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.

Selection of Optimal Time-to-go in Generalized Vector Explicit Guidance

A new method of selection of time-to-go (t(go)) for Generalized Vector Explicit Guidance (GENEX) law have been proposed in this paper. t(go) is known to be an important parameter in the control and cost function of GENEX guidance law. In this paper the formulation has been done to find an optimal value of t(go) that minimizes the performance cost. Mechanization of GENEX with this optimal t(go) reduces the lateral acceleration demand and consequently increases the range of the interceptor. This new formulation of computing t(go) comes in closed form and thus it can be implemented onboard. This new formulation is applied in the terminal phase of an surface-to-air interceptor for an angle constrained engagement. Results generated by simulation justify the use of optimal t(go).

Task assignment in a multiprocessor system

One of the key problems in the design of any incompletely connected multiprocessor system is to appropriately assign the set of tasks in a program to the Processing Elements (PEs) in the system. The task assignment problem has proven difficult both in theory and in practice. This paper presents a simple and efficient heuristic algorithm for assigning program tasks with precedence and communication constraints to the PEs in a Message-based Multiple-bus Multiprocessor System, M3, so that the total execution time for the program is minimized. The algorithm uses a cost function: “Minimum Distance and Parallel Transfer” to minimize the completion time. The effectiveness of the algorithm has been demonstrated by comparing the results with (i) the lower bound on the execution time of a program (task) graph and (ii) a random assignment.

Risk-sensitive optimal control for Markov decision processes with monotone cost

The existence of an optimal feedback law is established for the risk-sensitive optimal control problem with denumerable state space. The main assumptions imposed are irreducibility and a near monotonicity condition on the one-step cost function. A solution can be found constructively using either value iteration or policy iteration under suitable conditions on initial feedback law.

AIWIN - A fast and jigless inspection technique for machined parts

Precision inspection of manufactured components having multiple complex surfaces and variable tolerance definition is an involved, complex and time-consuming function. In routine practice, a jig is used to present the part in a known reference frame to carry out the inspection process. Jigs involve both time and cost in their development, manufacture and use. This paper describes 'as is where is inspection' (AIWIN), a new automated inspection technique that accelerates the inspection process by carrying out a fast registration procedure and establishing a quick correspondence between the part to inspect and its CAD geometry. The main challenge in doing away with a jig is that the inspection reference frame could be far removed from the CAD frame. Traditional techniques based on iterative closest point (ICP) or Newton methods require either a large number of iterations for convergence or fail in such a situation. A two-step coarse registration process is proposed to provide a good initial guess for a modified ICP algorithm developed earlier (Ravishankar et al., Int J Adv Manuf Technol 46(1-4):227-236, 2010). The first step uses a calibrated sphere for local hard registration and fixing the translation error. This transformation locates the centre for the sphere in the CAD frame. In the second step, the inverse transformation (involving pure rotation about multiple axes) required to align the inspection points measured on the manufactured part with the CAD point dataset of the model is determined and enforced. This completes the coarse registration enabling fast convergence of the modified ICP algorithm. The new technique has been implemented on complex freeform machined components and the inspection results clearly show that the process is precise and reliable with rapid convergence. © 2011 Springer-Verlag London Limited.

PLUTO plus : Near-Complete Modeling of Affine Transformations for Parallelism and Locality

Affine transformations have proven to be very powerful for loop restructuring due to their ability to model a very wide range of transformations. A single multi-dimensional affine function can represent a long and complex sequence of simpler transformations. Existing affine transformation frameworks like the Pluto algorithm, that include a cost function for modern multicore architectures where coarse-grained parallelism and locality are crucial, consider only a sub-space of transformations to avoid a combinatorial explosion in finding the transformations. The ensuing practical tradeoffs lead to the exclusion of certain useful transformations, in particular, transformation compositions involving loop reversals and loop skewing by negative factors. In this paper, we propose an approach to address this limitation by modeling a much larger space of affine transformations in conjunction with the Pluto algorithm's cost function. We perform an experimental evaluation of both, the effect on compilation time, and performance of generated codes. The evaluation shows that our new framework, Pluto+, provides no degradation in performance in any of the Polybench benchmarks. For Lattice Boltzmann Method (LBM) codes with periodic boundary conditions, it provides a mean speedup of 1.33x over Pluto. We also show that Pluto+ does not increase compile times significantly. Experimental results on Polybench show that Pluto+ increases overall polyhedral source-to-source optimization time only by 15%. In cases where it improves execution time significantly, it increased polyhedral optimization time only by 2.04x.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Location of concentrators in a computer communication network: a stochastic automation search method

