Iterative identification and control design using finite-signal-to-noise models

In this paper, a model is said to be validated for control design if using the model-based controller, the closed loop performance of the real plant satisfies a specified performance bound. To improve the model for control design, only closed loop response data is available to deduce a new model of the plant. Hence the procedure described herein involves three steps in each iteration: (i) closed loop identification; (ii) plant model extraction from the closed loop model; (iii) controller design. Thus our criteria for model validation involve both the control design procedure by which the closed loop system performance is evaluated, and the identification procedure by which a new model of the plant is deduced from the closed loop response data. This paper proposes new methods for both parts, and also proposes an iterative algorithm to connect the two parts. To facilitate both the identification and control tasks, the new finite-signal-to-noise (FSN) model of linear systems is utilized. The FSN model allows errors in variables whose noise covariances are proportional to signal covariances. Allowing the signal to noise ratios to be bounded but uncertain, a control theory to guarantee a variance upper bound is developed for the discrete version of this new FSN model. The identification of the closed loop system is accomplished by a new type of q-Markov Cover, adjusted to accommodate the assumed FSN structure of the model. The model of the plant is extracted from the closed loop identification model. This model is then used for control design and the process is repeated until the closed loop performance validates the model. If the iterations produce no such a controller, we say that this specific procedure cannot produce a model valid for control design and the level of the required performance must be reduced.     

Model-based topography estimation in trolling mode atomic force microscopy

In this study, a novel approach based on a modified Kalman filter algorithm is presented to directly estimate and measure the surface topography of samples by trolling mode atomic force microscopy. Trolling mode atomic force microscopy was introduced as an atomic force microscopy alternative to overcome imaging problems in liquid environments by reducing the liquid-resonator interaction forces. In conventional imaging techniques, the time to reach the steady state periodic motion of the oscillating probe restricts scanning speed. To overcome this limitation, we propose a novel imaging technique for trolling mode atomic force microscopy based on the system dynamics model and using the adaptive fading Kalman filter with forgetting factor. In this approach, the sample height is estimated directly without the need for any closed loop controller. As a result, the scanning speed is improved significantly, and topography is obtained more accurately compared to the conventional imaging method. Moreover, the effects of process noise, scanning speed, and parameter uncertainties on the performance of proposed approach are investigated.     

Smoothing algorithms for state–space models

Two-filter smoothing is a principled approach for performing optimal smoothing in non-linear non-Gaussian state–space models where the smoothing distributions are computed through the combination of ‘forward’ and ‘backward’ time filters. The ‘forward’ filter is the standard Bayesian filter but the ‘backward’ filter, generally referred to as the backward information filter, is not a probability measure on the space of the hidden Markov process. In cases where the backward information filter can be computed in closed form, this technical point is not important. However, for general state–space models where there is no closed form expression, this prohibits the use of flexible numerical techniques such as Sequential Monte Carlo (SMC) to approximate the two-filter smoothing formula. We propose here a generalised two-filter smoothing formula which only requires approximating probability distributions and applies to any state–space model, removing the need to make restrictive assumptions used in previous approaches to this problem. SMC algorithms are developed to implement this generalised recursion and we illustrate their performance on various problems.     

Nonlinear modeling and performance analysis of a closed-loop supply chain in the presence of stochastic noise

ABSTRACT

We study four-echelon supply chains consisting of manufacturer, wholesaler, retailer and customer with recovery center as hybrid recycling channels. In order to gain a larger market share, the retailer often takes the sales as a decision-making variable. For this purpose, in this supply chain, the retailer limits the forecast of market demand in future periods with expected logic. It also manages demand by leveraging prices and choosing market. In this paper, first, we investigate the state-space model of this supply chain system and examine the effect of complex dynamic and stochastic noise on the bullwhip effect. We analytically prove that this factor leads to the bullwhip effect. So, first, we filtered the information between nodes with extended Kalman filter after which we regulated the destructive effects of the bullwhip phenomenon by designing a non-linear quadratic Gaussian optimal controller. Eventually, the simulation results indicate the efficiency of the proposed method.     

Wiener Chaos and Nonlinear Filtering

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. The paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.     

