Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861

Distribution and Fluctuation of Firm Size in the Long-Run

The paper studies empirically and analytically growth and fluctuation of firm size distribution. An empirical analysis is carried out on several data sets on firm size, with emphasis on one-time distribution as well as growth-rate probability distribution. Two well-known scaling laws, Pareto's law and Gibrat's law, are discussed. Some theoretical discussion on their relationship is presented. We also discuss to what extent there may exist economic mechanisms that produce an unequal firm size distribution in the long run. The mechanisms we study have been known in the economic literature since long. Yet, they have not been studied in the context of a dynamic decision problem of the firm. We allow for heterogeneity of firms with respect to certain characteristics. We then show that there are mechanisms at work which may generate a twin-peaked distribution of firm size in the long-run, which will then be tested empiricallyFirm size, Pareto's law, Gibrat's law

Stabilization of controlled diffusions via Zubov's method

We consider a controlled stochastic system which is exponentially stabilizable in probability near an attractor. Our aim is to characterize the set of points which can be driven by a suitable control to the attractor with either positive probability or with probability one. This will be done by associating to the stochastic system a suitable control problem and the corresponding Zubov equation. We then show that this approach can be used as a basis for numerical computations of these sets

CO adsorption on neutral iridium clusters

The adsorption of carbon monoxide on neutral iridium clusters in the size range of n = 3 to 21 atoms is investigated with infrared multiple photon dissociation spectroscopy. For each cluster size only a single v(CO) band is present with frequencies in the range between 1962 cm-1 (n = 8) and 1985 cm-1 (n = 18) which can be attributed to an atop binding geometry. This behaviour is compared to the CO binding geometries on clusters of other group 9 and 10 transition metals as well as to that on extended surfaces. The preference of Ir for atop binding is rationalized by relativistic effects on the electronic structure of the later 5d metals

Biofabrication: an overview of the approaches used for printing of living cells

The development of cell printing is vital for establishing biofabrication approaches as clinically relevant tools. Achieving this requires bio-inks which must not only be easily printable, but also allow controllable and reproducible printing of cells. This review outlines the general principles and current progress and compares the advantages and challenges for the most widely used biofabrication techniques for printing cells: extrusion, laser, microvalve, inkjet and tissue fragment printing. It is expected that significant advances in cell printing will result from synergistic combinations of these techniques and lead to optimised resolution, throughput and the overall complexity of printed constructs

Argon physisorption as structural probe for endohedrally doped silicon clusters

Contains fulltext : 98812.pdf (publisher's version ) (Open Access

A receding horizon control approach to sampled-data implementation of continuous-time controllers

We propose a novel way for sampled-data implementation (with the zero order hold assumption) of continuous-time controllers for general nonlinear systems. We assume that a continuous-time controller has been designed so that the continuous-time closed-loop satisfies all performance requirements. Then, we use this control law indirectly to compute numerically a sampled-data controller. Our approach exploits a model predictive control (MPC) strategy that minimizes the mismatch between the solutions of the sampled-data model and the continuous-time closed-loop model. We propose a control law and present conditions under which stability and sub-optimality of the closed loop can be proved. We only consider the case of unconstrained MPC. We show that the recent results in [G. Grimm, M.J. Messina, A.R. Teel, S. Tuna, Model predictive control: for want of a local control Lyapunov function, all is not lost, IEEE Trans. Automat. Control 2004, to appear] can be directly used for analysis of stability of our closed-loop system

Continuous-time controller redesign for digital implementation: A trajectory based approach

Given a continuous-time nonlinear closed loop system, we investigate sampled-data feedback laws for which the trajectories of the sampled-data closed loop system converge to the continuous-time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero. We derive necessary and sufficient conditions for the existence of such sampled-data feedback laws and—in case of existence—provide explicit redesign formulas and algorithms for these controllers