The following problem is considered. Given the locations of the Central Processing Unit (ar;the terminals which have to communicate with it, to determine the number and locations of the concentrators and to assign the terminals to the concentrators in such a way that the total cost is minimized. There is alao a fixed cost associated with each concentrator. There is ail upper limit to the number of terminals which can be connected to a concentrator. The terminals can be connected directly to the CPU also In this paper it is assumed that the concentrators can bo located anywhere in the area A containing the CPU and the terminals. Then this becomes a multimodal optimization problem. In the proposed algorithm a stochastic automaton is used as a search device to locate the minimum of the multimodal cost function . The proposed algorithm involves the following. The area A containing the CPU and the terminals is divided into an arbitrary number of regions (say K). An approximate value for the number of concentrators is assumed (say m). The optimum number is determined by iteration later The m concentrators can be assigned to the K regions in (mk) ways (m > K) or (km) ways (K>m).(All possible assignments are feasible, i.e. a region can contain 0,1,…, to concentrators). Each possible assignment is assumed to represent a state of the stochastic variable structure automaton. To start with, all the states are assigned equal probabilities. At each stage of the search the automaton visits a state according to the current probability distribution. At each visit the automaton selects a 'point' inside that state with uniform probability. The cost associated with that point is calculated and the average cost of that state is updated. Then the probabilities of all the states are updated. The probabilities are taken to bo inversely proportional to the average cost of the states After a certain number of searches the search probabilities become stationary and the automaton visits a particular state again and again. Then the automaton is said to have converged to that state Then by conducting a local gradient search within that state the exact locations of the concentrators are determined This algorithm was applied to a set of test problems and the results were compared with those given by Cooper's (1964, 1967) EAC algorithm and on the average it was found that the proposed algorithm performs better.

Calculating the bound spectrum by path summation in action-angle variables

The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Enhancing 'Mobility' through Integrated Transportation and Traffic Management

During the course of preparation of a master plan for the transportation networks in Bangalore city, mapping the various initiatives and interventions planned towards addressing mobility, existing situation and implications of some of the proposed interventions was analysed. The inferences are based on existing transportation network; synthesis of various transportation related studies and proposed infrastructure initiatives (road works) in Bangalore. Broadly, they can be summarized as following five aspects: I. Need for ~Sreclassifying~T existing road networks (arterial and sub-arterial) with effective geospatial database in the back-end. II. The proposed Core Ring Road at surface grade may not be feasible. III. Current interventions encouraging more independent motorable transport by way of road widening, construction of underpasses, flyovers and grade-separators would not ease traffic congestion when addressed in isolation. IV. Factors affecting time and cost-overruns in infrastructure projects and ways to tackle are discussed. V. Initiatives required for addressing effective planning for operations recommended.

Formation of an unusual copper(II) complex from the degradation of a novel tricopper(II) carbohydrazone complex

An unusual copper(II) complex [Cu(L-1a)(2)Cl-2] CH3OH center dot H2O center dot H3O+Cl- (1a) was isolated from a solution of a novel tricopper(II) complex [Cu-3(HL1)Cl-2]Cl-3 center dot 2H(2)O (1) in methanol. where L-1a is 3-(2-pyridyl)triazolo [1,5-a]-pyridine, and characterized with single crystal X-ray diffraction study. The tricopper(II) complex of potential ligand 1,5-bis(di-2-pyridyl ketone) carbohydrazone (H2L1) was synthesized and physicochemically characterized, while the formation of the complex la was followed by time-dependant monitoring of the UV-visible spectra. which reveals degradation of ligand backbone as intensity loss of bands corresponding to O -> Cu(II) charge transfer.

