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An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
The paper attempts to define a desirable and reachable goal for a second generation SST. Justifications for the need of an SST are considered as is the ecological impact of a second generation SST project. Required technology advances to reach the range of 6500 nautical miles are examined along with structural weight reduction and drag reduction. Possible performance improvements due to design modifications are discussed, and environmental problems are discussed in detail with emphasis on sonic booms.
A general result for the controllability of linear systems using positive controls was given by Saperstone and Yorke (1971). These results are applied to systems with nearly nonnegative matrices and a theorem is developed which delineates the geometry of the reachable set.
A new logic is developed which permits continuously variable strength of belief in the truth of assertions. Four inference rules result, with formal logic as a limiting case. Quantification of belief is defined. Propagation of belief to linked assertions results from dependency-based techniques of truth maintenance so that local consistency is achieved or contradiction discovered in problem solving. Rules for combining, confirming, or disconfirming beliefs are given, and several heuristics are suggested that apply to revising already formed beliefs in the light of new evidence. The strength of belief that results in such revisions based on conflicting evidence are a highly subjective phenomenon. Certain quantification rules appear to reflect an orderliness in the subjectivity. Several examples of reasoning by plausible inference are given, including a legal example and one from robot learning. Propagation of belief takes place in directions forbidden in formal logic and this results in conclusions becoming possible for a given set of assertions that are not reachable by formal logic.
The effects of solar radiation pressure as the main environmental disturbance torque were incorporated into the model of the rigid orbiting shallow shell and computer simulation results indicate that within the linear range the rigid modal amplitudes are excited in proportion to the area to mass ratio. The effect of higher order terms in the gravity-gradient torque expressions previously neglected was evaluated and found to be negligible for the size structures under consideration. A graph theory approach was employed for calculating the eigenvalues of a large flexible system by reducing the system (stiffness) matrix to lower ordered submatrices. The related reachability matrix and term rank concepts are used to verify controllability and can be more effective than the alternate numerical rank tests. Control laws were developed for the shape and orientation control of the orbiting flexible shallow shell and numerical results presented.
Graph theoretic techniques are used to study controllability of linear systems which represent large flexible orbiting space systems with inherent damping. The controllability of the pair of matrices representing the system state and control influence matrices is assured when all states in the model are reachable in a digraph sense from at least one input and also when the term rank of a Boolean matrix whose non trivial components are based on the state and control influence matrices has a term rank of the order of the state vector. The damping matrix does not influence the required number of actuators but gives flexibility to the possibility locations of the actuators for which the system is controllable.
The first problem treated here is the realization and stabilization of linear neutral systems with discrete delays. It is shown that any autonomous linear neutral system with discrete delays is zero-state equivalent to an abstract linear system over a local ring of operators. Using the abstract model, the basic existence question for neutral realization is then settled. For general infinite dimensional linear systems, there is no precise analog of the finite dimensional state space isomorphism theorem. Because of this, the notion of spectral minimality must be introduced. For the case of single input-single output systems, realizations are obtained that are both minimal and spectrally minimal. Using the Cruz-Hale theory of stable D-operators, conditions are given that ensure that any poles introduced into the realization are strictly contained in the left half plane and indeed are characterized as characteristic values of the D-operator. The problem of the feedback stabilization of neutral systems is then considered using the abstract model. It is shown that, for neutral systems with commensurable delays and a stable D-operator in the sense of Cruz and Hale, Morses theorem (1976) on pole assignment over a PID implies stabilizability in the reachable case.
Since 1981, NASA has been supporting an Orbit Transfer Vehicle (OTV) propulsion technology development program which encompasses the efforts of three major engine manufacturers. A thrust variability ratio of 30:1 has been stipulated for the baseline 520 lbf-sec/lbm engines, in order to yield the versatility needed for low acceleration missions, orbit-transfer missions, and aeromaneuvering tasks. These goals may not be reachable either individually or collectively; the program supports generic technology benefitting all three engine concepts, as well as concept-specific technology. Engine/vehicle integration will determine the final configuration. The three engines under study differ as to turbomachinery types and operating speeds.
Corroded fasteners taken apart more easily. Lubricating holes bored to thread from three of flats. Holes facilitate application of penetrating oil to help loosen nut when rusted onto bolt. Holes make it possible to apply lubricants and rust removers directly to more of thread than otherwise reachable.
