It is shown how globally stable model reference adaptive control systems may be designed when one has access to only the plant's input and output signals Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Lyapunov's direct method and the Meyer-Kalman-Yacubovich lemma Derivatives of the plant output are not required, but are replaced by filtered derivative signals An augmented error signal replaces the error normally used, which is defined as the difference between the model and plant outputs However, global stability is assured in the sense that the normally used error signal approaches zero asymptotically

Model reference adaptive control with an augmented error signal

A survey of model reference adaptive techniques-Theory and applications

Normalized cross-correlation has been used extensively for many signal processing applications, but the traditional normalized correlation operation does not meet speed requirements for time-critical applications. In this paper, a new fast algorithm for the computation of the normalized cross-correlation (NCC) without using multiplications is presented. For a search window of size M and a template of size N the fast NCC requires only approximately 2N?(M?N+1) additions/subtractions without multiplications. Simulation results with 100,000 test signals show that the use of the fast NCC instead of the traditional approaches for the determination of the degree of similarity between a test signal and a reference signal (template) brings about a significant improvement in terms of false negative rate, identification rate and computational cost without a significant increase in false positive rate, especially when the signal-to-noise ratio (SNR) is higher than 3 dB.

Fast Normalized Cross-Correlation

Introduction P pointing control and rapid maneuvering capabilities have long been part of many space missions; examples include military observation platforms, communications satellites, and exploratory space missions. Rapid retargeting may be an intrinsic part of the mission profile, as in military and exploratory applications, or it may be required to correct, periodically, the guidance and navigation sensors of a spacecraft. Consequently, research in attitude maneuvers and time-optimal controls has been a consistently strong field of study. Of particular interest is the time-optimal attitude maneuver; this problem combines aspects of many different fields, such as mathematics, optimal control theory, spacecraft dynamics, elasticity, and structural mechanics. In the study of attitude maneuvers and control, researchers have investigated the response of satellite control systems to disturbances caused by the influence of solar pressure, gravity gradients, the effectiveness of active control devices, and the best placement of actuators and sensors on a given structure. Numerous studies have been conducted for specific satellite configurations to determine a time-optimal attitude control for a predetermined maneuver. Further, the mathematical procedures required to investigate this problem have inspired a number of papers on techniques to address the difficulties which arise from time-optimal control. This survey reviews the literature of the last thirty years, including many of the more recent advances in the field, covers the aforementioned topics as well as specific attitude maneuvers, and traces the development of time-optimal and near time-optimal control algorithms. We begin by considering the formulation of the time-optimal control problem and the difficulties faced in obtaining the solution. The equations for the rotational motion of any rigid body (Ruler's equations) are quite elegant and compact; they are also coupled and highly nonlinear. In addition, the high angular velocities of time-optimal maneuvers will cause gyroscopic stiffness through the nonlinear terms. Ruler's equations are expressed as

Survey of time-optimal attitude maneuvers

Disclosed is a pattern matching method and apparatus, in which an object pattern is collated with a master pattern using pattern matching. As a first step, an area corresponding to a master pattern size is sequentially extracted from a master sample image for forming the master pattern, each extracted pattern is collated and the other patterns in the master sample image. An extracted pattern which has a minimum similarity to all the other patterns, and, as a result, shows the most distinctive pattern, is used for the master pattern. Using the present method and apparatus, pattern matching having a higher recognition rate can be performed. Further, using the present pattern matching method, an apparatus can be obtained for positioning the object to be recognized with a highest positioning accuracy.

Pattern matching method and apparatus

This paper considers the model-reference adaptive control problem which has received considerable attention in the literature in the last few years. An adaptive control scheme is proposed which has terms in the Liapunov function used in the design procedure which are not included in previously proposed schemes. The relationship of this new scheme to existing schemes is shown by considering the root-loci of the linearized error equations between plant and model. Finally, a second order example is given which illustrates the difference between the two previously proposed model-reference adaptive methods and the one proposed in this paper.

Model-Reference Adaptive Control System Design Technique

The problem of locating a reference image within a larger image using a correlation technique is discussed. Although the particular application discussed is that of locating a reference image obtained from one video sensor or a photograph, within the larger field of view obtained from a second video sensor in real time (i.e., at the TV field rate), the results are general and useful for a number of applications. The tradeoffs necessary to obtain real time correlat are discussed and their effect on correlation accuracy is given.

Design of a Correlator for Real-Time Video Comparisons

: The problem of automatic hand-off of a target from a precision pointing and tracking system (PTS) to an imaging missile seeker is considered in this report. The approach taken is to search for the target in the seeker field of view (FOV) using the PTS video as a reference. When the target is located, the seeker line of sight is adjusted automatically such that the target is at the center of its FOV at which point the seeker tracker can lock on to the target. Location of the target in the seeker FOV can best be accomplished using correlation techniques. The approach taken is to consider the most accurate but yet most costly in computation time and hardware requirements. Tradeoffs are then considered in order to obtain a real-time correlator (i.e., one which can compute the correlation surface at the rate of the incoming live video from the seeker). The effect of these trade-offs on correlation accuracy and other system performance criteria is given. A correlation algorithm is chosen and an implementation of this algorithm is given. An alternate implementation using an analog adder rather than a digital adder tree is recommended.

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Automatic Target Hand-Off Using Correlation Techniques

A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.

Extended Lyapunov stability criterion using a nonlinear algebraic relation with application to adaptive control

An empirically obtained reaction control jet relay control law with deadband is used as the basis for determining an equivalent weighted time-fuel optimal switching curve according to a least-squares criterion. The derived transformation from the empirical to the optimal law is found to be reversible and to yield a unique transformed control law. The proposed method provides a basis for determining the behavior of an easily implemented relay control law using well-known optimal control results, as well as determining the equivalent relay law corresponding to an analytically determined optimal control law. A numerical example illustrates the transformation technique and simulation results are presented to compare the two control laws.

J. S. Boland

Papers

Model-Reference Adaptive Control System Design Technique

Design of a Correlator for Real-Time Video Comparisons

Automatic Target Hand-Off Using Correlation Techniques

Extended Lyapunov stability criterion using a nonlinear algebraic relation with application to adaptive control

Design analogy between optimal time-fuel and rate-ledge relay controllers