State diagrams and steady-state balance equations for open queuing network models

In this paper, the state diagrams and steady-state balance equations for two kinds of open queuing network models are presented. The first model comprises a network of single queues with single servers, while the second model comprises multiple servers for single queues. State diagrams are drawn for (2, 3) queuing networks with (i) single servers and (ii) multiple servers. Steady-state balance equations are derived from the state diagrams. The paper provides a method to solve open queuing networks by analyzing the stochastic process involved in the transition of states in a continuous time Markov chain which represents the state diagram of a queuing system.     

Bringing forth worlds

Kress encourages us to understand writing as “transformative engagement in the world,” and his emphasis on the materiality of modes draws our attention to the multiple possibilities offered by different materials and sensory channels. Writing involves the transformation of all aspects of the resources for meaning; thus writing is always an ethical act, and the worlds that different cultures and communities bring forth through their semiotic work offer different possibilities of being.     

Faceless students, virtual places: Emergence and communal accountability in online classrooms

A pedagogical problem growing out of virtual classrooms is the temptation to act without communal accountability, the reciprocal commitment among individuals to maintain the health of their interconnections. Drawing on an ethnographic study of a fully online composition class, I argue that teachers can encourage accountability within virtual sites by conceiving of the online classroom as an emergent phenomenon. The relationships and activities among language, physical reality, and interpretant provide the matrix out of which place organizes itself. This ecological orientation provides local and systemic strategies for fostering communal health. I begin my exploration of online place by describing the value of complex systems theory and emergence for conceptualizing place. Next, I describe the roles of language, physical reality, and interpretant, pointing out the contribution of each to the configuration of virtual place and to communal accountability. Then, I focus on the emergence of place, which reorganizes language, reality, and interpretant, opening up a new dimension to communal accountability.     

Optimal controller tuning for nonlinear processes

The present work proposes a systematic methodology for the optimal selection of controller parameters in the sense of minimizing a performance index, which is a quadratic function of the tracking error and the control effort. The performance index is calculated explicitly as an algebraic function of the controller parameters by solving Zubov's partial differential equation (PDE). Standard optimization techniques are then employed for the calculation of the optimal values of the controller parameters. The solution of Zubov's PDE is also used to estimate the closed-loop stability region for the chosen values of the controller parameters. The proposed approach is finally illustrated in a chemical reactor control problem.     

Consistency analysis of some closed-loop subspace identification methods

We study statistical consistency of two recently proposed subspace identification algorithms for closed-loop systems. These algorithms may be seen as implementations of an abstract state-space construction procedure described by the authors in previous work on stochastic realization of closed-loop systems. A detailed error analysis is undertaken which shows that both algorithms are biased due to an unavoidable mishandling of initial conditions which occurs in closed-loop identification. Instability of the open loop system may also be a cause of trouble.     

Discrete-time certainty equivalence output feedback: allowing discontinuous control laws including those from model predictive control

We present certainty equivalence output feedback results for discrete-time nonlinear systems that employ possibly discontinuous control laws in the feedback loop. Coupling assumptions of nominal robustness with uniform observability or detectability assumptions, we assert nominally robust stability for output feedback closed loops. We further show that model predictive control (MPC) can be used to generate a feedback control law that is robustly globally asymptotically stabilizing when used in a certainty equivalence output feedback closed loop. Allowing for discontinuous feedback control laws is important for systems employing MPC, since the method can, and sometimes necessarily does, result in discontinuous control laws.     

Nonlinear system identification via direct weight optimization

A general framework for estimating nonlinear functions and systems is described and analyzed in this paper. Identification of a system is seen as estimation of a predictor function. The considered predictor function estimate at a particular point is defined to be affine in the observed outputs and the estimate is defined by the weights in this expression. For each given point, the maximal mean-square error (or an upper bound) of the function estimate over a class of possible true functions is minimized with respect to the weights, which is a convex optimization problem. This gives different types of algorithms depending on the chosen function class. It is shown how the classical linear least squares is obtained as a special case and how unknown-but-bounded disturbances can be handled.Most of the paper deals with the method applied to locally smooth predictor functions. It is shown how this leads to local estimators with a finite bandwidth, meaning that only observations in a neighborhood of the target point will be used in the estimate. The size of this neighborhood (the bandwidth) is automatically computed and reflects the noise level in the data and the smoothness priors.The approach is applied to a number of dynamical systems to illustrate its potential.     

On controllability and trajectory tracking of a kinematic vehicle model

This paper presents some further results concerning the issues of controllability and trajectory tracking regarding a front-wheel drive vehicle kinematic model. A simple procedure for computing an open-loop control strategy that transfers the system between given initial and final states, is presented. In particular, the input function is computed by means of a set of linear algebraic equations. The resulting motion planning procedure allows us to present a control scheme for solving the trajectory (a time-parameterized reference signal) tracking problem. Various applications of the approach in forward and backward motions are considered, and simulation results are presented.     

Identification of piecewise affine systems based on statistical clustering technique

This paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model.