A Comparison of Balanced Truncation Methods for Closed Loop Systems

Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system

The generation of dual wavelength pulse fiber laser using fiber bragg grating

A stable simple generation of dual wavelength pulse fiber laser on experimental method is proposed and demonstrated by using Figure eight circuit diagram. The generation of dual wavelength pulse fiber laser was proposed using fiber Bragg gratings (FBGs) with two different central wavelengths which are 1550 nm and 1560 nm. At 600 mA (27.78 dBm) of laser diode, the stability of dual wavelength pulse fiber laser appears on 1550 nm and 1560 nm with the respective peak powers of -54.03 dBm and -58.00 dBm. The wavelength spacing of the spectrum is about 10 nm while the signal noise to ratio (SNR) for both peaks are about 8.23 dBm and 9.67 dBm. In addition, the repetition rate is 2.878 MHz with corresponding pulse spacing of about 0.5 μs, is recorded

Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated

FINITE-DIMENSIONAL APPROXIMATION FOR OPTIMAL FIXED-ORDER COMPENSATION OF DISTRIBUTED PARAMETER SYSTEMS

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57814/1/Finite-DimensionalapproximationforOptimalFixed-OrdercompensationofDistributedParameterSystems.pd

Automatic LQR Tuning Based on Gaussian Process Global Optimization

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four-dimensional tuning problems highlight the method's potential for automatic controller tuning on robotic platforms.Comment: 8 pages, 5 figures, to appear in IEEE 2016 International Conference on Robotics and Automation. Video demonstration of the experiments available at https://am.is.tuebingen.mpg.de/publications/marco_icra_201

Passive Dynamics in Mean Field Control

Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in distributed control. This paper considers a particular randomized distributed control architecture introduced in our own recent work. In numerical results it was found that the associated mean-field model had attractive properties for purposes of control. In particular, when viewed as an input-output system, its linearization was found to be minimum phase. In this paper we take a closer look at the control model. The results are summarized as follows: (i) The Markov Decision Process framework of Todorov is extended to continuous time models, in which the "control cost" is based on relative entropy. This is the basis of the construction of a family of controlled Markovian generators. (ii) A decentralized control architecture is proposed in which each agent evolves as a controlled Markov process. A central authority broadcasts a common control signal to each agent. The central authority chooses this signal based on an aggregate scalar output of the Markovian agents. (iii) Provided the control-free system is a reversible Markov process, the following identity holds for the linearization, $$\text{Real} (G(j\omega)) = \text{PSD}_Y(\omega)\ge 0, \quad \omega\in\Re,$$ where the right hand side denotes the power spectral density for the output of any one of the individual (control-free) Markov processes.Comment: To appear IEEE CDC, 201