O.R. Gonzalez

Stability analysis of digital linear flight controllers subject to electromagnetic disturbances

High intensity electromagnetic radiation has been demonstrated to be a source of computer upsets in commercially available digital flight control systems. Such upsets can degrade the quality of the control signal ranging from a perturbation error over a few sample periods to a permanent error mode or computer failure. Under these conditions, the primary concern of the control engineer is to insure that the closed-loop system remains stable. A stochastic disturbance model and a set of associated stability assessment tools are introduced for determining stability robustness of a nominal closed-loop system subject to electromagnetic disturbances. The focus is primarily on night control applications, but the methodology is suitable for any application where highly reliable digital control is needed. The technique is demonstrated on a simple test example and on a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft.

Modeling electromagnetic disturbances in closed-loop computer controlled flight systems

High intensity electromagnetic radiation has been demonstrated to be a source of computer upsets in commercially available digital flight control systems. In this paper we introduce an electromagnetic disturbance model which can be used for stability analysis and augmentation of any such digitally implemented control law. The model is composed of a Markovian exosystem supplying radiation events to a discrete-time jump linear system which models how the radiation interferes with the nominal operation of the closed-loop system. We discuss how this model can be used to characterize stability and how it can be parametrized and validated in an experimental setting.

Performance Analysis of Digital Flight Control Systems With Rollback Error Recovery Subject to Simulated Neutron-Induced Upsets

This paper introduces a class of stochastic hybrid models for the analysis of closed-loop control systems implemented with NASAs Recoverable Computer System (RCS). Such systems have been proposed to ensure reliable control performance in harsh environments. The stochastic hybrid model consists of a stochastic finite-state automaton driven by a Markov input process, which in turn drives a switched linear discrete-time dynamical system. Stability and output tracking performance are analyzed using an extension of the existing theory for Markov jump-linear systems. The theory is then applied to predict the tracking error performance of a Boeing 737 at cruising altitude and in closed-loop with an RCS subject to neutron-induced single-event upsets. The results are validated using experimental data obtained from a simulated neutron environment in NASAs SAFETI Laboratory.

On Fliess operators driven by L 2 -Itô random processes

Fliess operators with deterministic inputs have been studied since the late 1970s and are well understood. When the inputs are stochastic processes the theory is less developed. There have been several interesting approaches for Wiener process inputs. But the interconnection of systems is not well-posed in this context, and this limits their use in applications. This paper has two specific goals. The first goal is to describe the theoretical framework under which a Fliess operator can be driven by a class of L2-Ito random processes. The second goal is to derive a sufficient condition for the stochastic convergence of the series which defines the corresponding output process.

Digital linear state feedback control subject to electromagnetic disturbances

High intensity electromagnetic radiation has been demonstrated to be a source of computer upsets in commercially available digital flight control systems. In this paper we present an analysis of one consequence of an electromagnetic disturbance: the flipping of bits in a computer word. Specifically, we analyze the closed-loop stability of a digital linear state feedback control law when the electromagnetic radiation causes the gain vector to be corrupted by bit errors in its floating-point representation. As an example, we analyze a stabilizing controller for the longitudinal dynamics of the AFTI/F-16 aircraft.

Internal models in regulation, stabilization, and tracking

Abstract The internal model concept is fundamental in control problems. In linear control systems, internal models have been described in terms of poles in the unstable (bad) region of the complex plane which contain the needed information for the control system to attain the desired objective. It has been erroneously believed for some time that such internal models did not exist in the non-robust regulation problem when a two-input, two-output plant was considered. It is shown here that such internal models always exist not only in regulation, but also in stabilization and tracking if the appropriate physically meaningful maps are considered, thus completely resolving the existing discrepancy between abstract results and intuition on one hand, and linear regulation literature results on the other. Both robust and non-robust control problems are considered and a complete treatment of internal models in all the basic problems is presented.

Stability Analysis of Stochastic Hybrid Jump Linear Systems Using a Markov Kernel Approach

In this paper, the state dynamics of a supervisor implemented with a digital sequential system are represented with a finite state machine (FSM). The supervisor monitors a symbol sequence derived from a linear closed-loop systems performance and generates a switching signal for the closed-loop system. The effect of random events on the performance of the closed-loop system is analyzed by adding an exogenous Markov process input to the FSM, and by appropriately augmenting a switched system representation of the supervisor and the closed-loop system. For this class of hybrid jump linear systems, the switching signal is, in general, a non-Markovian process, making it hard to analyze its stability properties. This is ameliorated by introducing a sufficient mean square stability test that uses only upper bounds on the one-step transition probabilities of the switching signal. These bounds are explicitly derived from a Markov kernel associated with the hybrid system model. This stability test becomes necessary and sufficient when the switching signal is Markovian. To determine tighter stability bounds, procedures to determine the upper-bound transition probability matrices when the FSM has a Moore or a Mealy type output map are presented. Two examples illustrate the applicability of the presented results.

Tracking performance analysis of a distributed recoverable Boeing 747 flight control system subject to digital upsets

A performance model is introduced for estimating the tracking error of a Boeing 747 closed-loop digital flight control system implemented on a distributed recoverable computing platform, inspired by NASAs ROBUS-2 communication system, when it is subjected to digital upsets. A methodology is then developed for computing a mean-square error tracking performance metric as a function of the number of processing elements used, the number of redundancy management units employed, and the level of upsets the system experiences.

Tracking Performance of Distributed Recoverable Flight Control Systems Subject to High Intensity Radiated Fields

Theoretical tools are presented to analyze the relationship between the design choices for a class of NASA-inspired fault-tolerant, reconfigurable computer architectures and the tracking performance degradation of a digital flight control system implemented on such a platform while operating in a high-intensity radiated field (HIRF) environment. A HIRF experiment was conducted at the NASA Langley Research Center to validate the theory for a distributed Boeing 747 flight control system subject to HIRF upsets.

On nonlinear discrete-time systems driven by Markov chains

Abstract The behavior of a class of hybrid systems in discrete-time can be represented by nonlinear difference equations with a Markov input. The analysis of such a system usually starts by establishing the Markov property of the joint process formed by combining the systems state and input. There are, however, no complete proofs of this property. This paper aims to address this problem by presenting a complete and explicit proof that uses only fundamental measure-theoretical concepts.