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Aframework is presented in which temporally periodic, linear, distributed parameter systems can be converted to a time-invariant system. This conversion is key for the control of the secondary instabilities in three-dimensional channel flow induced by an upstream traveling wave of zero-net mass flux of wall transpiration. Linearized dynamical equations derived from Floquet analysis have shown that the instabilities are a direct result of the primary disturbance of the traveling wave but do not provide an analytical framework upon which to design a feedback controller. The necessary observation, although simple but subtle, is that the dynamics of the steady-state flow induced by a traveling wave must be linearized and decomposed in a frame of reference moving with the traveling wave. The resulting linear time-invariant equations are appropriate for system theoretic feedback control synthesis, i.e., H2 andH∞ methods. Although the linearization method produces a time-invariant linear system in the moving frame, the controller is periodic from a fixed reference frame. This approach for constructing a time-invariant system with periodic inputs is applicable to any system in which the dynamics are described as a combination of a static base and a periodic primary disturbance.

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors' estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e.; the spectrum, of the Laplacian for a family of graphs with self-loops. © 2014 Elsevier Ltd. All rights reserved.

This report concerns vehicle fault detection and identification. The design of a vehicle health monitoring system based on analytical redundancy approach is described. A residual generator and a residual processor are designed to detect and identify actuator and sensor faults of the PATH Buick LeSabre. The residual generator, which includes fault detection filters and parity equations, uses the control commands and sensor measurements to generate the residuals which have a unique static pattern in response to each fault. Then, the residual processor interrogates the residuals by matching the residuals to one of several known patterns and computes the probability of each pattern defined hypothesis.

This report is continuation of the work of (Douglas et al., 1996) and (Douglas et al., 1997) which concerns vehicle fault detection and identification.  A vehicle health monitoring approach based on analytical redundancy is described. Fault detection filters and parity equations use the control commands and sensor measurements to generate the residuals which have a unique static pattern in response to each fault. This allows the faults not only to be detected, but also identified. Sensor noise, process disturbances, system parameter variations, unmodeled dynamics and nonlinearities can distort these static patterns.   A Shiryayev sequential probability ratio test that has been extended to multiple hypotheses examines the fault detection filter and parity equation residuals and generates the probability of the presence of a fault.  A point design of fault detection filters and parity equations is developed for the longitudinal dynamics of the PATH Buick LeSabre. Fault detection filters are evaluated using empirical data obtained from U.C. Berkeley. The preliminary evaluation is promising in that the fault detection filters can detect and identify actuator and sensor faults as expected even under various disturbances and uncertainties.

This report concerns vehicle fault detection and identification. A vehicle health monitoring approach based on analytical redundancy is described. To detect and identify actuator and sensor faults, fault detection filters and parity equations are developed for the longitudinal dynamics of the PATH Buick LeSabre. Fault detection filters and parity equations use the control commands and sensor measurements to generate the residuals which have a unique static pattern in response to each fault. This allows the faults not only to be detected, but also identified. Fault detection filters and parity equations are .rst evaluated using simulated data generated by a high-fidelity vehicle simulation. Then, fault detection filters and parity equations are evaluated using empirical data recorded when driving a PATH Buick LeSabre at Crow's Landing. Finally, a real-time testing environment is developed using Linux operating system and C language. This allows the fault detection filters and parity equations to be evaluated in real-time on a PATH Buick LeSabre. The real-time evaluation at Crow's Landing demonstrates that the fault detection .lters can detect and identify actuator and sensor faults as expected even under various disturbances and uncertainties including sensor noise, road noise, system parameter variations, unmodeled dynamics and nonlinearities.

This report continues work on the design of a health monitoring system for automated vehicles. The approach is designed to fuse data from dissimilar instruments using modeled dynamic relationships and fault detection and identification filters. Issues relating to sensor models, output separability, steady-state fault persistence and the spectral content of sensor faults are considered.

This work focuses on vehicle fault detection and identification. It also describes a vehicle health management approach based on analytic redundancy. It describes a point design of fault detection filters and parity equations that are developed for the vehicle longitudinal mode. A preliminary design of a range sensor fault monitoring system is outlined as an application of a new decentralized fault detection filter. This system combines dynamic state information already generated by the existing filter designs with inter-vehicle analytic redundancy

In this report, a preliminary design of a health monitoring system for automated vehicles is developed and results of tests in a high-fidelity nonlinear simulation are reported. Two car models are described: low- dimensional linear models for fault detection filter design and high fidelity nonlinear model is used for evaluation and to obtain the linear models used for design. The faults and the fault detection filters and system are then described. An evaluation of the performance of the fault detection filters in a nonlinear simulation are presented. A fault detection filter residual processing system, using a neural network, is then described.

