Sensor data scheduling for linear quadratic Gaussian control with full state feedback

Networked control systems (NCSs) have attracted much attention in the past decade due to their many advantages and growing number of applications. Different than classic control systems, resources in NCSs, such as network bandwidth and communication energy, are often limited, which degrade the closed-loop system performance and may even cause the system to become unstable. Seeking a desired trade-off between the closed-loop system performance and the limited resources is thus one heated area of research. In this paper, we analyze the trade-off between the sensor-to-controller communication rate and the closed-loop system performance indexed by the conventional LQG control cost. We present and compare several sensor data schedules, and demonstrate that two event-based sensor data schedules provide better trade-off than an optimal offline schedule. Simulation examples are provided to illustrate the theories developed in the paper. © 2012 AACC American Automatic Control Council).

Linear quadratic game and non-cooperative predictive methods for potential application to modelling driver-AFS interactive steering control

This paper is concerned with the modelling of strategic interactions between the human driver and the vehicle active front steering (AFS) controller in a path-following task where the two controllers hold different target paths. The work is aimed at extending the use of mathematical models in representing driver steering behaviour in complicated driving situations. Two game theoretic approaches, namely linear quadratic game and non-cooperative model predictive control (non-cooperative MPC), are used for developing the driver-AFS interactive steering control model. For each approach, the open-loop Nash steering control solution is derived; the influences of the path-following weights, preview and control horizons, driver time delay and arm neuromuscular system (NMS) dynamics are investigated, and the CPU time consumed is recorded. It is found that the two approaches give identical time histories as well as control gains, while the non-cooperative MPC method uses much less CPU time. Specifically, it is observed that the introduction of weight on the integral of vehicle lateral displacement error helps to eliminate the steady-state path-following error; the increase in preview horizon and NMS natural frequency and the decline in time delay and NMS damping ratio improve the path-following accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

Fixed-lag blind equalization and sequence estimation in digital communications systems using sequential importance sampling

We present methods for fixed-lag smoothing using Sequential Importance sampling (SIS) on a discrete non-linear, non-Gaussian state space system with unknown parameters. Our particular application is in the field of digital communication systems. Each input data point is taken from a finite set of symbols. We represent transmission media as a fixed filter with a finite impulse response (FIR), hence a discrete state-space system is formed. Conventional Markov chain Monte Carlo (MCMC) techniques such as the Gibbs sampler are unsuitable for this task because they can only perform processing on a batch of data. Data arrives sequentially, so it would seem sensible to process it in this way. In addition, many communication systems are interactive, so there is a maximum level of latency that can be tolerated before a symbol is decoded. We will demonstrate this method by simulation and compare its performance to existing techniques.

Monte Carlo filtering and smoothing with application to time-varying spectral estimation

We develop methods for performing filtering and smoothing in non-linear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Forward Smoothing Using Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively. Essentially, it is an on-line or "forward only" implementation of a forward filtering backward smoothing SMC algorithm proposed by Doucet, Godsill and Andrieu (2000). Compared to the standard \emph{path space} SMC estimator whose asymptotic variance increases quadratically with time even under favorable mixing assumptions, the non asymptotic variance of the proposed SMC estimator only increases linearly with time. We show how this allows us to perform recursive parameter estimation using an SMC implementation of an on-line version of the Expectation-Maximization algorithm which does not suffer from the particle path degeneracy problem.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

Monte Carlo approaches to nonlinear optimal control

This paper explores the use of Monte Carlo techniques in deterministic nonlinear optimal control. Inter-dimensional population Markov Chain Monte Carlo (MCMC) techniques are proposed to solve the nonlinear optimal control problem. The linear quadratic and Acrobot problems are studied to demonstrate the successful application of the relevant techniques.

Reinforcement learning with reference tracking control in continuous state spaces

The contribution described in this paper is an algorithm for learning nonlinear, reference tracking, control policies given no prior knowledge of the dynamical system and limited interaction with the system through the learning process. Concepts from the field of reinforcement learning, Bayesian statistics and classical control have been brought together in the formulation of this algorithm which can be viewed as a form of indirect self tuning regulator. On the task of reference tracking using a simulated inverted pendulum it was shown to yield generally improved performance on the best controller derived from the standard linear quadratic method using only 30 s of total interaction with the system. Finally, the algorithm was shown to work on the simulated double pendulum proving its ability to solve nontrivial control tasks. © 2011 IEEE.

Output disturbance rejection using parallel model predictive control

The solution time of the online optimization problems inherent to Model Predictive Control (MPC) can become a critical limitation when working in embedded systems. One proposed approach to reduce the solution time is to split the optimization problem into a number of reduced order problems, solve such reduced order problems in parallel and selecting the solution which minimises a global cost function. This approach is known as Parallel MPC. The potential capabilities of disturbance rejection are introduced using a simulation example. The algorithm is implemented in a linearised model of a Boeing 747-200 under nominal flight conditions and with an induced wind disturbance. Under significant output disturbances Parallel MPC provides a significant improvement in performance when compared to Multiplexed MPC (MMPC) and Linear Quadratic Synchronous MPC (SMPC). © 2013 IEEE.