Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Analysis of an LMS linear equalizer for fading channels in decision directed mode

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer in decision directed mode (DD-LMS-LE). We study how well this equalizer tracks the optimal Wiener equalizer. Initially we study a fixed channel.For a fixed channel, we obtain the existence of DD attractors near the Wiener filter at high SNRs using an ODE (Ordinary Differential Equation) approximating the DD-LMS-LE. We also show, via examples, that the DD attractors may not be close to the Wiener filters at low SNRs. Next we study a time varying fading channel modeled by an Auto-regressive (AR) process of order 2. The DD-LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs. We show via examples that the LMS equalizer ODE show tracks the ODE corresponding to the instantaneous Wiener filter when the SNR is high. This may not happen at low SNRs.

Tracking performance of an LMS-Linear Equalizer for fading channels

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer. We study how well this equalizer tracks the optimal Wiener equalizer. We model the channel by an Auto-regressive (AR) process. Then the LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs (ordinary differential equations). Using these ODEs, the error between the LMS equalizer and the instantaneous Wiener filter is shown to decay exponentially/polynomially to zero unless the channel is marginally stable in which case the convergence may not hold.Using the same ODEs, we also show that the corresponding Mean Square Error (MSE) converges towards minimum MSE(MMSE) at the same rate for a stable channel. We further show that the difference between the MSE and the MMSE does not explode with time even when the channel is unstable. Finally we obtain an optimum step size for the linear equalizer in terms of the AR parameters, whenever the error decay is exponential.

Time-Optimal Convergence to a Rectilinear Path in the Presence of Wind

This paper considers the problem of determining the time-optimal path of a fixed-wing Miniature Air Vehicle (MAV), in the presence of wind. The MAV, which is subject to a bounded turn rate, is required to eventually converge to a straight line starting from a known initial position and orientation. Earlier work in the literature uses Pontryagin's Minimum Principle (PMP) to solve this problem only for the no-wind case. In contrast, the present work uses a geometric approach to solve the problem completely in the presence of wind. In addition, it also shows how PMP can be used to partially solve the problem. Using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for cases with steady and time-varying wind. Some issues on real-time path planning are also addressed.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Robust multiplexed model predictive control

This paper extends the recently developed multiplexed model predictive control (MMPC) concept to ensure satisfaction of hard constraints despite the action of persistent, unknown but bounded disturbances. MMPC uses asynchronous control moves on each input channel instead of synchronised moves on all channels. It offers reduced computation, by dividing the online optimisation into a smaller problem for each channel, and potential performance improvements, as the response to a disturbance is quicker, albeit via only one channel. Robustness to disturbances is introduced using the constraint tightening approach, tailored to suit the asynchronous updates of MMPC and the resulting time-varying optimisations. Numerical results are presented, involving a simple mechanical example and an aircraft control example, showing the potential computational and performance benefits of the new robust MMPC.

Time Variation in an Optimal Asymmetric Preference Monetary Policy Model

This paper considers a time varying parameter extension of the Ruge-Murcia (2003, 2004) model to explore whether some of the variation in parameter estimates seen in the literature could arise from this source. A time varying value for the unemployment volatility parameter can be motivated through several means including variation in the slope of the Phillips curve or variation in the preferences of the monetary authority.We show that allowing time variation for the coefficient on the unemployment volatility parameter improves the model fit and it helps to provide an explanation of inflation bias based on asymmetric central banker preferences, which is consistent across subsamples.

Modelo de canal para caracterizar la señal dispersada por un parque eólico en la banda UHF e influencia sobre la calidad de servicio de DVB-T

288 p. : il.

Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Solutions for New Terrestrial Broadcasting Systems Offering Simultaneously Stationary and Mobile Services

221 p.

