Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

Solutions for New Terrestrial Broadcasting Systems Offering Simultaneously Stationary and Mobile Services

221 p.

Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)

An efficient frequency-domain algorithm for wave scattering problems with application to jet noise

This paper presents a pseudo-time-step method to calculate a (vector) Green function for the adjoint linearised Euler equations as a scattering problem in the frequency domain, for use as a jet-noise propagation prediction tool. A method of selecting the acoustics-related solution in a truncated spatial domain while suppressing any possible shear-layer-type instability is presented. Numerical tests for 3-D axisymmetrical parallel mean flows against semi-analytical reference solutions indicate that the new iterative algorithm is capable of producing accurate solutions with modest computational requirements.

Fluorescence and aggregation behavior of a polyimide in solutions

The UV-visible absorption and fluorescence spectra of a soluble polyimide, YS-30, in several organic solvents were measured over a wide range of concentration. The experimental results show that there exist both intramolecular and intermolecular electron donor acceptor interactions for YS-30 molecules. The fluorescence behavior of YS-30 in N,N-dimethylacetamide and in chloroform solutions is similar in general, except that its ground-state intermolecular charge transfer emission is more obvious in N,N-dimethylacetamide solution. This difference is attributed to the greater extent of disruption of the chain packing by solvent or/and the more efficient radiationless energy dissipation process from the excited state complexes to chloroform. The intensity ratio of intermolecular charge transfer emission to intramolecular charge transfer emission is used to characterize the state of aggregation of YS-30 molecules in solutions. The plot of this ratio versus concentration indicates the existence of two critical concentrations. It is also found from the same plot that the decrease of coil size is very pronounced during the initial stage of shrinkage.

Biosorption of copper(II) from aqueous solutions by green alga Cladophora fascicularis

Biosorption is an effective means of removal of heavy metals from wastewater. In this work the biosorption behavior of Cladophora fascicularis was investigated as a function of pH, amount of biosorbent, initial Cu2+ concentration, temperature, and co-existing ions. Adsorption equilibria were well described by Langmuir isotherm models. The enthalpy change for the biosorption process was found to be 6.86 kJ mol(-1) by use of the Langmuir constant b. The biosorption process was found to be rapid in the first 30 min. The presence of co-existing cations such as Na+, K+, Mg2+, and Ca2+ and anions such as chloride, nitrate, sulfate, and acetate did not significantly affect uptake of Cu2+ whereas EDTA substantially affected adsorption of the metal. When experiments were performed with different desorbents the results indicated that EDTA was an efficient desorbent for the recovery of Cu2+ from biomass. IR spectral analysis suggested amido or hydroxy, C=O, and C-O could combine strongly with Cu2+.

Biosorption of copper (II) and lead (II) from aqueous solutions by nonliving green algae Cladophora fascicularis: Equilibrium, kinetics and environmental effects

Biosorption of Cu2+ and Pb2+ by Cladophora fascicularis was investigated as a function of initial pH, initial heavy metal concentrations, temperature and other co-existing ions. Adsorption equilibriums were well described by Langmuir and Freundlich isotherm models. The maximum adsorption capacities were 1.61 mmol/ g for Cu2+ and 0.96 mmol/ g for Pb2+ at 298K and pH 5.0. The adsorption processes were endothermic and biosorption heats calculated by the Langmuir constant b were 39.0 and 29.6 kJ/ mol for Cu2+ and Pb2+, respectively. The biosorption kinetics followed the pseudo- second order model. No significant effect on the uptake of Cu2+ and Pb2+ by co-existing cations and anions was observed, except EDTA. Desorption experiments indicated that Na(2)EDTA was an efficient desorbent for the recovery of Cu2+ and Pb2+ from biomass. The results showed that Cladophora fascicularis was an effective and economical biosorbent material for the removal and recovery of heavy metal ions from wastewater.