Using Filipov's Theorem, it is shown that the conditions oif nonfinite escape of trajectories, reachability, and convexity of the dynamics over all admissible controls are needed for the existence of a time optimal solution for the robotic equation. With a lower bound for the finite-escape time established using a Liapunov approach, and an upper bound for the time to reach the target established using the exact linearization idea, a single inequality is found which is closely related to the coriolis and the centrifugal terms, the absence of which implies that the domain of existence of the optimal solution can be made arbitrarily large with a large torque constraint. As the work space is finite, this is essentially a global result in practical situations.
An extension of the results from Goodwin, Ramadge and Caines (1980) to the case where the input of the linear system saturates is presented. A necessary condition for closed loop stability of such a system is shown to be that the system must remain in a region from which y(t) = 0 is reachable with saturating inputs. With a slight modification of the original algorithm, the closed loop system is shown to be stable whenever the plant is exponentially stable.
The application of the penetrator to a Mars Return Sample Mission (MRSM) has direct advantages to meet science objectives and mission safety. Based on engineering data and work currently conducted at Ball Aerospace Systems Division, the concept of penetrators as scientific instruments is entirely practical. The primary utilization of a penetrator for MRSM would be to optimize the selection of the sample site location and to help in selection of the actual sample to be returned to Earth. It is recognized that the amount of sample to be returned is very limited, therefore the selection of the sample site is critical to the success of the mission. The following mission scenario is proposed. The site selection of a sample to be acquired will be performed by science working groups. A decision will be reached and a set of target priorities established based on data to give geochemical, geophysical and geological information. The first task of a penetrator will be to collect data at up to 4 to 6 possible landing sites. The penetrator can include geophysical, geochemical, geological and engineering instruments to confirm that scientific data requirements at that site will be met. This in situ near real-time data, collected prior to final targeting of the lander, will insure that the sample site is both scientifically valuable and also that it is reachable within limits of the capability of the lander.
A reconfigurable nonlinear control system design methodology is proposed to automatically correct computed slew torque commands of space-based pointing systems for the effects of slew-induced structural deformations. The possibility of forcing an elastic structure, such as that of a space-based instrument frame, to deform in a preselected way in response to rapid slews is demonstrated. To accomplish this, a supervisory controller must select a pair of algorithms, one for structural counterexcitation and the other for slew torque correction. It is shown how the reachability and subsequent tracking of the appropriate 'slow manifold', where the control algorithms are valid, can be ensured by a fast tracking loop, with time-varying gain dependent only on the commanded angular acceleration.
A decision-net solution involving a novel hierarchical classifier and a set of multiple directed graphs, as well as a neural-net solution, are respectively presented for large-class problem and mixture problem treatments of imaging spectrometer data. The clustering method for hierarchical classifier design, when used with multiple directed graphs, yields an efficient decision net. New directed-graph rules for reducing local maxima as well as the number of perturbations required, and the new starting-node rules for extending the reachability and reducing the search time of the graphs, are noted to yield superior results, as indicated by an illustrative 500-class imaging spectrometer problem.
The nonspherical shapes of asteroids are considered through a generalization of the Harris (1979) model of asteroid spin rates' collisional evolution. Since a body in spin equilibrium rotates about its axis of maximum moment of inertia, the computation of the mean-squared impact parameter through averaging over all directions of flux is not strictly valid; nevertheless, these complications have been found not to alter the conclusions reachable by means of the simpler model.
Deadbeat control theory gives a feedback solution to the time optimal control of discrete time systems. Experience has shown the results to be impractical because they ignore bounds on the actuator strength. This paper develops two algorithms for generating time optimal control in feedback form for discrete systems with bounded controls. The results are also applicable for generating recovery regions and the set of reachable states. For multiple control problems a method of generating sublayers is developed which decreases off-line and on-line computational effort. Two algorithms are presented with somewhat different computational and storage requirements. The algorithms are practical within certain dimension constraints, and are natural for implementation with parallel processing.
Two recent (unpublished) HI emission/absorption studies carried out with good sensitivity using the Arecibo 21 cm beam are discussed. One study (Colgan, Salpeter and Terzian) looked for high velocity clouds of our own Galaxy in absorption in the directions of 63 of the brightest continuum sources reachable with the Arecibo telescope. HI emission mapping in the neighborhood of these directions was also carried out. The other study (Corbelli and Schneider) looked for absorption along lines of sight to about 50 weaker sources which pass within a few diameters of nearby disk galaxies. Neither study detected any absorption.
Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The method is generalized to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero-reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.