Optimal control of grinding mill circuit using model predictive static programming: A new nonlinear MPC paradigm

The recently developed reference-command tracking version of model predictive static programming (MPSP) is successfully applied to a single-stage closed grinding mill circuit. MPSP is an innovative optimal control technique that combines the philosophies of model predictive control (MPC) and approximate dynamic programming. The performance of the proposed MPSP control technique, which can be viewed as a `new paradigm' under the nonlinear MPC philosophy, is compared to the performance of a standard nonlinear MPC technique applied to the same plant for the same conditions. Results show that the MPSP control technique is more than capable of tracking the desired set-point in the presence of model-plant mismatch, disturbances and measurement noise. The performance of MPSP and nonlinear MPC compare very well, with definite advantages offered by MPSP. The computational speed of MPSP is increased through a sequence of innovations such as the conversion of the dynamic optimization problem to a low-dimensional static optimization problem, the recursive computation of sensitivity matrices and using a closed form expression to update the control. To alleviate the burden on the optimization procedure in standard MPC, the control horizon is normally restricted. However, in the MPSP technique the control horizon is extended to the prediction horizon with a minor increase in the computational time. Furthermore, the MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for online applications of the nonlinear MPC philosophy to real-world industrial process plants. (C) 2014 Elsevier Ltd. All rights reserved.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Optimal Guidance for Accurate Lunar Soft Landing with Minimum Fuel Consumption using Model Predictive Static Programming

In this paper the soft lunar landing with minimum fuel expenditure is formulated as a nonlinear optimal guidance problem. The realization of pinpoint soft landing with terminal velocity and position constraints is achieved using Model Predictive Static Programming (MPSP). The high accuracy of the terminal conditions is ensured as the formulation of the MPSP inherently poses final conditions as a set of hard constraints. The computational efficiency and fast convergence make the MPSP preferable for fixed final time onboard optimal guidance algorithm. It has also been observed that the minimum fuel requirement strongly depends on the choice of the final time (a critical point that is not given due importance in many literature). Hence, to optimally select the final time, a neural network is used to learn the mapping between various initial conditions in the domain of interest and the corresponding optimal flight time. To generate the training data set, the optimal final time is computed offline using a gradient based optimization technique. The effectiveness of the proposed method is demonstrated with rigorous simulation results.

MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR

The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experience illustrates how can we solve 44 optimization problems which are asymmetric with respect to the number of integer and continuous variables and the number of constraints. We also report a comparative with the speedup and efficiency of several strategies implemented for some available number of threads.

Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Open Personalization: Involving Third Parties in Improving the User Experience of Websites

Traditional software development captures the user needs during the requirement analysis. The Web makes this endeavour even harder due to the difficulty to determine who these users are. In an attempt to tackle the heterogeneity of the user base, Web Personalization techniques are proposed to guide the users’ experience. In addition, Open Innovation allows organisations to look beyond their internal resources to develop new products or improve existing processes. This thesis sits in between by introducing Open Personalization as a means to incorporate actors other than webmasters in the personalization of web applications. The aim is to provide the technological basis that builds up a trusty environment for webmasters and companion actors to collaborate, i.e. "an architecture of participation". Such architecture very much depends on these actors’ profile. This work tackles three profiles (i.e. software partners, hobby programmers and end users), and proposes three "architectures of participation" tuned for each profile. Each architecture rests on different technologies: a .NET annotation library based on Inversion of Control for software partners, a Modding Interface in JavaScript for hobby programmers, and finally, a domain specific language for end-users. Proof-of-concept implementations are available for the three cases while a quantitative evaluation is conducted for the domain specific language.

Synthetic molecular machines for active self-assembly : prototype algorithms, designs, and experimental study

Computer science and electrical engineering have been the great success story of the twentieth century. The neat modularity and mapping of a language onto circuits has led to robots on Mars, desktop computers and smartphones. But these devices are not yet able to do some of the things that life takes for granted: repair a scratch, reproduce, regenerate, or grow exponentially fast–all while remaining functional.

This thesis explores and develops algorithms, molecular implementations, and theoretical proofs in the context of “active self-assembly” of molecular systems. The long-term vision of active self-assembly is the theoretical and physical implementation of materials that are composed of reconfigurable units with the programmability and adaptability of biology’s numerous molecular machines. En route to this goal, we must first find a way to overcome the memory limitations of molecular systems, and to discover the limits of complexity that can be achieved with individual molecules.

One of the main thrusts in molecular programming is to use computer science as a tool for figuring out what can be achieved. While molecular systems that are Turing-complete have been demonstrated [Winfree, 1996], these systems still cannot achieve some of the feats biology has achieved.

One might think that because a system is Turing-complete, capable of computing “anything,” that it can do any arbitrary task. But while it can simulate any digital computational problem, there are many behaviors that are not “computations” in a classical sense, and cannot be directly implemented. Examples include exponential growth and molecular motion relative to a surface.