User-Level Sandboxing: a Safe and Efficient Mechanism for Extensibility

Extensible systems allow services to be configured and deployed for the specific needs of individual applications. This paper describes a safe and efficient method for user-level extensibility that requires only minimal changes to the kernel. A sandboxing technique is described that supports multiple logical protection domains within the same address space at user-level. This approach allows applications to register sandboxed code with the system, that may be executed in the context of any process. Our approach differs from other implementations that require special hardware support, such as segmentation or tagged translation look-aside buffers (TLBs), to either implement multiple protection domains in a single address space, or to support fast switching between address spaces. Likewise, we do not require the entire system to be written in a type-safe language, to provide fine-grained protection domains. Instead, our user-level sandboxing technique requires only paged-based virtual memory support, and the requirement that extension code is written either in a type-safe language, or by a trusted source. Using a fast method of upcalls, we show how our sandboxing technique for implementing logical protection domains provides significant performance improvements over traditional methods of invoking user-level services. Experimental results show our approach to be an efficient method for extensibility, with inter-protection domain communication costs close to those of hardware-based solutions leveraging segmentation.

Finding optimal alternatives based on efficient comparative preference inference

Choosing the right or the best option is often a demanding and challenging task for the user (e.g., a customer in an online retailer) when there are many available alternatives. In fact, the user rarely knows which offering will provide the highest value. To reduce the complexity of the choice process, automated recommender systems generate personalized recommendations. These recommendations take into account the preferences collected from the user in an explicit (e.g., letting users express their opinion about items) or implicit (e.g., studying some behavioral features) way. Such systems are widespread; research indicates that they increase the customers' satisfaction and lead to higher sales. Preference handling is one of the core issues in the design of every recommender system. This kind of system often aims at guiding users in a personalized way to interesting or useful options in a large space of possible options. Therefore, it is important for them to catch and model the user's preferences as accurately as possible. In this thesis, we develop a comparative preference-based user model to represent the user's preferences in conversational recommender systems. This type of user model allows the recommender system to capture several preference nuances from the user's feedback. We show that, when applied to conversational recommender systems, the comparative preference-based model is able to guide the user towards the best option while the system is interacting with her. We empirically test and validate the suitability and the practical computational aspects of the comparative preference-based user model and the related preference relations by comparing them to a sum of weights-based user model and the related preference relations. Product configuration, scheduling a meeting and the construction of autonomous agents are among several artificial intelligence tasks that involve a process of constrained optimization, that is, optimization of behavior or options subject to given constraints with regards to a set of preferences. When solving a constrained optimization problem, pruning techniques, such as the branch and bound technique, point at directing the search towards the best assignments, thus allowing the bounding functions to prune more branches in the search tree. Several constrained optimization problems may exhibit dominance relations. These dominance relations can be particularly useful in constrained optimization problems as they can instigate new ways (rules) of pruning non optimal solutions. Such pruning methods can achieve dramatic reductions in the search space while looking for optimal solutions. A number of constrained optimization problems can model the user's preferences using the comparative preferences. In this thesis, we develop a set of pruning rules used in the branch and bound technique to efficiently solve this kind of optimization problem. More specifically, we show how to generate newly defined pruning rules from a dominance algorithm that refers to a set of comparative preferences. These rules include pruning approaches (and combinations of them) which can drastically prune the search space. They mainly reduce the number of (expensive) pairwise comparisons performed during the search while guiding constrained optimization algorithms to find optimal solutions. Our experimental results show that the pruning rules that we have developed and their different combinations have varying impact on the performance of the branch and bound technique.

BARRIERS AND SOLUTIONS TO OPEN SOURCE APPROPRIATE TECHNOLOGY FOR SUSTAINABLE DEVELOPMENT: INNOVATION THROUGH COLLABORATION

It has been proposed that the field of appropriate technology (AT) - small-scale, energy efficient and low-cost solutions, can be of tremendous assistance in many of the sustainable development challenges, such as food and water security, health, shelter, education and work opportunities. Unfortunately, there has not yet been a significant uptake of AT by organizations, researchers, policy makers or the mainstream public working in the many areas of the development sector. Some of the biggest barriers to higher AT engagement include: 1) AT perceived as inferior or ‘poor persons technology’, 2) questions of technological robustness, design, fit and transferability, 3) funding, 4) institutional support, as well as 5) general barriers associated with tackling rural poverty. With the rise of information and communication technologies (ICTs) for online networking and knowledge sharing, the possibilities to tap into the collaborative open-access and open-source AT are growing, and so is the prospect for collective poverty reducing strategies, enhancement of entrepreneurship, communications, education and a diffusion of life-changing technologies. In short, the same collaborative philosophy employed in the success of open source software can be applied to hardware design of technologies to improve sustainable development efforts worldwide. To analyze current barriers to open source appropriate technology (OSAT) and explore opportunities to overcome such obstacles, a series of interviews with researchers and organizations working in the field of AT were conducted. The results of the interviews confirmed the majority of literature identified barriers, but also revealed that the most pressing problem for organizations and researchers currently working in the field of AT is the need for much better communication and collaboration to share the knowledge and resources and work in partnership. In addition, interviews showcased general receptiveness to the principles of collaborative innovation and open source on the ground level. A much greater focus on networking, collaboration, demand-led innovation, community participation, and the inclusion of educational institutions through student involvement can be of significant help to build the necessary knowledge base, networks and the critical mass exposure for the growth of appropriate technology.

