Approximate Optimal Atmospheric Entry Trajectories

Approximate optimal atmospheric entry trajectories maximizing terminal function of velocity, heading angle, flight path angle, and altitud

A robust momentum management and attitude control system for the space station

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very assurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance

System characterization of positive real conditions

Necessary and sufficient conditions for positive realness in terms of state space matrices are presented under the assumption of complete controllability and complete observability of square systems with independent inputs. As an alternative to the positive real lemma and to the s-domain inequalities, these conditions provide a recursive algorithm for testing positive realness which result in a set of simple algebraic conditions. By relating the positive real property to the associated variational problem, a unified derivation of necessary and sufficient conditions for optimality of both singular and nonsingular problems is derived

The separate computation of arcs for optimal flight paths with state variable inequality constraints

Computation of arcs for optimal flight paths with state variable inequality constraint

Peak-Seeking Control Using Gradient and Hessian Estimates

A peak-seeking control method is presented which utilizes a linear time-varying Kalman filter. Performance function coordinate and magnitude measurements are used by the Kalman filter to estimate the gradient and Hessian of the performance function. The gradient and Hessian are used to command the system toward a local extremum. The method is naturally applied to multiple-input multiple-output systems. Applications of this technique to a single-input single-output example and a two-input one-output example are presented

Systems and Methods for Peak-Seeking Control

A computerized system and method for peak-seeking-control that uses a unique Kalman filter design to optimize a control loop, in real time, to either maximize or minimize a performance function of a physical object ("plant"). The system and method achieves more accurate and efficient peak-seeking-control by using a time-varying Kalman filter to estimate both the performance function gradient (slope) and Hessian (curvature) based on direct position measurements of the plant, and does not rely upon modeling the plant response to persistent excitation. The system and method can be naturally applied in various applications in which plant performance functions have multiple independent parameters, and it does not depend upon frequency separation to distinguish between system dimensions

Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique

Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry

The box-ball system is an integrable cellular automaton on one dimensional lattice. It arises from either quantum or classical integrable systems by the procedures called crystallization and ultradiscretization, respectively. The double origin of the integrability has endowed the box-ball system with a variety of aspects related to Yang-Baxter integrable models in statistical mechanics, crystal base theory in quantum groups, combinatorial Bethe ansatz, geometric crystals, classical theory of solitons, tau functions, inverse scattering method, action-angle variables and invariant tori in completely integrable systems, spectral curves, tropical geometry and so forth. In this review article, we demonstrate these integrable structures of the box-ball system and its generalizations based on the developments in the last two decades.Comment: 73 page

Evidence for a functional role of the second C5a receptor C5L2

During experimental sepsis in rodents after cecal ligation and puncture (CLP), excessive C5a is generated, leading to interactions with C5aR, loss of innate immune functions of neutrophils, and lethality. In the current study, we have analyzed the expression of the second C5a receptor C5L2, the putative â defaultâ or nonsignaling receptor for C5a. Rat C5L2 was cloned, and antibody was developed to C5L2 protein. After CLP, blood neutrophils showed a reduction in C5aR followed by its restoration, while C5L2 levels gradually increased, accompanied by the appearance of mRNA for C5L2. mRNA for C5L2 increased in lung and liver during CLP. Substantially increased C5L2 protein (defined by binding of 125Iâ antiâ C5L2 IgG) occurred in lung, liver, heart, and kidney after CLP. With the use of serum ILâ 6 as a marker for sepsis, infusion of antiâ C5aR dramatically reduced serum ILâ 6 levels, while antiâ C5L2 caused a nearly fourfold increase in ILâ 6 when compared with CLP controls treated with normal IgG. When normal blood neutrophils were stimulated in vitro with LPS and C5a, the antibodies had similar effects on release of ILâ 6. These data provide the first evidence for a role for C5L2 in balancing the biological responses to C5a.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154410/1/fsb2fj043424fje.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154410/2/fsb2fj043424fje-sup-0040.pd

Regulatory role of C5a in LPS-induced IL-6 production by neutrophils during sepsis

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154469/1/fsb2fj030708fje-sup-0001.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154469/2/fsb2fj030708fje.pd