Sonja Glavaski

Empirical Model Reduction of Controlled Nonlinear Systems

In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems results in the usual balanced truncation. For nonlinear systems, the method makes used of the Karhunen-Lo`eve decomposition of the state-space, and is an extension of the method of empirical eigenfunctions used in fluid dynamics. We show that the new method is equivalent to balanced-truncation in the linear case, and perform an example reduction for a nonlinear mechanical system.

Vehicle networks: achieving regular formation

In this paper, we consider a network of vehicles exchanging information among themselves with the intension of achieving a specified polygonal formation. A stochastic model for information transmission and reception is considered, allowing for the random breaking of the communication links among the vehicles. The network achieves the formation through decentralized feedback control, which is constructed from the available information. Several information flow laws are considered in order to improve the performance of the vehicle network.

Piloted Simulation of Fault, Detection, Isolation, and Reconfiguration Algorithms for a Civil Transport Aircraft

Honeywell Labs has been researching and developing together with NASA Langley Research Center (LaRC) algorithms for aircraft failure management and recovery. The algorithms have been integrated into a Control Upset Prevention and Recovery System (CUPRSys) that provides control law reconflguration, fault detection, fault isolation and pilot cueing. This paper describes the capabilities of CUPRSys and the results from an evaluation of CUPRSys by an experimental test pilot in the Integration Flight Deck (IFD) at LaRC. Also included in the paper are details about the IFD and the MATLAB simulation environment used for design. The piloted evaluation was performed at three ∞ight conditions and the results for one representative maneuver are presented. Pilot ratings were obtained for maneuvers for the un-failed aircraft, for the failed aircraft without reconflguration and for the failed aircraft with reconflguration. Only reduction of surface efiectiveness faults were considered. The piloted simulation results suggest that CUPRSys provides a robust control law with promising fault detection, isolation and reconflguration capability.

A Nonlinear Hybrid Life Support System: Dynamic Modeling, Control Design, and Safety Verification

We present control design for a variable configuration CO2 removal (VCCR) system, which exhibits a hybrid dynamical character due to the various modes in which one needs to operate the system. The VCCR is part of an overall NASA Air Recovery System of an intended human life support system for space exploration. The objective of the control system is to maintain CO2 and O concentrations in the crew cabin within safe bounds. We present a novel adaptation of the model predictive control technique to a nonlinear hybrid dynamic system. We exploit the problem structure and map the hybrid optimization problem into a continuous nonlinear program (NLP) with the aid of an appropriate representation of time and set definitions. We present a systematic approach for designing the objective function for the nonlinear model predictive control (NMPC) regulation problem that achieves a long-term, cyclic steady state. We also present a simple switching feedback controller and compare the performance of the two controllers during off-nominal and failure conditions to highlight the benefits of a systematically designed NMP controller. We then perform safety verification of both control designs-the model predictive control with techniques from statistical learning theory and the switching feedback controller with Barrier certificates computed using sum of squares programming. The two approaches yield consistent results.

Safety verification of controlled advanced life support system using barrier certificates

In this paper we demonstrate how to construct barrier certificates for safety verification of nonlinear hybrid systems using sum of squares methodologies, with particular emphasis on the computational challenges of the technique when applied to an Advanced Life Support System. The controlled system aims to ensure that the carbon dioxide and oxygen concentrations in a Variable Configuration CO2 Removal (VCCR) subsystem never reach unacceptable values. The model we use is in the form of a hybrid automaton consisting of six modes each with nonlinear continuous dynamics of state dimension 10. The sheer size of the system makes the task of safety verification difficult to tackle with any other methodology. This is the first application of the sum of squares techniques to the safety verification of an intrinsically hybrid system with such high dimensional continuous dynamics.

Analysis of aircraft pitch axis stability augmentation system using sum of squares optimization

In this paper, we use SOS (sum of squares) programming approaches to analyze the stability and robustness properties of the controlled pitch axis (6 state system) of a nonlinear model of an aircraft. The controller is a LTI dynamic inversion based control law designed for the short period dynamics of the aircraft. The closed loop system is tested for its robustness to uncertainty in the location of center of gravity along the body x-axis. Results in the form of stability regions about a trim point are computed and verified using simulations.

Connectivity and convergence of formations

In this work we consider the stability of vehicle formations in the case of a varying communication topology. We use a decentralized control law approach and explore the challenges and issues that arise in this framework. The vehicles considered are homogeneous, with discrete-time dynamics, and the communication between them is defined based on a predefined proximity rule. The resulting closed loop system is a switched dynamical system and in this paper we describe sufficient conditions that would lead to the stability of the vehicle formations.

Controlled hybrid system safety verification: advanced life support system testbed

In this paper we demonstrate the use of barrier certificates as a method to verify safe performance of a hybrid variable configuration CO/sub 2/ removal (VCCR) system. We designed a simple nonlinear feedback controller that tracks a desired CO/sub 2/ profile, while ensuring that the CO/sub 2/ and O/sub 2/ concentrations stay within acceptable limits. Though the controller and its switching rules are simple, we do not have a closed form expression for the equilibrium sets of the closed loop hybrid system, and hence Lyapunov stability analysis and computation of region of attraction are impossible. We used sum-of-squares programming approach to construct and verify that our control law provides safe functionality of VCCR system.

Control Design for a Hybrid Dynamic System: A NASA Life Support System

We consider the control problem of a Variable Configuration CO2 Removal system (VCCR), which exhibits a hybrid dynamical character due to the various configurations/modes in which one could operate the system. The VCCR is part of an overall Air Recovery System of an intended human life-support system for space exploration. The objective of the control problem is to track a desired concentration profile of CO2 in a crew cabin while also ensuring safety in terms of keeping the CO2 and O2 concentrations in the crew cabin within permissible bounds. We present a mathematical programming based control synthesis formulation, as well as a simulation-based hybrid feedback controller. We exploit the problem structure and map the hybrid optimization problem onto a continuous nonlinear program with the aid of an appropriate representation of time and set definitions. We also discuss case studies showing the performance of these controllers during off-nominal and failure conditions.

Failure accommodating aircraft control

Describes development and performance analysis of a failure accommodation system for the commuter and business aircraft control recovery. First, system failures are detected and isolated using a hierarchy of techniques that is chosen to ensure minimal disruption of operations and to minimize the number of false alarms. Successive layers in the diagnostics hierarchy are increasingly invasive. Once a failure has been detected and identified, the failure can be accommodated in several ways, from passive pilot cueing to active autopilot reconfiguration. An autopilot reconfiguration algorithm to accommodate failures wherever possible is developed. Some preliminary pilot cueing strategies and displays to alert pilots to true failures, provide guidance on recommended responses, and inform the pilot of any reconfigurations are also introduced.