Distributed nonlinear optimization algorithms for general network problems

There are a number of large networks which occur in many problems dealing with the flow of power, communication signals, water, gas, transportable goods, etc. Both design and planning of these networks involve optimization problems. The first part of this paper introduces the common characteristics of a nonlinear network (the network may be linear, the objective function may be non linear, or both may be nonlinear). The second part develops a mathematical model trying to put together some important constraints based on the abstraction for a general network. The third part deals with solution procedures; it converts the network to a matrix based system of equations, gives the characteristics of the matrix and suggests two solution procedures, one of them being a new one. The fourth part handles spatially distributed networks and evolves a number of decomposition techniques so that we can solve the problem with the help of a distributed computer system. Algorithms for parallel processors and spatially distributed systems have been described.There are a number of common features that pertain to networks. A network consists of a set of nodes and arcs. In addition at every node, there is a possibility of an input (like power, water, message, goods etc) or an output or none. Normally, the network equations describe the flows amoungst nodes through the arcs. These network equations couple variables associated with nodes. Invariably, variables pertaining to arcs are constants; the result required will be flows through the arcs. To solve the normal base problem, we are given input flows at nodes, output flows at nodes and certain physical constraints on other variables at nodes and we should find out the flows through the network (variables at nodes will be referred to as across variables).The optimization problem involves in selecting inputs at nodes so as to optimise an objective function; the objective may be a cost function based on the inputs to be minimised or a loss function or an efficiency function. The above mathematical model can be solved using Lagrange Multiplier technique since the equalities are strong compared to inequalities. The Lagrange multiplier technique divides the solution procedure into two stages per iteration. Stage one calculates the problem variables % and stage two the multipliers lambda. It is shown that the Jacobian matrix used in stage one (for solving a nonlinear system of necessary conditions) occurs in the stage two also.A second solution procedure has also been imbedded into the first one. This is called total residue approach. It changes the equality constraints so that we can get faster convergence of the iterations.Both solution procedures are found to coverge in 3 to 7 iterations for a sample network.The availability of distributed computer systems — both LAN and WAN — suggest the need for algorithms to solve the optimization problems. Two types of algorithms have been proposed — one based on the physics of the network and the other on the property of the Jacobian matrix. Three algorithms have been deviced, one of them for the local area case. These algorithms are called as regional distributed algorithm, hierarchical regional distributed algorithm (both using the physics properties of the network), and locally distributed algorithm (a multiprocessor based approach with a local area network configuration). The approach used was to define an algorithm that is faster and uses minimum communications. These algorithms are found to converge at the same rate as the non distributed (unitary) case.

Analysis of edge delaminations in laminates through combined use of quasi-three-dimensional, eight-noded, two-noded and transition elements

The use of appropriate finite elements in different regions of a stressed solid can be expected to be economical in computing its stress response. This concept is exploited here in studying stresses near free edges in laminated coupons. The well known free edge problem of [0/90], symmetric laminate is considered to illustrate the application of the concept. The laminate is modelled as a combination of three distinct regions. Quasi-three-dimensional eight-noded quadrilateral isoparametric elements (Q3D8) are used at and near the free edge of the laminate and two-noded line elements (Q3D2) are used in the region away from the free edge. A transition element (Q3DT) provides a smooth inter-phase zone between the two regions. Significant reduction in the problem size and hence in the computational time and cost have been achieved at almost no loss of accuracy.

Algorithms for Routing and Centralized Scheduling in IEEE 802.16 Mesh Networks

IEEE 802.16 standards for Wireless Metropolitan Area Networks (WMANs) include a mesh mode of operation for improving the coverage and throughput of the network. In this paper, we consider the problem of routing and centralized scheduling for such networks. We first fix the routing, which reduces the network to a tree. We then present a finite horizon dynamic programming framework. Using it we obtain various scheduling algorithms depending upon the cost function. Next we consider simpler suboptimal algorithms and compare their performances.

On generating optimal signal probabilities for random tests: A genetic approach

Genetic Algorithms are robust search and optimization techniques. A Genetic Algorithm based approach for determining the optimal input distributions for generating random test vectors is proposed in the paper. A cost function based on the COP testability measure for determining the efficacy of the input distributions is discussed, A brief overview of Genetic Algorithms (GAs) and the specific details of our implementation are described. Experimental results based on ISCAS-85 benchmark circuits are presented. The performance pf our GA-based approach is compared with previous results. While the GA generates more efficient input distributions than the previous methods which are based on gradient descent search, the overheads of the GA in computing the input distributions are larger. To account for the relatively quick convergence of the gradient descent methods, we analyze the landscape of the COP-based cost function. We prove that the cost function is unimodal in the search space. This feature makes the cost function amenable to optimization by gradient-descent techniques as compared to random search methods such as Genetic Algorithms.