Passive self-assembly systems cannot implement these behaviors because (a) molecular motion relative to a surface requires a source of fuel that is external to the system, and (b) passive systems are too slow to assemble exponentially-fast-growing structures. We call these behaviors “energetically incomplete” programmable behaviors. This class of behaviors includes any behavior where a passive physical system simply does not have enough physical energy to perform the specified tasks in the requisite amount of time.

As we will demonstrate and prove, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. Using an external source of fuel solves part of the the problem, so the system is not “energetically incomplete.” But the programmable system also needs to have sufficient expressive power to achieve the specified behaviors. Perhaps surprisingly, some of these systems do not even require Turing completeness to be sufficiently expressive.

Building on a large variety of work by other scientists in the fields of DNA nanotechnology, chemistry and reconfigurable robotics, this thesis introduces several research contributions in the context of active self-assembly.

We show that simple primitives such as insertion and deletion are able to generate complex and interesting results such as the growth of a linear polymer in logarithmic time and the ability of a linear polymer to treadmill. To this end we developed a formal model for active-self assembly that is directly implementable with DNA molecules. We show that this model is computationally equivalent to a machine capable of producing strings that are stronger than regular languages and, at most, as strong as context-free grammars. This is a great advance in the theory of active self- assembly as prior models were either entirely theoretical or only implementable in the context of macro-scale robotics.

We developed a chain reaction method for the autonomous exponential growth of a linear DNA polymer. Our method is based on the insertion of molecules into the assembly, which generates two new insertion sites for every initial one employed. The building of a line in logarithmic time is a first step toward building a shape in logarithmic time. We demonstrate the first construction of a synthetic linear polymer that grows exponentially fast via insertion. We show that monomer molecules are converted into the polymer in logarithmic time via spectrofluorimetry and gel electrophoresis experiments. We also demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism. This shows the growth of a population of polymers in logarithmic time. We characterize the DNA insertion mechanism that we utilize in Chapter 4. We experimentally demonstrate that we can control the kinetics of this re- action over at least seven orders of magnitude, by programming the sequences of DNA that initiate the reaction.

In addition, we review co-authored work on programming molecular robots using prescriptive landscapes of DNA origami; this was the first microscopic demonstration of programming a molec- ular robot to walk on a 2-dimensional surface. We developed a snapshot method for imaging these random walking molecular robots and a CAPTCHA-like analysis method for difficult-to-interpret imaging data.

Beyond Watson and Crick : programming the self-assembly and reconfiguration of DNA nanostructures based on stacking interactions

Life is the result of the execution of molecular programs: like how an embryo is fated to become a human or a whale, or how a person’s appearance is inherited from their parents, many biological phenomena are governed by genetic programs written in DNA molecules. At the core of such programs is the highly reliable base pairing interaction between nucleic acids. DNA nanotechnology exploits the programming power of DNA to build artificial nanostructures, molecular computers, and nanomachines. In particular, DNA origami—which is a simple yet versatile technique that allows one to create various nanoscale shapes and patterns—is at the heart of the technology. In this thesis, I describe the development of programmable self-assembly and reconfiguration of DNA origami nanostructures based on a unique strategy: rather than relying on Watson-Crick base pairing, we developed programmable bonds via the geometric arrangement of stacking interactions, which we termed stacking bonds. We further demonstrated that such bonds can be dynamically reconfigurable.

The first part of this thesis describes the design and implementation of stacking bonds. Our work addresses the fundamental question of whether one can create diverse bond types out of a single kind of attractive interaction—a question first posed implicitly by Francis Crick while seeking a deeper understanding of the origin of life and primitive genetic code. For the creation of multiple specific bonds, we used two different approaches: binary coding and shape coding of geometric arrangement of stacking interaction units, which are called blunt ends. To construct a bond space for each approach, we performed a systematic search using a computer algorithm. We used orthogonal bonds to experimentally implement the connection of five distinct DNA origami nanostructures. We also programmed the bonds to control cis/trans configuration between asymmetric nanostructures.

The second part of this thesis describes the large-scale self-assembly of DNA origami into two-dimensional checkerboard-pattern crystals via surface diffusion. We developed a protocol where the diffusion of DNA origami occurs on a substrate and is dynamically controlled by changing the cationic condition of the system. We used stacking interactions to mediate connections between the origami, because of their potential for reconfiguring during the assembly process. Assembling DNA nanostructures directly on substrate surfaces can benefit nano/microfabrication processes by eliminating a pattern transfer step. At the same time, the use of DNA origami allows high complexity and unique addressability with six-nanometer resolution within each structural unit.

The third part of this thesis describes the use of stacking bonds as dynamically breakable bonds. To break the bonds, we used biological machinery called the ParMRC system extracted from bacteria. The system ensures that, when a cell divides, each daughter cell gets one copy of the cell’s DNA by actively pushing each copy to the opposite poles of the cell. We demonstrate dynamically expandable nanostructures, which makes stacking bonds a promising candidate for reconfigurable connectors for nanoscale machine parts.