Advertising an event

The paper considers a problem of how to minimize advertising costs to sell seats for a particular event, for instance, a sports game, a rock concert or a ballet performance. We take into consideration a word-of-mouth effect, which means that people buying a ticket tell their friends about it, so that advertising is unnecessary to inform those people.The problem is one of optimal control and the number of seats sold and the advertising effort of the organizers are the state and control variables, respectively. We show that, besides being dependent on the cost and revenue parameters, the optimal advertising policy is also affected by the length of the planning period and the relation between the number of seats and the total number of potential attendees.     

Identification of multi-input systems: variance analysis and input design issues

This paper examines the identification of multi-input systems. Motivated by an experiment design problem (should one excite the various inputs simultaneously or separately), we examine the effect of an additional input on the variance of the estimated coefficients of parametrized rational transfer function models, with special emphasis on the commonly used FIR, ARX, ARMAX, OE and BJ model structures. We first show that, for model structures that have common parameters in the input-output and noise models (e.g. ARMAX), any additional input contributes to a reduction of the covariance of all parameter estimates. We then show that the accuracy improvement extends beyond the case of common parameters in all transfer functions, and we show exactly which parameter estimates are improved when a new input is added. We also conclude that it is always better to excite all inputs simultaneously.     

Synthesis of optimal controllers for piecewise affine systems with sampled-data switching

This paper discusses the optimal control problem of the continuous-time piecewise affine (PWA) systems with sampled-data switching, where the switching action is executed based upon a condition on the state at each sampling time. First, an algebraic characterization for the problem to be feasible is derived. Next, an optimal continuous-time controller is derived for a general class of PWA systems with sampled-data switching, for which the optimal control problem is feasible but whose subsystems in some modes may be uncontrollable in the usual sense. Finally, as an application of the proposed approach, the high-speed and energy-saving control problem of the CPU processing is formulated, and the validity of the proposed methods is shown by numerical simulations.     

Communication and control co-design for networked control systems

This paper discusses the stabilization of a networked control system (NCS) in which sensors and actuators of a plant exchange information with a remote controller via a shared communication medium. Access to that medium is governed by a pair of periodic communication sequences. Under the model utilized here, the controller and plant handle communication disruptions by “ignoring” (in a sense to be made precise) sensors and actuators that are not actively communicating. This choice has the effect of significantly reducing the complexity of selecting control/communication policies. It is shown that, for discrete-time NCS, the reachability and observability of the plant can be preserved if the communication sequences are chosen properly. We propose a method for exponentially stabilizing a NCS by first identifying a pair of communication sequences that preserve reachability and observability and then designing an observer-based feedback controller based on those sequences.     

Boundary control of linearized Saint-Venant equations oscillating modes

The paper investigates the control of oscillating modes occurring in open-channels, due to the reflection of propagating waves on the boundaries. These modes are well represented by linearized Saint-Venant equations, a set of hyperbolic partial differential equations which describe the dynamics of one-dimensional open-channel flow around a given stationary regime. We use a distributed transfer function approach to compute a dynamic boundary controller that cancels the oscillating modes over all the canal pool. This result is recovered with a Riemann invariants approach in the case of a frictionless horizontal canal pool. The effect of a proportional boundary control on the poles of the transfer matrix is then characterized by a root locus, and we derive an asymptotic result for high frequencies closed-loop poles.     

Constraints propagation techniques on intervals for a guaranteed localization using redundant data

In order to estimate continuously the dynamic location of a car, dead reckoning and absolute sensors are usually merged. The models used for this fusion are non-linear and, therefore, classical tools (such as Bayesian estimation) cannot provide a guaranteed estimation. In some applications, integrity is essential and the ability to guaranty the result is a crucial point. There are bounded-error approaches that are insensitive to non-linearity. In this context, the random errors are only modeled by their maximum bounds. This paper presents a new technique to merge the data of redundant sensors with a guaranteed result based on constraints propagation techniques on real intervals. We have thus developed an approach for the fusion of the two ABS wheel encoders of the rear wheels of a car, a fiber optic gyro and a differential GPS receiver in order to estimate the absolute location of a car. Experimental results show that the precision that one can obtain is acceptable, with a guaranteed result, in comparison with an extended Kalman filter. Moreover, constraints propagation techniques are well adapted to a real-time context.     

Parameter bounds evaluation of Wiener models with noninvertible polynomial nonlinearities

In this paper a three stage procedure is presented for deriving parameters bounds of SISO Wiener models when the nonlinear block is modeled by a possibly noninvertible polynomial and the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear part are bounded by a tight orthotope. Then, given the estimated uncertain nonlinearity and the output measurements collected exciting the system with an input dynamic signal, bounds on the unmeasurable inner signal are computed. Finally, such bounds, together with noisy output measurements, are used for bounding the parameters of the linear block.     

Stability tests and stabilization for piecewise linear systems based on poles and zeros of subsystems

This paper provides several stability tests for piecewise linear systems and proposes a method of stabilization for bimodal systems. In particular, we derive an explicit and exact stability test for planar systems, which is given in terms of coefficients of transfer functions of subsystems. Restricting attention to the bimodal and planar case, we show simple stability tests. In addition, we drive a necessary stability condition and a sufficient stability condition for higher-order and bimodal systems. They are given in terms of the eigenvalue loci and the observability of subsystems. All the stability tests provided in this paper are computationally tractable, and our results are applied to the stabilizability problem. We confirm the exactness and effectiveness of our approach by illustrative examples.     

A C-tree decomposition algorithm for 2D and 3D geometric constraint solving

In this paper, we propose a method which can be used to decompose a 2D or 3D constraint problem into a C-tree. With this decomposition, a geometric constraint problem can be reduced into basic merge patterns, which are the smallest problems we need to solve in order to solve the original problem in certain sense. Based on the C-tree decomposition algorithm, we implemented a software package MMP/Geometer. Experimental results show that MMP/Geometer finds the smallest decomposition for all the testing examples efficiently.     

Spiral-fashion embroidery path generation in embroidery CAD systems

The spiral fashion is an important kind of embroidery fashion. In the spiral fashion embroidery, a user-designed region is embroidered with a thread along a uniform spiral path whose shape is similar to the region's contours. An approach which can automatically generate this kind of embroidery path is proposed in this paper. In this approach, the region is decomposed into several ring-shaped sub-regions at first. Then these sub-regions are organized into a binary tree and the spiral lines in these sub-regions are connected to form a single path.