Efficient advanced encryption standard implementation using lookup and normal basis

A new type of advanced encryption standard (AES) implementation using a normal basis is presented. The method is based on a lookup technique that makes use of inversion and shift registers, which leads to a smaller size of lookup for the S-box than its corresponding implementations. The reduction in the lookup size is based on grouping sets of inverses into conjugate sets which in turn leads to a reduction in the number of lookup values. The above technique is implemented in a regular AES architecture using register files, which requires less interconnect and area and is suitable for security applications. The results of the implementation are competitive in throughput and area compared with the corresponding solutions in a polynomial basis.

STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION

Stationary solutions to the equations of nonlinear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean free path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cutoff in energy space-particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for the substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven nonresonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off-a diagnostic that is in principle accessible to observation.

Voltage over-scaling:A cross-layer design perspective for energy efficient systems

Today's multi-media electronic era is driven by the increasing demand for small multifunctional devices able to support diverse services. Unfortunately, the high levels of transistor integration and performance required by such devices lead to an unprecedented increase of on-chip power that significantly limits the battery lifetime and even poses reliability concerns. Several techniques have been developed to address the power increase, but voltage over-scaling (VOS) is considered to be one of the most effective ones due to the quadratic dependence of voltage on dynamic power consumption. However, VOS may not always be applicable since it increases the delay in all paths of a system and may limit high performance required by today's complex applications. In addition, application of VOS is further complicated since it increases the variations in transistor characteristics imposed by their tiny size which can lead to large delay and leakage variations, making it difficult to meet delay and power budgets. This paper presents a review of various cross-layer design options that can provide solutions for dynamic voltage over-scaling and can potentially assist in meeting the strict power budgets and yield/quality requirements of future systems. © 2011 IEEE.

HERQULES:System level cross-layer design exploration for efficient energy-quality trade-offs

In this paper, we present a unique cross-layer design framework that allows systematic exploration of the energy-delay-quality trade-offs at the algorithm, architecture and circuit level of design abstraction for each block of a system. In addition, taking into consideration the interactions between different sub-blocks of a system, it identifies the design solutions that can ensure the least energy at the "right amount of quality" for each sub-block/system under user quality/delay constraints. This is achieved by deriving sensitivity based design criteria, the balancing of which form the quantitative relations that can be used early in the system design process to evaluate the energy efficiency of various design options. The proposed framework when applied to the exploration of energy-quality design space of the main blocks of a digital camera and a wireless receiver, achieves 58% and 33% energy savings under 41% and 20% error increase, respectively. © 2010 ACM.

An efficient genetic algorithm for the design optimization of cold-formed steel portal frame buildings

The design optimization of a cold-formed steel portal frame building is considered in this paper. The proposed genetic algorithm (GA) optimizer considers both topology (i.e., frame spacing and pitch) and cross-sectional sizes of the main structural members as the decision variables. Previous GAs in the literature were characterized by poor convergence, including slow progress, that usually results in excessive computation times and/or frequent failure to achieve an optimal or near-optimal solution. This is the main issue addressed in this paper. In an effort to improve the performance of the conventional GA, a niching strategy is presented that is shown to be an effective means of enhancing the dissimilarity of the solutions in each generation of the GA. Thus, population diversity is maintained and premature convergence is reduced significantly. Through benchmark examples, it is shown that the efficient GA proposed generates optimal solutions more consistently. A parametric study was carried out, and the results included. They show significant variation in the optimal topology in terms of pitch and frame spacing for a range of typical column heights. They also show that the optimized design achieved large savings based on the cost of the main structural elements; the inclusion of knee braces at the eaves yield further savings in cost, that are significant.