Time-frequency spectral estimation of speech

In recent years there has been a growing interest amongst the speech research community into the use of spectral estimators which circumvent the traditional quasi-stationary assumption and provide greater time-frequency (t-f) resolution than conventional spectral estimators, such as the short time Fourier power spectrum (STFPS). One distribution in particular, the Wigner distribution (WD), has attracted considerable interest. However, experimental studies have indicated that, despite its improved t-f resolution, employing the WD as the front end of speech recognition system actually reduces recognition performance; only by explicitly re-introducing t-f smoothing into the WD are recognition rates improved. In this paper we provide an explanation for these findings. By treating the spectral estimation problem as one of optimization of a bias variance trade off, we show why additional t-f smoothing improves recognition rates, despite reducing the t-f resolution of the spectral estimator. A practical adaptive smoothing algorithm is presented, whicy attempts to match the degree of smoothing introduced into the WD with the time varying quasi-stationary regions within the speech waveform. The recognition performance of the resulting adaptively smoothed estimator is found to be comparable to that of conventional filterbank estimators, yet the average temporal sampling rate of the resulting spectral vectors is reduced by around a factor of 10. © 1992.

The nonlinear heat release response of stratified lean-premixed flames to acoustic velocity oscillations

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to high-amplitude acoustic forcing in a laboratory-scale stratified burner operated with CH4 and air at atmospheric pressure. The double-swirler, double-channel annular burner was specially designed to generate high-amplitude acoustic velocity oscillations and a radial equivalence ratio gradient at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the response are not considered in the present investigation. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a constant temperature anemometer and photomultiplier tubes with narrow-band OH*/CH* interference filters. Time-averaged and phase-synchronized CH* chemiluminescence intensities were measured using an intensified CCD camera. The measurements show that flame stabilization mechanisms vary depending on equivalence ratio gradients for a constant global equivalence ratio (φg=0.60). Under uniformly premixed conditions, an enveloped M-shaped flame is observed. In contrast, under stratified conditions, a dihedral V-flame and a toroidal detached flame develop in the outer stream and inner stream fuel enrichment cases, respectively. The modification of the stabilization mechanism has a significant impact on the nonlinear response of stratified flames to high-amplitude acoustic forcing (u'/U∼0.45 and f=60, 160Hz). Outer stream enrichment tends to improve the flame's stiffness with respect to incident acoustic/vortical disturbances, whereas inner stream stratification tends to enhance the nonlinear flame dynamics, as manifested by the complex interaction between the swirl flame and large-scale coherent vortices with different length scales and shedding points. It was found that the behavior of the measured flame describing functions (FDF), which depend on radial fuel stratification, are well correlated with previous measurements of the intensity of self-excited combustion instabilities in the stratified swirl burner. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, its effect on flame location and the interaction with unsteady flow structures. © 2011 The Combustion Institute.

Effects of nonuniform reactant stoichiometry on combustion instability

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to acoustic forcing in a laboratory-scale stratified burner. The double-swirler, double-channel annular burner was specially designed to generate acoustic velocity oscillations and radial fuel stratification at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the flame response are not considered. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a hot wire anemometer and photomultiplier tubes with narrowband OH*/CH* interference filters. Time-averaged CH* chemiluminescence intensities were measured using an intensified CCD camera. Results show that flame stabilization mechanisms vary depending on stratification ratio for a constant global equivalence ratio. For a uniformly premixed condition, an enveloped M-shaped flame is observed. For stratified conditions, however, a dihedral V-flame and a detached flame are developed for outer stream and inner stream fuel enrichment cases, respectively. Flame transfer function (FTF) measurement results indicate that a V-shaped flame tends to damp incident flow oscillations, while a detached flame acts as a strong amplifier relative to the uniformly premixed condition. The phase difference of FTF increases in the presence of stratification. More importantly, the dynamic characteristics obtained from the forced stratified flame measurements are well correlated with unsteady flame behavior under limit-cycle pressure oscillations. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, which has not been well explored to date. Copyright © 2011 by ASME.

Decentralised minimal-time dynamic consensus

This paper considers a group of agents that aim to reach an agreement on individually received time-varying signals by local communication. In contrast to static network averaging problem, the consensus considered in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises a minimal number of local observations of a randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically as suggested by Olshevsky and Tsitsiklis. © 2012 AACC American Automatic Control Council).

A dependent partition-valued process for multitask clustering and time evolving network modelling

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.