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This papers analyzes a class of non-linear additive-increase multiplicative-decrease (AIMD) protocols that are widely deployed in communication networks. It is demonstrated that the use of these protocols guarantee that the system has a unique stable outcome to which it converges geometrically under all starting points. The development is based on a contraction argument and the derivation of explicit bounds on the contraction coefficient of corresponding operators in terms of the network parameters. In particular, bounds on the corresponding rate of convergence are obtained, improving upon known bounds for standard (linear) AIMD networks. [ABSTRACT FROM AUTHOR]

This papers analyzes a class of non-linear additive-increase multiplicative-decrease (AIMD) protocols that are widely deployed in communication networks. It is demonstrated that the use of these protocols guarantee that the system has a unique stable outcome to which it converges geometrically under all starting points. The development is based on a contraction argument and the derivation of explicit bounds on the contraction coefficient of corresponding operators in terms of the network parameters. In particular, bounds on the corresponding rate of convergence are obtained, improving upon known bounds for standard (linear) AIMD networks. [ABSTRACT FROM AUTHOR]

We present a gestural interface for entering text on a mobile device via continuous movements, with control based on feedback from a probabilistic language model. Text is represented by continuous trajectories over a hexagonal tessellation, and entry becomes a manual control task. The language model is used to infer user intentions and provide predictions about future actions, and the local dynamics adapt to reduce effort in entering probable text. This leads to an interface with a stable layout, aiding user learning, but which appropriately supports the user via the probability model. Experimental results demonstrate that the application of this technique reduces variance in gesture trajectories, and is competitive in terms of throughput for mobile devices. This paper provides a practical example of a user interface making uncertainty explicit to the user, and probabilistic feedback from hypothesised goals has general application in many gestural interfaces, and is well-suited to support multimodal interaction. [ABSTRACT FROM AUTHOR]

We apply a constrained Hidden Markov Model architecture to the problem of simultaneous localization and surveying from sensor logs of mobile agents navigating in unknown environments. We show the solution of this problem for the case of one robot and extend our model to the more interesting case of multiple agents, that interact with each other through proximity sensors. Since exact learning in this case becomes exponentially expensive, we develop an approximate method for inference using loopy belief propagation and apply it to the localization and surveying problem with multiple interacting robots. In support of our analysis, we report experimental results showing that with the same amount of data, approximate learning with the interaction signals outperforms exact learning ignoring interactions. [ABSTRACT FROM AUTHOR]

In this chapter, we address the situation where agents need to learn from one another by exchanging learned knowledge. We employ hierarchical Bayesian modelling, which provides a powerful and principled solution. We point out some shortcomings of parametric hierarchical Bayesian modelling and thus focus on a nonparametric approach. Nonparametric hierarchical Bayesian modelling has its roots in Bayesian statistics and, in the form of Dirichlet process mixture modelling, was recently introduced into the machine learning community. In this chapter, we hope to provide an accessible introduction to this particular branch of statistics. We present the standard sampling-based learning algorithms and introduce a particular EM learning approach that leads to efficient and plausible solutions. We illustrate the effectiveness of our approach in context of a recommendation engine where our approach allows the principled combination of content-based and collaborative filtering. [ABSTRACT FROM AUTHOR]

In the last few years some articles have emphasized certain fundamental inconsistencies underlying feedback control theory. The paper of Willems [1] Georgiou and Smith [2], later the works of Makila [3],[4], of Leithead et al. [5] have stressed the inconsistency of standard formalisms of linear time-invariant systems when the signals are double sided and the systems are open loop unstable. We establish a framework for a consistent time domain and frequency domain representation of discrete time linear time-invariant systems and, furthermore, that supports the consistent analysis of discrete time linear time-invariant feedback systems when signals are double sided and the systems are open loop unstable. [ABSTRACT FROM AUTHOR]

We consider a linear system, such as an estimator or a controller, in which several signals are transmitted over wireless communication channels. With the coding and medium access schemes of the communication system fixed, the achievable bit rates are determined by the allocation of communications resources such as transmit powers and bandwidths, to different channels. Assuming conventional uniform quantization and a standard white-noise model for quantization errors, we consider two specific problems. In the first, we assume that the linear system is fixed and address the problem of allocating communication resources to optimize system performance. We observe that this problem is often convex (at least, when we ignore the constraint that individual quantizers have an integral number of bits), hence readily solved. We describe a dual decomposition method for solving these problems that exploits the problem structure. We briefly describe how the integer bit constraints can be handled, and give a bound on how suboptimal these heuristics can be. The second problem we consider is that of jointly allocating communication resources and designing the linear system in order to optimize system performance. This problem is in general not convex. We present an iterative heuristic method based on alternating convex optimization over subsets of variables, which appears to work well in practice. [ABSTRACT FROM AUTHOR]

We present a geometrical approach for designing robust minimum variance (RMV) beamformers against steering vector uncertainties. Conventional techniques enclose the uncertainties with a convex set; the antenna weights are then designed to minimize the maximum array output variance over this set. In contrast, we propose to cover the uncertainty by a second-order cone (SOC). The optimization problem, with optional robust interference rejection constraints, then reduces to the minimization of the array output variance over the intersection of the SOC and a hyperplane. This is cast into a standard second-order cone programming (SOCP) problem and solved efficiently. We study the computationally efficient case wherein the uncertainties are embedded in complex-plane trapezoids. The idea is then extended to arbitrary uncertainty geometries. Effectiveness of the proposed approach over other schemes and its fast convergence in signal power estimation are demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

