ℓasso MPC: Smart regulation of over-actuated systems

In this paper, a novel MPC strategy is proposed, and referred to as asso MPC. The new paradigm features an 1-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. This cost choice is motivated by the successful development of LASSO theory in signal processing and machine learning. In the latter fields, sum-of-norms regularisation have shown a strong capability to provide robust and sparse solutions for system identification and feature selection. In this paper, a discrete-time dual-mode asso MPC is formulated, and its stability is proven by application of standard MPC arguments. The controller is then tested for the problem of ship course keeping and roll reduction with rudder and fins, in a directional stochastic sea. Simulations show the asso MPC to inherit positive features from its corresponding regressor: extreme reduction of decision variables' magnitude, namely, actuators' magnitude (or variations), with a finite energy error, being particularly promising for over-actuated systems. © 2012 AACC American Automatic Control Council).

Modelling and control of nonlinear systems using Gaussian processes with partial model information

Gaussian processes are gaining increasing popularity among the control community, in particular for the modelling of discrete time state space systems. However, it has not been clear how to incorporate model information, in the form of known state relationships, when using a Gaussian process as a predictive model. An obvious example of known prior information is position and velocity related states. Incorporation of such information would be beneficial both computationally and for faster dynamics learning. This paper introduces a method of achieving this, yielding faster dynamics learning and a reduction in computational effort from O(Dn2) to O((D - F)n2) in the prediction stage for a system with D states, F known state relationships and n observations. The effectiveness of the method is demonstrated through its inclusion in the PILCO learning algorithm with application to the swing-up and balance of a torque-limited pendulum and the balancing of a robotic unicycle in simulation. © 2012 IEEE.

Quantitative convergence analysis of multi-agent systems

We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions of contractiveness and (weak) connectedness (across an interval.) Convergence is shown to be exponential when either the system or the function characterizing the contraction is linear. Copyright © 2007 IFAC.

Adapting data processing to compare model and experiment accurately: A discrete element model and magnetic resonance measurements of a 3d cylindrical fluidized bed

Discrete element modeling is being used increasingly to simulate flow in fluidized beds. These models require complex measurement techniques to provide validation for the approximations inherent in the model. This paper introduces the idea of modeling the experiment to ensure that the validation is accurate. Specifically, a 3D, cylindrical gas-fluidized bed was simulated using a discrete element model (DEM) for particle motion coupled with computational fluid dynamics (CFD) to describe the flow of gas. The results for time-averaged, axial velocity during bubbling fluidization were compared with those from magnetic resonance (MR) experiments made on the bed. The DEM-CFD data were postprocessed with various methods to produce time-averaged velocity maps for comparison with the MR results, including a method which closely matched the pulse sequence and data processing procedure used in the MR experiments. The DEM-CFD results processed with the MR-type time-averaging closely matched experimental MR results, validating the DEM-CFD model. Analysis of different averaging procedures confirmed that MR time-averages of dynamic systems correspond to particle-weighted averaging, rather than frame-weighted averaging, and also demonstrated that the use of Gaussian slices in MR imaging of dynamic systems is valid. © 2013 American Chemical Society.

Trajectory control based on discrete full-range dynamics

There has been an increasing interest in the use of mechanical dynamics, (e.g., assive, Elastic, And viscous dynamics) for energy efficient and agile control of robotic systems. Despite the impressive demonstrations of behavioural performance, The mechanical dynamics of this class of robotic systems is still very limited as compared to those of biological systems. For example, Passive dynamic walkers are not capable of generating joint torques to compensate for disturbances from complex environments. In order to tackle such a discrepancy between biological and artificial systems, We present the concept and design of an adaptive clutch mechanism that discretely covers the full-range of dynamics. As a result, The system is capable of a large variety of joint operations, including dynamic switching among passive, actuated and rigid modes. The main innovation of this paper is the framework and algorithm developed for controlling the trajectory of such joint. We present different control strategies that exploit passive dynamics. Simulation results demonstrate a significant improvement in motion control with respect to the speed of motion and energy efficiency. The actuator is implemented in a simple pendulum platform to quantitatively evaluate this novel approach.

