Trapping Brownian ensemble optimally using Broadcast Stochastic Receding Horizon Control

Collision of suspended entities with surrounding molecules in a fluid environment leads to random movements of these entities, known as Brownian motion. Suppression of this motion in a Brownian ensemble has recently become essential for facilitating emerging applications in biology and in micro and nano scale self-assembled systems. How optimally this suppression can be performed remains an open question of great interest to both the natural science and the control engineering communities. In this paper, we address this question theoretically by introducing a novel “Broadcast Stochastic Receding Horizon Control” strategy for trapping an ensemble of non-interacting Brownian particles. The strategy designs a control input, independent of the number of particles, using measurements from a single particle as the only available feedback information and broadcasts it to all particles in the ensemble. We show the existence of a minimum region in which all particles can be driven and trapped indefinitely using the proposed control action. Under specific conditions, we guarantee the trapping of all particles in this region with probability 1. Finally, we demonstrate the efficacy of our control design in a simulation environment by trapping 100 Brownian particles in one, two and three dimensional homogeneous medium.     

A framework for design of scheduled output feedback model predictive control

We present a stabilizing scheduled output feedback Model Predictive Control (MPC) algorithm for constrained nonlinear systems with large operating regions. We design a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which on-line switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. This algorithm provides a general framework for scheduled output feedback MPC design.     

Energy sector planning using multiple-index pinch analysis

Pinch analysis was initially developed as a methodology for optimizing energy efficiency in process plants. Applications of pinch analysis applications are based on common principles of using stream quantity and quality to determine optimal system targets. This initial targeting step identifies the pinch point, which then allows complex problems to be decomposed for the subsequent design of an optimal network using insights drawn from the targeting stage. One important class of pinch analysis problems is energy planning with footprint constraints, which began with the development of carbon emissions pinch analysis; in such problems, energy sources and demands are characterized by carbon footprint as the quality index. This methodology has been extended by using alternative quality indexes that measure different sustainability dimensions, such as water footprint, land footprint, emergy transformity, inoperability risk, energy return on investment and human fatalities. Pinch analysis variants still have the limitation of being able to use one quality index at a time, while previous attempts to develop pinch analysis methods using multiple indices have only been partially successful for special cases. In this work, a multiple-index pinch analysis method is developed by using an aggregate quality index, based on a weighted linear function of different quality indexes normally used in energy planning. The weights used to compute the aggregate index are determined via the analytic hierarchy process. A case study for Indian power sector is solved to illustrate how this approach allows multiple sustainability dimensions to be accounted for in energy planning.     

Mathematical simulation of wet spinning coagulation process: Dynamic modeling and numerical results

A dynamic model of polymer wet spinning coagulation process is proposed in this article. The model is based on the double diffusion phenomenon, phase separation process, continuity balance, and momentum balance of the entire coagulation process. The uniqueness of the model lies in its dynamic feature. The model can simulate the system's dynamic response to variations in system inputs/parameters. Steady‐state system solutions can also be produced as the long‐time solutions of the dynamic model; a settling time can be observed at the same time. This paper employs a computationally efficient method of lines numerical algorithm for solving the dynamic model. A simulation experiment on a selected non‐solvent‐solvent‐polymer ternary system is carried out to verify the model as well as the numerical method. The dynamic simulation results are analyzed and discussed. At the end of the article, h‐refinement and p‐refinement are used to confirm the spatial convergence of the numerical solutions. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3432–3440, 2016     

Towards embedded model predictive control for System-on-a-Chip applications

We propose a framework for embedding model predictive control for Systems-on-a-Chip applications. In order to allow the implementation of such a computationally expensive controller on chip, we propose reducing the precision of the microprocessor to the minimum while maintaining near optimal control performance. Taking advantage of the low precision, a logarithmic number system based microprocessor architecture is used, that allows the design of a reduced size processor, providing further energy and computational cost savings. The design parameters for this high-performance embedded controller are chosen using a combination of finite element method simulations and bit-accurate hardware emulations in a number of parametric tests. We provide the methodology for choosing the design parameters for two particular control problems; the temperature regulation in a wafer cross-section geometry, and the control of temperature in a non-isothermal fluid flow problem in a microdevice. Finally, we provide the microprocessor architecture details and estimates for the performance of the resulting embedded model predictive controller.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.     

Broadcast stochastic receding horizon control of multi-agent systems

Optimal regulation of stochastically behaving agents is essential to achieve a robust aggregate behavior in a swarm of agents. How optimally these behaviors are controlled leads to the problem of designing optimal control architectures. In this paper, we propose a novel broadcast stochastic receding horizon control architecture as an optimal strategy for stabilizing a swarm of stochastically behaving agents. The goal is to design, at each time step, an optimal control law in the receding horizon control framework using collective system behavior as the only available feedback information and broadcast it to all agents to achieve the desired system behavior. Using probabilistic tools, a conditional expectation based predictive model is derived to represent the ensemble behavior of a swarm of independently behaving agents with multi-state transitions. A stochastic finite receding horizon control problem is formulated to stabilize the aggregate behavior of agents. Analytical and simulation results are presented for a two-state multi-agent system. Stability of the closed-loop system is guaranteed using the supermartingale theory. Almost sure (with probability 1) convergence of the closed-loop system to the desired target is ensured. Finally, conclusions are presented.     

Lumped heat and mass transfer coefficient for simulation of a pressure swing adsorption process

The practical implications of replacing various individual transport resistances such as gas-solid mass and heat transfer, and gas phase axial dispersions of mass and heat in a numerical model of a pressure swing adsorption (PSA) process by a single, empirical, lumped, effective mass transport coefficient were evaluated. A non-isothermal, adiabatic, four-step Skarstrom-like PSA process for production of pure helium from a binary helium-nitrogen mixture using 5A zeolite adsorbent was considered. It was found that the above-described model simplification was adequate to describe key process performances such as the bed size factor and the product recovery vis-a-vis a detailed model where the effects of all individual resistances were explicitly included.