A stochastic approach for the optimization of open-loop engine control systems

The operation of sensors and actuators in engine control systems is always affected by errors, which are stochastic in nature. In this paper it is shown that, because of the non-linear interactions between engine performance and control laws in an open-loop engine control system, these errors can give rise to unexpected deviations of control variables, fuel consumption and emissions from the optimal values, which are not predictable in an elementary way.A model for vehicle performance evaluation on a driving cycle is presented, which provides the expected values of fuel consumption and emissions in the case of stochastic errors in sensors and actuators, utilizing only steady-state engine data.The stochastic model is utilized to obtain the optimal control laws; the resultant non-linear constrained minimization problem is solved by an Augmented Lagrangian approach, using a Quasi-Newton technique. The results of the stochastic optimization analysis indicate that significant reductions in performance degradation may be achieved with respect to the solutions provided by the classical deterministic approach.     

The construction of filters in non-linear deterministic systems

The method of residuals (see, e.g. [1–31]) is used to solve the problem of estimation when both object and observations involve noise, and the input determination problem [3–5] is considered. These estimation problems are solved by minimizing a certain functional, and this in turn involves solving a boundary-value problem at each instant of time. Depending on the recurrent method used to solve the relevant family of boundary-value problems, one obtains different representations of optimal non-linear niters for the estimated quantities. The choice of a specific representation depends on the degree to which the object with whose help the filter is being designed is well conditioned. A locally optimal filter of a design similar to that of filters for linear problems is constructed.     

Linear Kalman–Bucy Filter with Autoregressive Signal and Noise

In the Kalman—Bucy filter problem, the observed process consists of the sum of a signal and a noise. The filtration begins at the same moment as the observation process and it is necessary to estimate the signal. As a rule, this problem is studied for the scalar and vector Markovian processes. In this paper, the scalar linear problem is considered for the system in which the signal and noise are not Markovian processes. The signal and noise are independent stationary autoregressive processes with orders of magnitude higher than 1. The recurrent equations for the filter process, its error, and its conditional cross correlations are derived. These recurrent equations use previously found estimates and some last observed data. The optimal definition of the initial data is proposed. The algebraic equations for the limit values of the filter error (the variance) and cross correlations are found. The roots of these equations make possible the conclusions concerning the criterion of the filter process convergence. Some examples in which the filter process converges and does not converge are given. The Monte Carlo method is used to control the theoretical formulas for the filter and its error.     

Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time inhomogeneity of the jump size density. We apply the explicit formula to obtain the optimal filter for the corresponding filtering problem.     

A Benders decomposition algorithm for a multi-area,multi-stage integrated resource planning in power systems

The aim of this paper is to propose an integrated model for resource planning in power systems by taking into account both supply and demand sides options simultaneously. At supply-side, investment in generation capacity and transmission lines is considered. Demand side management (DSM) technologies are also incorporated to correct the shape of the load duration curve in terms of peak clipping and load shifting programmes. A mixed integer non-linear programming model is developed to find the optimal location and timing of electricity generation/transmission as well as DSM options. To solve the resulting complex model, nonlinearity caused by transmission loss terms are first eliminated using the piecewise linearization technique. Then, a Benders decomposition (BD) algorithm is developed to solve the linearized model. The performance of the proposed BD algorithm is validated via applying it to the 6-bus Garver test system and a modified 21-bus IEEE reliability test system.     

Optimal control of Markovian jump processes with partial information and applications to a parallel queueing model

We consider a stochastic control problem over an infinite horizon where the state process is influenced by an unobservable environment process. In particular, the Hidden-Markov-model and the Bayesian model are included. This model under partial information is transformed into an equivalent one with complete information by using the well-known filter technique. In particular, the optimal controls and the value functions of the original and the transformed problem are the same. An explicit representation of the filter process which is a piecewise-deterministic process, is also given. Then we propose two solution techniques for the transformed model. First, a generalized verification technique (with a generalized Hamilton–Jacobi–Bellman equation) is formulated where the strict differentiability of the value function is weaken to local Lipschitz continuity. Second, we present a discrete-time Markovian decision model by which we are able to compute an optimal control of our given problem. In this context we are also able to state a general existence result for optimal controls. The power of both solution techniques is finally demonstrated for a parallel queueing model with unknown service rates. In particular, the filter process is discussed in detail, the value function is explicitly computed and the optimal control is completely characterized in the symmetric case.     