Coalition and distribution in fuzzy dynamic supply chain systems

In this paper, two models of coalition and income's distribution in FSCS (fuzzy supply chain systems) are proposed based on the fuzzy set theory and fuzzy cooperative game theory. The fuzzy dynamic coalition choice's recursive equations are constructed in terms of sup-t composition of fuzzy relations, where t is a triangular norm. The existence of the fuzzy relations in FSCS is also proved. On the other hand, the approaches to ascertain the fuzzy coalition through the choice's recursive equations and distribute the fuzzy income in FSCS by the fuzzy Shapley values are also given. These models are discussed in two parts: the fuzzy dynamic coalition choice of different units in FSCS; the fuzzy income's distribution model among different participators in the same coalition. Furthermore, numerical examples are given aiming at illustrating these models., and the results show that these models are feasible and validity in FSCS.

AN EFFICIENT ITERATIVE DFT-BASED CHANNEL ESTIMATION FOR MIMO-OFDM SYSTEMS ON MULTIPATH CHANNELS

In this paper, an efficient iterative discrete Fourier transform (DFT) -based channel estimator with good performance for multiple-input and multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems such as IEEE 802.11n which retain some sub-carriers as null sub-carriers (or virtual carriers) is proposed. In order to eliminate the mean-square error (MSE) floor effect existed in conventional DFT-based channel estimators, we proposed a low-complexity method to detect the significant channel impulse response (CIR) taps, which neither need any statistical channel information nor a predetermined threshold value. Analysis and simulation results show that the proposed method has much better performance than conventional DFT-based channel estimators and without MSE floor effect.

2-DELTA-FUNCTION GENERALIZED PLASMA POLE MODEL FOR 1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES IN MANY-ELECTRON SYSTEMS

To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-delta-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single delta-function GPP model has the drawback of over simplifications and for the crystals without the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-delta GPP model is an optimization of the two approaches. We analyze the two-delta GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these delta-functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.

A discrete square global grid system based on the parallels plane projection

Knowledge Innovation Project of Chinese Academy of Sciences [KZCX3-SW-347]; National Science Fund for Distinguished Young Scholar [40225004]

Switching Between Discrete and Continuous Process Models to Predict Molecular Genetic Activity

Two kinds of process models have been used in programs that reason about change: Discrete and continuous models. We describe the design and implementation of a qualitative simulator, PEPTIDE, which uses both kinds of process models to predict the behavior of molecular energetic systems. The program uses a discrete process model to simulate both situations involving abrupt changes in quantities and the actions of small numbers of molecules. It uses a continuous process model to predict gradual changes in quantities. A novel technique, called aggregation, allows the simulator to switch between theses models through the recognition and summary of cycles. The flexibility of PEPTIDE's aggregator allows the program to detect cycles within cycles and predict the behavior of complex situations.

Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

Reuseable Silicon IP Cores for Discrete Wavelet Transform Applications

Architectures and methods for the rapid design of silicon cores for implementing discrete wavelet transforms over a wide range of specifications are described. These architectures are efficient, modular, scalable, and cover orthonormal and biorthogonal wavelet transform families. They offer efficient hardware utilization by exploiting a number of core wavelet filter properties and allow the creation of silicon designs that are highly parameterized, including in terms of wavelet type and wordlengths. Control circuitry is embedded within these systems allowing them to be cascaded for any desired level of decomposition without any interface glue logic. The time to produce chip designs for a specific wavelet application is typically less than a day and these are comparable in area and performance to handcrafted designs. They are also portable across a wide range of silicon foundries and suitable for field programmable gate array and programmable logic data implementation. The approach described has also been extended to wavelet packet transforms.

Wireless networked control systems with QoS-based sampling

Closing feedback loops using an IEEE 802.11b ad hoc wireless communication network incurs many challenges sensitivity to varying channel conditions and lower physical transmission rates tend to limit the bandwidth of the communication channel. Given that the bandwidth usage and control performance are linked, a method of adapting the sampling interval based on an 'a priori', static sampling policy has been proposed and, more significantly, assuring stability in the mean square sense using discrete-time Markov jump linear system theory. Practical issues including current limitations of the 802.11 b protocol, the sampling policy and stability are highlighted. Simulation results on a cart-mounted inverted pendulum show that closed-loop stability can be improved using sample rate adaptation and that the control design criteria can be met in the presence of channel errors and severe channel contention.