In this paper we present a new steering controller for cars equipped with 4-wheel steer-by-wire. The controller commands the front and rear steering angles with the objective of tracking reference yaw rate and sideslip signals corresponding to the desired vehicle handling behaviour. The structure of the controller is based on a simplified model of the lateral dynamics of 4-wheel steering cars. We show that the proposed structure facilitates the design of a robust steering controller valid for varying vehicle speed. The controller, which has been designed using classical techniques according to the Individual Channel Design (ICD) methodology, incorporates an anti-windup scheme to mitigate the effects of the saturation of the rear steering actuators. We analyse the robust stability of the resulting non-linear control system and present simulation results illustrating the performance of the controller on a detailed non-linear vehicle model. [ABSTRACT FROM AUTHOR]

Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of nonlinear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coefficients to be optimized. This chapter illustrates possible application of Gaussian process models within model predictive control. The extra information provided by the Gaussian process model is used in predictive control, where optimization of the control signal takes the variance information into account. The predictive control principle is demonstrated via the control of a pH process benchmark. [ABSTRACT FROM AUTHOR]

With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the covariance function of the process, we can evaluate these moments exactly or approximately (within a Taylor approximation of the covariance function). We apply our results to the iterative multiple-step ahead prediction of non-linear dynamic systems with propagation of the uncertainty as we predict ahead in time. Finally, using numerical examples, we compare the Gaussian approximation to the numerical approximation of the true predictive distribution by simple Monte-Carlo. [ABSTRACT FROM AUTHOR]

Gaussian Process prior models, as used in Bayesian non-parametric statistical models methodology are applied to implement a nonlinear adaptive control law. The expected value of a quadratic cost function is minimised, without ignoring the variance of the model predictions. This leads to implicit regularisation of the control signal (caution) in areas of high uncertainty. As a consequence, the controller has dual features, since it both tracks a reference signal and learns a model of the system from observed responses. The general method and its unique features are illustrated on simulation examples. [ABSTRACT FROM AUTHOR]

Kernel-based non-parametric models have been applied widely over recent years. However, the associated computational complexity imposes limitations on the applicability of those methods to problems with large data-sets. In this paper we develop a filtering approach based on a Gaussian process regression model. The idea is to generate a small-dimensional set of filtered data that keeps a high proportion of the information contained in the original large data-set. Model learning and prediction are based on the filtered data, thereby decreasing the computational burden dramatically. Keywords: Filtering transformation, Gaussian process regression model, Karhunen-Loeve expansion, Kernel-based non-parametric models, Principal component analysis. [ABSTRACT FROM AUTHOR]

While there is strong motivation for using Gaussian Processes (GPs) due to their excellent performance in regression and classification problems, their computational complexity makes them impractical when the size of the training set exceeds a few thousand cases. This has motivated the recent proliferation of a number of cost-effective approximations to GPs, both for classification and for regression. In this paper we analyze one popular approximation to GPs for regression: the reduced rank approximation. While generally GPs are equivalent to infinite linear models, we show that Reduced Rank Gaussian Processes (RRGPs) are equivalent to finite sparse linear models. We also introduce the concept of degenerate GPs and show that they correspond to inappropriate priors. We show how to modify the RRGP to prevent it from being degenerate at test time. Training RRGPs consists both in learning the covariance function hyperparameters and the support set. We propose a method for learning hyperparameters for a given support set. We also review the Sparse Greedy GP (SGGP) approximation (Smola and Bartlett, 2001), which is a way of learning the support set for given hyperparameters based on approximating the posterior. We propose an alternative method to the SGGP that has better generalization capabilities. Finally we make experiments to compare the different ways of training a RRGP. We provide some Matlab code for learning RRGPs. [ABSTRACT FROM AUTHOR]

This chapter presents a review of the explicit approaches to optimal control. It is organized as follows. Section 1 gives a summary of the main results of the optimal control theory. Section 2 presents briefly the methods for unconstrained optimal state feedback control of linear systems. Sections 3, 4 and 5 consider in details the explicit methods for constrained linear quadratic regulation (LQR) together with several examples. The main motivation behind the explicit solution is that it avoids the need for real-time optimization, and thus allows implementation at high sampling frequencies in real-time systems with high reliability and low software complexity. These sections include formulation of the constrained LQR problem, summary of the implicit approaches, basics of the model predictive control (MPC), description of the exact and the approximate approaches to explicit solution of MPC problems and the experimental evaluation of explicit MPC controller performance for laboratory gas-liquid separation plant. [ABSTRACT FROM AUTHOR]

Recent research on switched and hybrid systems has resulted in a renewed interest in determining conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems. While efficient numerical solutions to this problem have existed for some time, compact analytical conditions for determining whether or not such a function exists for a finite number of systems have yet to be obtained. In this paper we present a geometric approach to this problem. By making a simplifying assumption we obtain a compact time-domain condition for the existence of such a function for a pair of LTI systems. We show a number of new and classical Lyapunov results can be obtained using our framework. In particular, we demonstrate that our results can be used to obtain compact time-domain versions of the SISO Kalman-Yacubovich-Popov lemma, the Circle Criterion, and stability multiplier criteria. Finally, we conclude by posing a number of open questions that arise as a result of our approach. [ABSTRACT FROM AUTHOR]

Revolutionary advances in technology have generated numerous complex systems that have become integral parts of our socioeconomic environment. The study of such systems - those which contain many interacting parts - is currently attracting considerable attention. In this paper, the author retraces his personal attempts, over a period of four decades, to develop simple models for adaptation, learning, identification and control using artificial neural networks, and hybrid systems, and goes on to describe how they are providing insights into dealing with complex interconnected systems. [ABSTRACT FROM AUTHOR]