Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

The condensed nearest neighbor rule using the concept of mutual nearest neighborhood (Corresp.)

A two-stage iterative algorithm for selecting a subset of a training set of samples for use in a condensed nearest neighbor (CNN) decision rule is introduced. The proposed method uses the concept of mutual nearest neighborhood for selecting samples close to the decision line. The efficacy of the algorithm is brought out by means of an example.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Optimal reservoir operation for irrigation of multiple crops using genetic algorithms

This paper presents a genetic algorithm (GA) model for obtaining an optimal operating policy and optimal crop water allocations from an irrigation reservoir. The objective is to maximize the sum of the relative yields from all crops in the irrigated area. The model takes into account reservoir inflow, rainfall on the irrigated area, intraseasonal competition for water among multiple crops, the soil moisture dynamics in each cropped area, the heterogeneous nature of soils. and crop response to the level of irrigation applied. The model is applied to the Malaprabha single-purpose irrigation reservoir in Karnataka State, India. The optimal operating policy obtained using the GA is similar to that obtained by linear programming. This model can be used for optimal utilization of the available water resources of any reservoir system to obtain maximum benefits.

Optimal Receive Antenna Selection in Time-Varying Fading Channels with Practical Training Constraints

Hardware constraints, which motivate receive antenna selection, also require that various antenna elements at the receiver be sounded sequentially to obtain estimates required for selecting the `best' antenna and for coherently demodulating data thereafter. Consequently, the channel state information at different antennas is outdated by different amounts and corrupted by noise. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, a preferable strategy is to linearly weight the channel estimates of different antennas differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then characterize explicitly the optimal selection weights that minimize the SEP. We also consider packet reception, in which multiple symbols of a packet are received by the same antenna. New suboptimal, but computationally efficient weighted selection schemes are proposed for reducing the packet error rate. The benefits of weighted selection are also demonstrated using a practical channel code used in third generation cellular systems. Our results show that optimal weighted selection yields a significant performance gain over conventional unweighted selection.

Synthesis of Cost-Optimal Shell-and-Tube Heat Exchangers

Synthesis of cost-optimal shell-and-tube heat exchangers is a difficult task since it involves a large number of parameters. An attempt is made in this article to simplify the process of choosing the parameter values that will minimize the cost of any heat exchanger satisfying a given heat duty and a particular set of constraints. The simplification is based on decoupling of the geometric and the thermal aspects of the problem. The concept of curves for cost-optimal design is introduced and is shown to simplify the synthesis process for shell-and-tube heat exchangers.

Adaptive optimal load balancing in a nonhomogeneous multiserver system with a central job scheduler

A model comprising several servers, each equipped with its own queue and with possibly different service speeds, is considered. Each server receives a dedicated arrival stream of jobs; there is also a stream of generic jobs that arrive to a job scheduler and can be individually allocated to any of the servers. It is shown that if the arrival streams are all Poisson and all jobs have the same exponentially distributed service requirements, the probabilistic splitting of the generic stream that minimizes the average job response time is such that it balances the server idle times in a weighted least-squares sense, where the weighting coefficients are related to the service speeds of the servers. The corresponding result holds for nonexponentially distributed service times if the service speeds are all equal. This result is used to develop adaptive quasi-static algorithms for allocating jobs in the generic arrival stream when the load parameters are unknown. The algorithms utilize server idle-time measurements which are sent periodically to the central job scheduler. A model is developed for these measurements, and the result mentioned is used to cast the problem into one of finding a projection of the root of an affine function, when only noisy values of the function can be observed

Optimal explicit guidance of multistage launch vehicle along three-dimensional trajectory

Details of an efficient optimal closed-loop guidance algorithm for a three-dimensional launch are presented with simulation results. Two types of orbital injections, with either true anomaly or argument of perigee being free at injection, are considered. The resulting steering-angle profile under the assumption of uniform gravity lies in a canted plane which transforms a three-dimensional problem into an equivalent two-dimensional one. Effects of thrust are estimated using a series in a recursive way. Encke's method is used to predict the trajectory during powered flight and then to compute the changes due to actual gravity using two gravity-related vectors. Guidance parameters are evaluated using the linear differential correction method. Optimality of the algorithm is tested against a standard ground-based trajectory optimization package. The performance of the algorithm is tested for accuracy, robustness, and efficiency for a sun-synchronous mission involving guidance for a multistage vehicle that requires large pitch and yaw maneuver. To demonstrate applicability of the algorithm to a range of missions, injection into a geostationary transfer orbit is also considered. The performance of the present algorithm is found to be much better than others.

