
Mission Planning to Vehicle Control

Principal Investigator: Professor Gary Balas

Accomplishments: 2002
 

• Continued support, development and extension of a high fidelity, fixed-wing UAV model based on the F-16 aircraft described in NASA Technical Paper 1538. This nonlinear F-16 aircraft serves as the  OCP baseline fixed-wing UAV model and is distributed with all  releases of the OCP.

• Real-time implementation of nonlinear receding horizon control (RHC) for the longitudinal axis of the F-16 UAV. This represents a factor of 400 speed improvement relative to previous year simulation  results. Selection of horizon length, control basis function, optimization accuracy and initial stabilizing controller, to improve  optimization numerics, resulted in two orders of magnitude reduction in RHC computation time.

• Real-time implementation flight management approach under QNX on a Pentium II 266 MHz processor. The flight management framework employs an outer-loop RHC trajectory generation algorithm with a robust  multivariable inner-loop controller for the longitudinal and  lateral-directional axes of the F-16 UAV nonlinear simulation. Simulations show accurate tracking of moderately aggressive maneuvers in the presences of actuator and flight envelope constraints. These results validate that the flight management approach can be implemented in real-time on the Boeing fixed-wing UAV final exam test platform.

• Development of anytime control algorithms for linear systems with guaranteed computation time. These algorithms allow controllers to taken advantage of dynamic scheduling where allotted CPU time can vary.  Anytime control algorithms incorporate trade offs between performance and CPU time. A smooth switching scheme is used which ensures smooth transitions of states and outputs as well guarantees stability.

• Submitted to the IEEE Press the volume entitled "Software Enabled Control: Information Technologies for Dynamical Systems" for publication. The manuscript is co-edited by Tariq Samad and Gary Balas. Publication of the volume is scheduled for March 2003.

Accomplishments:  2001

• Integration of the F-16 like model with inner-loop control and outer-loop guidance within  the OCP environment. The OCP simulation consisted of a F-16 model OCP C++  component, a LPV longitudinal and classical lateral-directional

 inner-loop controller and  an outer-loop guidance and way-point generator all hosted within Simulink. The F-16 like model response is interfaced with Aviator Visual Design Simulator (AVDS) for  real-time visualization of the aircraft. The simulation allowed the replacement of the outer guidance loop with a joystick to command pitch, roll, yaw and speed. This work was performed in close collaboration with Honeywell Technology Center (development of outer-loop guidance algorithms), Boeing (F-16 OCP component/AVDS interface development) and RasSimTech  (AVDS interface).
 
• Synthesized receding horizon controllers (RHC) based on the LPV CLF for the quasi-LPV model of F-16 like aircraft. The RHC designs out performed the quasi-LPV controller on the exact nonlinear aircraft simulation. RHC/LPV on-line control customization algorithms have the potential to increase autonomy and system life of UAVs.

• Developed numerically efficient algorithms to solve fully nonlinear F-16 RHC problem using NPSOL. A compromise between accuracy of solution and computational expense was investigated to address real-time computational constraints and issues. Accurate and efficient optimization code is key to the successful, real-time implementation of RHC algorithms.

• On-line, linear system-theoretic algorithms have been developed to handle variable length preview information.  The length and accuracy of preview information provided by the mission planner allows on-line adaptation of the inner-loop controller. These algorithms make optimal use of sensor and command preview information leading to increased responsiveness  of the UAV vehicle.

• Theoretical results on the stability and performance enhancement of receding horizon control with a disturbance rejection objective, under the hypotheses: an existing controller is available and the disturbance, over the upcoming

 horizon length, is known. Our goal is to use the existing controller, a preview of disturbances and commands and on-line
 optimization to improve the disturbance rejection and tracking accuracy properties of the design. These results
 are directly applicable to UAV trajectory tracking tasks, where the desired trajectory is known a short time in advance.
 
• Formulation of an LMI search method for non-quadratic sum-of-squares polynomial Lyapunov functions that simultaneously stabilizes a switched linear system.  For the given class of switched linear system,  it is shown that one needs to only search over homogeneous forms for  stabilizing solutions.  A possible application is to prove stability of

  a system where an on-line supervisor can abruptly switch between controllers while the plant is running.
 
• Linear matrix inequalities (LMIs) are used extensively in the synthesis and analysis of controllers for the SEC program. To efficiently solve these equations, semi-definite programming software (SDP) solvers, e.g. the LMI Matlab Toolbox (LMILab), are used. Development of fast, efficient and accurate SDP solvers is an active research area in the applied math, optimization and the operations research community. Many freely available, public domain SDP solvers exist and most take advantage of sparsity in the LMI constraints, offering perhaps significant decreases in computation time required to solve SEC control problems.  Each offer different algorithms to solve the LMI optimization. A Matlab based translation code has been developed to translate LMI problems formulated in LMILab to other freely available SDP solvers. This allows LMI problems formulated within LMILab to be solve the optimization problem with six freely available SDP solvers.

 
• Gary Balas (Univ. of Minnesota) and Tariq Samad (Honeywell Laboratories) are editing a contributed volume titled "Software-Enabled Control: Information Technology for Dynamical Systems." IEEE Press has agreed to publish this volume. The editors have received summaries of proposed contributions from a number of SEC researchers, and the current table of contents includes twenty chapters. Chapter drafts are due by the end of August 2001.