Samer S. Saab

On the P-type learning control

Sufficient conditions for the robustness and convergence of P-type learning control algorithms for a class of time-varying, nonlinear systems are presented. The authors prove the uniform boundedness of the system state and the input control with respect to the existence of errors of initialization, measurement noises, and fluctuations of system dynamics. Furthermore, the system output converges uniformly to the desired one in absence of all disturbances. Finally, specialization of the results to linear systems are presented. >

Univariate modeling and forecasting of energy consumption : the case of electricity in Lebanon

In Lebanon, electric power is becoming the main energy form relied upon in all economic sectors of the country. Also, the time series of electrical energy consumption in Lebanon is unique due to intermittent power outages and increasing demand. Given these facts, it is critical to model and forecast electrical energy consumption. The aim of this study is to investigate different univariate-modeling methodologies and try, at least, a one-step ahead forecast for monthly electric energy consumption in Lebanon. Three univariate models are used, namely, the autoregressive, the autoregressive integrated moving average (ARIMA) and a novel configuration combining an AR(1) with a highpass filter. The forecasting performance of each model is assessed using different measures. The AR(1)/highpass filter model yields the best forecast for this peculiar energy data.

On a discrete-time stochastic learning control algorithm

The learning gain, for a selected learning algorithm, is derived based on minimizing the trace of the input error covariance matrix for linear time-varying systems. It is shown that, if the product of the input/output coupling matrices is a full-column rank, then the input error covariance matrix converges uniformly to zero in the presence of uncorrelated random disturbances. However, the state error covariance matrix converges uniformly to zero in presence of measurement noise. Moreover, it is shown that, if a certain condition is met, then the knowledge of the state coupling matrix is not needed to apply the proposed stochastic algorithm. The proposed algorithm is shown to suppress a class of nonlinear and repetitive state disturbance. The application of this algorithm to a class of nonlinear systems is also considered. A numerical example is included to illustrate the performance of the algorithm.

A discrete-time learning control algorithm for a class of linear time-invariant systems

A discretized version of the D-type learning control algorithm is presented for a MIMO linear discrete-time system. A necessary and sufficient condition for uniform convergence of the proposed learning algorithm is presented. Then, we prove that the same condition is sufficient for the global robustness of the proposed learning algorithm to state disturbances, measurement noise at the output, and reinitialization error are present at each iteration. A numerical example is given to illustrate the results. >

Stochastic P-type/D-type iterative learning control algorithms

This paper presents stochastic algorithms that compute optimal and sub-optimal learning gains for a P-type iterative learning control algorithm (ILC) for a class of discrete-time-varying linear systems. The optimal algorithm is based on minimizing the trace of the input error covariance matrix. The state disturbance, reinitialization errors and measurement errors are considered to be zero-mean white processes. It is shown that if the product of the input-output coupling matrices C ( t + 1 ) B ( t ) is full column rank, then the input error covariance matrix converges to zero in presence of uncorrelated disturbances. Another sub-optimal P-type algorithm, which does not require the knowledge of the state matrix, is also presented. It is shown that the convergence of the input error covariance matrices corresponding to the optimal and sub-optimal P-type and D-type algorithms are equivalent, and all converge to zero at a rate inversely proportional to the number of learning iterations. A transient-response performance comparison, in the domain of learning iterations, for the optimal and sub-optimal P- and D-type algorithms is investigated. A numerical example is added to illustrate the results.

Selection of the learning gain matrix of an iterative learning control algorithm in presence of measurement noise

Arbitrary high precision output tracking is one of the most desirable control objectives found in industrial applications regardless of measurement errors. The main purpose of this paper is to supply to the iterative learning control (ILC) designer guidelines to select the corresponding learning gain in order to achieve this control objective. For example, if certain conditions are met, then it is necessary for the learning gain to converge to zero in the learning iterative domain. In particular, this paper presents necessary and sufficient conditions for boundedness of trajectories and uniform tracking in presence of measurement noise and a class of random reinitialization errors for a simple ILC algorithm. The system under consideration is a class of discrete-time affine nonlinear systems with arbitrary relative degree and arbitrary number of system inputs and outputs. The state function does not need to satisfy a Lipschitz condition. This work also provides a recursive algorithm that generates the appropriate learning gain functions that meet the arbitrary high precision output tracking objective. The resulting tracking output error is shown to converge to zero at a rate inversely proportional to square root of the number of learning iterations in presence of measurement noise and a class of reinitialization errors. Two illustrative numerical examples are presented.

A stochastic iterative learning control algorithm with application to an induction motor

A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the learning gain matrix of a P-type ILC for linear discrete-time varying systems with arbitrary relative degree. It is shown that, in the case where the number of inputs is not greater than the number of outputs, the input error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of uncorrelated random state disturbance, reinitialization errors and measurement noise. The state error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of measurement noise. In the case where the number of inputs is greater than the number of outputs, then the system output error converges to zero at a rate inversely proportional to the number of iterations in presence of measurement noise. Another suboptimal recursive algorithm is also proposed based on unknown system dynamics and unknown disturbance statistics. The convergence characteristics are shown to be similar to the ones of the optimal recursive algorithm. The proposed ILC algorithms are applied to two different models of an induction motor for angular speed tracking control. One model describes its dynamics in stator fixed (a, b) reference frame without current loops and the other model is also in stator fixed reference(a, b) reference frame but with high-gain current loops. The simulation results show good tracking performance in the presence of noise with erroneous model parameters and noise statistics. An open-loop control is also proposed to improve the tracking rate of the proposed ILC algorithms.

Optimal selection of the forgetting matrix into an iterative learning control algorithm

A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the optimal forgetting matrix and the learning gain matrix of a P-type iterative learning control (ILC) for linear discrete-time varying systems with arbitrary relative degree. This note shows that a forgetting matrix is neither needed for boundedness of trajectories nor for output tracking. In particular, it is shown that, in the presence of random disturbances, the optimal forgetting matrix is zero for all learning iterations. In addition, the resultant optimal learning gain guarantees boundedness of trajectories as well as uniform output tracking in presence of measurement noise for arbitrary relative degree.

A map matching approach for train positioning. II. Application and experimentation

For pt.I see ibid., vol.49, no.2, p.467-75 (2000). In this paper, applications of the map matching algorithm proposed in part I are presented. In particular, steady-state Kalman filters are proposed and applied for filtering the yaw rate and tachometer signals. In addition, experimental results, using a quartz yaw rate sensor and axle encoders aboard a freight train, are included to show the performance of the proposed map matching algorithm.

Automatic alignment and calibration of an inertial navigation system

In this paper we derive a simple six degree of freedom navigator, Earth-surface navigator, for terranean vehicle application, using low grade gyros. The calibration and alignment of the navigator are investigated when the system is at rest. Based on the observability of the error model when the system is at rest, a state transformation is presented. This transformation decouples the observable modes, which are based on physical insight from the unobservable modes. An example is given to illustrate the performance of a Kalman filter for calibration and alignment.<<ETX>>