The Global Positioning System has great potential for the development of new collision avoidance systems and is being considered for the next-generation traffic alert and collision avoidance system. The navigation states estimated by Global Positioning System code information can be broadcast to nearby airplanes via the current traffic alert and collision avoidance system equipment. In this paper, the problem of aircraft collision detection system using Global Positioning System carrier-phase information is addressed. A new approach to the carrier-phase-based relative position estimation problem is proposed that uses particle filters in which the samples are drawn from Cartesian position space coordinates. The particle filters with position samples makes the Global Positioning System carrier-phase-based position estimation algorithm robust and practical in that the algorithm is not sensitive to changes of Global Positioning System satellites and cycle slips. The same algorithm can be used to estimate the vehicle attitude if multiple Global Positioning System antennas are used. For a reliable and enhanced collision avoidance system, three-dimensional trajectories are projected using relative position, velocity, and attitude estimates. It is shown that the performance of the Global Positioning System carrier-phase-based collision-detecting algorithm meets the accuracy requirements for a precise approach of flight with significantly less collision false alarms and no miss alarms. DOI: 10.2514/1.43517

Lever-arm uncertainty can be an important error source in the integration of the Global Positioning System (GPS) and inertial navigation system (INS). This paper presents both numerical and experimental studies on the estimation of the lever arm in the integration of a very-low-grade inertial measurement unit (IMU) with an accurate single-antenna GPS measurement system. Covariance simulation results showed that maneuvers play an important role on the estimation of the lever arm and attitude. The length of the lever arm has a rather insignificant effect on the estimation of these. Experimental tests conducted with a low-cost microelectromechanical system (MEMS) IMU and a carrier-phase differential GPS (CDGPS) measurement system showed that the lever arm can be estimated with centimeter-level accuracy. The test results confirmed that angular motions and horizontal accelerations improve the estimates of the lever arm and yaw angle, respectively. Index Terms--Global positioning system (GPS), inertial measurement unit (IMU), inertial navigation, inertial navigation system (INS), lever arm, observability.

Observability properties of errors in an integrated navigation system are studied with a control-theoretic approach in this paper. A navigation system with a low-grade inertial measurement unit and an accurate single-antenna Global Positioning System (GPS) measurement system is considered for observability analysis. Uncertainties in attitude, gyro bias, and GPS antenna lever arm were shown to determine unobservable errors in the position, velocity, and accelerometer bias. It was proved that all the errors can be made observable by maneuvering. Acceleration changes improve the estimates of attitude and gyro bias. Changes in angular velocity enhance the lever arm estimate. However, both the motions of translation and constant angular velocity have no influence on the estimation of the lever arm. A covariance simulation with an extended Kalman filter was performed to confirm the observability analysis. Index Terms--Global Positioning System, GPS/INS, inertial measurement unit (IMU), inertial navigation, lever arm, observability.

An observability analysis of a GPS/INS system during maneuvers is presented based upon a perturbation model with respect to the Earth-centered-Earth-fixed (ECEF) coordinate system. Analysis is performed on two types of maneurvers, linear acceleration and steady turn. These maneuvers could be used for in-flight INS alignment using GPS. During the constant linear acceleration without rotation relative to the Earth, the linear system model is shown to be time-invariant. The observability analysis for the time invariant linear system model shows that linear acceleration does not change the number of observable modes but rather the structure of the observable space. For a nonconstant linear acceleration or a steady turn, the perturbation linear system becomes time varying. For this time-varying system, three types of observability are considered, complete, differential, and instantaneous observability. Instantaneous observabifity is the strangest properties and means that the state of the system at any time may be determined instantaneously from observation of the output and its derivatives. Instantaneous observability is important for fast in-flight INS alignment. It is shown that the number of instataneously observable modes is increased by at least 2 during a maneuver. Hence, some linear combinations of the attitude angles become instantaneously observable.