Convolution kernels implementation of cardinalized probability hypothesis density filter

The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.     

High-Gain Scheduling of the Proportional-Integral-Observer

Estimation of states and unknown inputs simultaneously can be done by Proportional-Integral-Observer (PIO). This observer is used in nonlinear and robust control. It has additional integral feedback loop in comparison with the usual Luenberger observer. Increasing the gain of this observer the performance would be increased, however due to this high gain the performance is influenced by measurement noise. Advanced PI-Observer (API) algorithm is a method which is used for scheduling the optimal gain of PI-Observer based on the cost function and by using a bank of PI-Observer. In this contribution the proposed method obtains relative optimal gain by using a given cost function. Afterwards the absolute optimal gain is computed by changing the design parameters at each step based on the desired performance criteria. The absolute optimal gain is found instead of relative optimal gain in comparison with the API-Observer. Simulation results estimating contact forces acting to a vibrating elastic beam based on indirect measurements illustrate the improvement of the proposed method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

利用循环展开最大化软件流水线性能

软件流水线通过重叠连续的循环实体来实现有效的精细调度．然而,其性能可能受限制于循环里缺乏足够的并行操作或者资源需求．‘‘先展开后调度”技术在进行软件流水线调度之前先展开循环,从而能够发现更多的并行操作和充分利用关键资源．研究循环展开如何影响软件流水线的性能和资源利用,并进一步提出如何选择优化的循环展开次数．     

Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors

We consider the nonlinear filtering problem where the observation noise process is n-ple Markov Gaussian. A Kallianpur–Striebel type Bayes formula for the optimal filter is obtained.     

Optimization approach to the design of frequency sampling filters

Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.This work was partially funded by The National Supercomputing Center for Energy and the Environment, University of Nevada Las Vegas, Las Vegas, Nevada and by NSF Grant MIP-9200581.     

Noise analysis and suppression method in attitude determination using the global positioning system (GPS)

A noise suppression method is developed for attitude determination using the global positioning system. The influence of noise on attitude determination application is analyzed to determine the relationship of errors. In order to suppress the noise, the total least squares method is utilized for double difference carrier phase measurements and unit vectors between satellites and antennas. Experimental results indicate that compared to the traditional least squares method without noise suppression, the accuracy of the measurement of attitude angles is increased by about 30-50%. The increased computation time of this method does not significantly influence the real time performance for land vehicle application.     

Optimal Noise Rejection in Structural Analysis by Means of Generalized Sampled-Data Hold Functions

In this paper, a technique for optimal noise rejection, based on generalized sampled-data hold functions is applied to the control of civil engineering structures. The technique consists in suitably modulating the sampled outputs of the system under control by periodically varying functions in order to attenuate the effect of the disturbances on the system states to an acceptable level, by minimizing a quadratic cost function. This minimization is performed by feeding back the outputs of the system, which are assumed to be corrupted by measurement noise. Moreover, in the present paper, the robustness properties of the GSHF based optimal regulator is analyzed and guaranteed stability margins, expressed in terms of elementary cost and system matrices, are proposed for such a type of optimal regulators. The effectiveness of the method is demonstrated by various simulation results. The results of the paper can be used to assess the detrimental effect of noise on the closed-loop system and the tradeoff involved in assuring good sampled-data performance and sufficient robustness.     

Finite dimensional optimal filters for a class of ltô- processes with jumping parameters

We consider a finite state Markov process θ, feeding the coefficients of a linear Itô-equation with state ξ. The θ-process is observed in white noise, and it is shown that the optimal nonlinear filter for ξ, is of finite dimension. We also derive finite dimensional equations for optimal prediction and smoothing.     

Filtering Problem for Discrete Volterra Equations with Combined Disturbances

Abstract

A minimax filtering problem for discrete Volterra equations with combined noise models is considered. The combined models are defined as the sums of uncertain bounded deterministic functions and stochastic white noises. However, the corresponding variational problem turns out to be very difficult for direct solution. Therefore, simplified filtering algorithms are developed. The levels of nonoptimality for these simplified algorithms are introduced as the ratios of the filtering performances for the simplified and optimal estimators.

In opposite to the original variational problem, these levels can be easily evaluated numerically. Thus, simple filtering algorithms with guaranteed performance are obtained. Numerical experiments confirm the efficiency of our approach.