Optimal Input Design for Dynamic Model Prediction Accuracy

Arriving at optimal signal timing parameters to improve the efficiency of traffic flow has been one of the major challenges faced by traffic engineers. The choice of a robust optimization framework and an accurate traffic model plays a significant role in determining optimal signal timing parameters. Though traffic flow is intuitively stochastic, few studies incorporate stochasticity in their optimization framework for traffic signal design. This study proposes two simulation-based stochastic optimization algorithms—an evolutionary algorithm-based framework and a simultaneous perturbation stochastic approximation (SPSA) algorithm-based framework for the optimal signal design of an isolated intersection using a calibrated microsimulation environment with reasonable accuracy. A software-in-the loop approach is used to control the traffic signals in the microsimulation environment. SPSA is a gradient descent algorithm with a powerful approach for approximating the gradient with just two function evaluations per gradient approximation. To evaluate the performance of the two frameworks, the study optimizes the signal timings for a case study on an isolated intersection in an urban arterial in Chennai. On comparing the two algorithms, it is found that SPSA performed better and took 100 function evaluations less than that taken by GA. A better (near optimal) initial solution is found to yield a faster rate of convergence for both algorithms. As the proposed optimization framework incorporates the stochastic nature of traffic in the optimization algorithm, it can accommodate the temporal variations in traffic and thereby provide traffic engineers a robust signal control strategy for improving the efficiency of traffic flow.

Increased travel times are often observed on urban roads, with signalized intersections being the major bottlenecks. The inability of existing static signal timings in accommodating the actual demand fluctuations could be one of the contributing factors. A traffic-responsive signal control system that changes signal timings according to traffic volume fluctuations may alleviate this problem. However, such problems are conventionally formulated based on the data collected from location-based sensors, which are infrastructure intensive and costly and fail to capture mixed and disordered traffic conditions. Considering these limitations, this paper presents an optimal signal design using sample travel time information collected from mobile data sources such as GPS/Bluetooth/Wi-Fi sensors that work independently of the traffic conditions and are relatively cost-effective. The proposed adaptive signal design minimizes total intersection delay at isolated intersections for every cycle based on the traffic conditions observed in the previous cycle. The mathematical programming-based formulation uses shock waves formed during the red and green phases to estimate optimal-phase durations. Results revealed that the proposed design is capable of handling traffic flow fluctuations without requiring the entire traffic stream data. The system demonstrated that sample data from four probe vehicles per phase is adequate for real-time optimal signal design. Results showed that the proposed model outperformed the existing Webster’s signal design procedure with a delay reduction of 11.78% when compared theoretically and 10.41% when implemented in VISSIM.

The optimal input signal design is a procedure of generating an informative excitation signal to extract the model parameters with maximum accuracy during the estimation process. Non-integer order calculus is a very useful tool, which is often utilized for modeling and control purposes. In the paper, we present a novel optimal input formulation and a numerical scheme for fractional order LTI system identification. The Oustaloup recursive approximation (ORA) method is used to determine the fractional order differentiation in an integer order state-space form. Then, the presented methodology is adopted to obtain an optimal input signal for fractional order system identification from the order interval \(0.5 \le \alpha \le 2.0\). The fundamental step in the presented method was to reformulate the problem into a similar fractional optimal input design problem described by Lagrange formula with the set of constraints. The methodology presented in the paper was verified using a numerical example, and the computational results were discussed.

This paper considers optimal input design when the intended use of the identified model is to construct a feed-forward controller based on measurable disturbances. The objective is to find a minimum power excitation signal to be used in system identification experiment, such that the corresponding model-based feed-forward controller guarantees, with a given probability, that the variance of the output signal is within given specifications. To start with, some low order model problems are analytically solved and fundamental properties of the optimal input signal solution are presented. The optimal input signal contains feed-forward control and depends of the noise model and transfer function of the system in a specific way. Next, we show how to apply the partial correlation approach to closed loop optimal experiment design to the general feed-forward problem. A framework for optimal input signal design for feed-forward control is presented and numerically evaluated on a temperature control problem.

The design of optimal input signals for the identification of linear systems with feedback is considered for the case when the loop gain is large. The latter condition permits simplification of the description of the complete system and leads to a practical procedure for the design of the optimal input signal. Results of application to a diffusion furnace are included.

Most of the literature on MIMO systems which assume Rayleigh flat fading, model the multipath channel propagation taking the channel correlation into account make simplifying assumptions on the statistics (e.g. uniform linear arrays with rich scattering all around the antennas). These assumptions lead to symmetric and separable correlation structure and leads to some insights on the impact of correlation on capacity and on the optimal signalling. In the recent past, several multiple-element antenna geometries, different the linear arrays, which exploit the ability to excite different spatial modes in the radiated E-field vector have been proposed in the cellular radio access link context. The aforementioned channel model is not rich to capture the EM properties of the antenna elements and its relation on the availability of scattering resources. In this paper, we propose a channel model based on EM theory which incorporates the joint impact of the antenna element properties (radiation pattern, mutual coupling between elements, etc.) and the scattering environment. This model provides a good compromise between complexity and tractability. We use this channel model to propose a rank and determinant criterion for array design in a multiple-antenna system for maximizing the ergodic capacity

ABBA codes, a class of quasi-orthogonal space-time block codes (STBC) proposed by Tirkkonen et al., have been studied extensively for various applications. Yuen et al. have recently shown that a refined version of ABBA codes admit pair-wise real-symbol decoding, i.e. with minimum decoding complexity (MDC) achievable by non-orthogonal STBC. In this paper, we derive the exact symbol pair-wise error probability and the union bound on the symbol error rate (SER). The union bound is only 0.1 dB from the simulated SER at medium or high SNR < 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . Thus, by minimizing the SER union bound, we can find the optimal signal designs for any constellation with an arbitrary geometrical shape. Furthermore, we propose a new method combining signal rotation and power allocation for inphase-quadrature power-unbalanced constellations such as rectangular QAM. Our new optimal signal designs perform better than the existing ones and offer lower encoding/decoding complexities.