In this paper, we address the modeling and analysis issues associated with a generic theater level campaign where two adversaries pit their military resources against each other over a sequence of multiple engagements. In particular, we consider the scenario of an air raid campaign where one adversary uses suppression of enemy air defense (SEAD) aircraft and bombers (BMBs) against the other adversary's invading ground troops (GTs) that are defended by their mobile air defense (AD) units. The original problem is decomposed into a temporal and a spatial resource allocation problem. The temporal resource allocation problem is formulated and solved in a game-theoretical framework as a multiple resource interaction problem with linear attrition functions. The spatial resource allocation problem is posed as a risk minimization problem in which the optimal corridor of ingress and optimal movement of the GTs and AD units are decided by the adversaries. These two solutions are integrated using an aggregation/deaggregation approach to evaluate resource strengths and distribute losses. Several simulation experiments were carried out to demonstrate the main ideas. Index Terms--Air campaign modeling, applied game theory, military campaigns, resource allocation, resource interaction models.

The fault detection process is approximated with a disturbance attenuation problem. The solution to this problem, for both linear time-varying and time-invariant systems, leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected. In the limit, when the disturbance attenuation bound is brought to zero, a complete transmission block is achieved by embedding the nuisance inputs into an unobservable, invariant subspace. Since this is the same invariant subspace structure seen in some types of detection filters, we can claim that the asymptotic game filter is itself a detection filter. One can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space. The resulting lower dimensional filter will then be sensitive only to the failure to be detected. A pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time-invariant and time-varying problems in both full-order and reduced-order forms. Index Terms - Analytic redundancy, detection filters, differential games, disturbance attenuation, singular optimal control, unknown input observer.

In this paper, a feedback controller called a periodic regulator is developed for implementing an optimal periodic process to a physical system under state deviations and constant parameter variation. The objective of the periodic regulator is to bring the perturbed plant back to a neighboring optimal periodic path in such a manner that the infinite-time second-variation of the cost is minimized. Since the periodic path is optimal with respect to a time-averaged cost, it possesses unique properties which set it apart from the general class of periodic regulators. Specifically, the transition matrix associated with the variational problem evaluated over one period is symplectic and generically possesses two unity eigenvalues coupled in the same Jordan box; the primary eigenvector associated with the unity eigenvalue corresponds to the orbital velocity direction. It is shown that there exists a locally stable subspace in the neighborhood of the periodic orbit. Moreover, a simple condition is given for defining the state variation which guarantees that it is contained in this stable subspace. This state variation is defined in terms of an index point on the nominal periodic path such that the projection of the state variation onto the orbital velocity vector is zero. The periodic regulator is extended to include a known constant perturbation of a system parameter away from its reference value; a controller including feedback of the parameter variation is derived which provides first-order convergence to a new optimal periodic trajectory. Finally, the periodic regulator developed is applied to a simple two-state periodic optimal control problem to demonstrate its convergence properties.

This paper discusses the control of linear systems with uncertain parameters in the control coefficient matrix, under the influence of both process and measurement noise. A disturbance attenuation approach is used, and from this a multiplayer game problem is generated. First, the minimax formulation is presented, which represents an upper bound on the game cost criterion. Second, a dynamic programming approach is used to solve the game. It is necessary to significantly extend the method over earlier implementations, as the class of problems does not satisfy certain assumptions generally made. It is shown that for this class of problems, the controller determined from the dynamic programming approach is equivalent to the minimax controller. Therefore, the minimax controller is also a saddle-point strategy for the differential game. Controller development appears to be much simpler from the dynamic programming standpoint. A simple scalar example is presented.

A particular class of stochastic control problems constrained to different information patterns is considered. This class consists of minimizing the expectation of an exponential cost criterion with quadratic argument subject to a discrete-time Gauss-Markov dynamic system, i.e., the linear-exponential-Gaussian (LEG) control problem. Besides the one-step delayed information pattern previously considered, the classical (includes current observations) and the one-step delayed information-sharing (OS-DIS) patterns are assumed. After determining the centralized controller based upon the classical information pattern, the optimal decentralized controller based upon the OSDIS pattern and the solution to a static team problem is found to be affine. A unifying approach to determine controllers based upon these three information patterns is obtained by noting that the value of a quadratic exponent of an exponential function is independent of the information structure. Even though the controllers are determined by a backward recursion of this exponent, the value of the cost criterion is not; rather a coefficient of the exponential delineates the value of the cost criterion with respect to the information patterns. Both necessary and sufficient conditions for the controllers to be minimizing are obtained regardless of the exponential form. The negative exponential form is included which is unimodal but not convex.

A large deviation result is employed to solve the state estimation problem of a continuous time Gauss-Markov system with an exponential cost. The exponential cost is the expected value of an exponential function of the state estimation-error. A scalar [Theta] appearing in the cost, termed as the risk factor, determines the penalty on the higher order moments of the error. In contrast to the minimum variance estimate, penalty on large deviations of the estimation error is possible.