Occurrence of maximum Tc at an optimal carrier concentration in superconducting bismuth and thallium cuprates

The superconducting transition temperatures in Bi2Ca1−xLnxSr2Cu2O8+δ, TlCa1−xLnxSr2Cu2O6+δ, and Tl0.8Ca1−xLnxBa2Cu23O6+δ (Ln=Y or rare earth) vary with composition and show a maximum at a specific value of x or δ. This observation suggests that an optimal carrier concentration is required to attain maximum Tc in such cuprates which seem to be two‐band systems

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

A near-optimal initial seed value selection in K-means means algorithm using a genetic algorithm

The K-means algorithm for clustering is very much dependent on the initial seed values. We use a genetic algorithm to find a near-optimal partitioning of the given data set by selecting proper initial seed values in the K-means algorithm. Results obtained are very encouraging and in most of the cases, on data sets having well separated clusters, the proposed scheme reached a global minimum.

Optimal explicit terminal guidance for a launch vehicle

It is observed that general explicit guidance schemes exhibit numerical instability close to the injection point. This difficulty is normally attributed to the demand for exact injection which, in turn, calls for finite corrections to be enforced in a relatively short time. The deviations in vehicle state which need corrective maneuvers are caused by the off-nominal operating conditions. Hence, the onset of terminal instability depends on the type of off-nominal conditions encountered. The proposed separate terminal guidance scheme overcomes the above difficulty by minimizing a quadratic penalty on injection errors rather than demanding an exact injection. There is also a special requirement in the terminal phase for the faster guidance computations. The faster guidance computations facilitate a more frequent guidance update enabling an accurate terminal thrust cutoff. The objective of faster computations is realized in the terminal guidance scheme by employing realistic assumptions that are accurate enough for a short terminal trajectory. It is observed from simulations that one of the guidance parameters (P) related to the thrust steering angular rates can indicate the onset of terminal instability due to different off-nominal operating conditions. Therefore, the terminal guidance scheme can be dynamically invoked based on monitoring of deviations in the lone parameter P.

Optimal scheduling of a processor executing a communication protocol stack

We consider the problem of optimally scheduling a processor executing a multilayer protocol in an intelligent Network Interface Controller (NIC). In particular, we assume a typical LAN environment with class 4 transport service, a connectionless network service, and a class 1 link level protocol. We develop a queuing model for the problem. In the most general case this becomes a cyclic queuing network in which some queues have dedicated servers, and the others have a common schedulable server. We use sample path arguments and Markov decision theory to determine optimal service schedules. The optimal throughputs are compared with those obtained with simple policies. The optimal policy yields upto 25% improvement in some cases. In some other cases, the optimal policy does only slightly better than much simpler policies.

Optimal pulse spacing for dynamical decoupling in the presence of a purely dephasing spin bath

Maintaining quantum coherence is a crucial requirement for quantum computation; hence protecting quantum systems against their irreversible corruption due to environmental noise is an important open problem. Dynamical decoupling (DD) is an effective method for reducing decoherence with a low control overhead. It also plays an important role in quantum metrology, where, for instance, it is employed in multiparameter estimation. While a sequence of equidistant control pulses the Carr-Purcell-Meiboom-Gill (CPMG) sequence] has been ubiquitously used for decoupling, Uhrig recently proposed that a nonequidistant pulse sequence the Uhrig dynamic decoupling (UDD) sequence] may enhance DD performance, especially for systems where the spectral density of the environment has a sharp frequency cutoff. On the other hand, equidistant sequences outperform UDD for soft cutoffs. The relative advantage provided by UDD for intermediate regimes is not clear. In this paper, we analyze the relative DD performance in this regime experimentally, using solid-state nuclear magnetic resonance. Our system qubits are C-13 nuclear spins and the environment consists of a H-1 nuclear spin bath whose spectral density is close to a normal (Gaussian) distribution. We find that in the presence of such a bath, the CPMG sequence outperforms the UDD sequence. An analogy between dynamical decoupling and interference effects in optics provides an intuitive explanation as to why the CPMG sequence performs better than any nonequidistant DD sequence in the presence of this kind of environmental noise.