The problem of optimal signal design for coherent detection of binary signals in Gaussian noise is revisited under power and secrecy constraints. In particular, the aim is to select the binary transmitted signals in an optimal manner so that the probability of error is minimized at an intended receiver while the probability of error at an eavesdropper is maintained above a threshold value and the signal powers are limited. It is shown that an optimal solution exists in the form of antipodal signaling along the eigenvector corresponding to the solution of a maximum (possibly generalized) eigenvalue problem, which is specified explicitly based on the channel coefficient matrices and the noise covariance matrices at the intended receiver and the eavesdropper. Furthermore, optimal signal design can be performed in an efficient manner by solving a semidefinite programming (SDP) relaxation followed by a matrix rank-one decomposition. Numerical examples are provided to illustrate optimal solutions for three different but exhaustive cases.

We focus on sounding signal design for single-input single-output. It is shown analytically that the optimum sounding signal for the time static case, fdT = 0, is one whose frequency spectrum has constant magnitude across the band. Equivalently the autocorrelation of the sounding signal should be an impulse. Simulation results show that the optimum sounding signal outperforms the random sounding signals.

For multi-channel process, due to disadvantages of the open-loop single variable step method, multi-channel test method is used. That means all of the channels are tested at the same time. In order to eliminate cross-effect of the different test signals, it requires that all the test signals are uncorrelated. Several test signals are introduced and analyzed. Based on two familiar identification methods: correlation analysis method and least-squares method, we put our strength on the way to get uncorrelated test signals. A novel design for the period length of uncorrelated pseudo random binary sequence (PRBS) is proposed. Use this design method, identifiable PRBS signals can be gained and their periods are the shortest. Simulation results show the effectiveness.

A synchronous code-division multiple-access (CDMA) channel is considered for which power control is available. Each of the users is assigned a quality-of-service (QoS) threshold that is measured in terms of a signal-to-interference ratio (SIR), and to cover the situation of multiple classes of users, these are allowed to be unequal to each other. The receiver is taken to be of the nonlinear decision-feedback type in which the users are successively detected. Given the processing gain of the system, which is no greater than the number of users, we minimize the required total power (i.e., the sum of the users' received powers) over all sets of signature sequences and power-control policies that allow the users to meet their required QoS constraints.

The theory of optimal experimental designs is concerned with the construction of designs that are optimum with respect to some statistical criteria. Some of these criteria include the alphabetic optimality criteria such as; D-, A-, E-, T-, G- and C- criterion. Compound optimality criteria are those that combine two or more alphabetic optimality criteria. Design that require optimality criteria have specific desired properties that do very well in one design and at the same time perform poorly in another design. Thus, a compound optimality criterion gives a balance to the desirability of any two or more alphabetic optimality criteria. The present paper aims to introduce CD- and DT- criteria which are compound optimality criteria for second order rotatable designs constructed using Balanced Incomplete Block Designs (BIBDs) in four dimensions.

OPTIMAL SEARCH DESIGNS, OR DESIGNS OPTIMAL UNDER BIAS FREE OPTIMALITY CRITERIA

This paper deals with the optimal design of monolithic piezoelectric microactuators with integrated proprioceptive sensors. Dedicated to the microrobotic and micromechatronic fields, this work details the modelling and the characterization of compliant structures with integrated actuating and sensing elements. The proposed optimal design procedure addresses not only static criteria but also dynamic ones. This leads to microdevices which are better performing with regards to mechanical (displacement, force, etc) and control (dynamics, stability, precision) characteristics. The efficient design of such devices is achieved using a flexible building block method. A topological optimization method combined with an evolutionary algorithm is used to optimize the design of a truss-like planar structure. This method chooses the best location among the different piezoelectric elements. Different mechanical, actuation or sensing elements are accordingly chosen from a data bank. From the control point of view, optimization criteria are considered, to enforce the observability of the vibrational dominant modes of the structure. Therefore, control and observation Gramians are exploited in the optimal design to shape the open-loop frequency response of both actuation and sensing functions of the integrated device. In the last part of the paper, based on these results, the optimal design and manufacture of an innovative piezoelectric flexible microgripper is proposed. The prototype is manufactured from a monolithic piezoelectric material (PIC 151). Its reduced size (15 mm × 18 mm) fits the requirements of both microrobotic and micromechatronic applications, and it is suitable for micromanipulation tasks. Closing the paper, the characterization and the performance of this integrated microactuator and the efficiency of the optimal design procedure for micromechatronic applications are shown.

This paper presents a proposal of novel signal design problem at isolated intersections, which assumes that the effective green times assigned to each signal phase follow dynamic user optimal (DUO) principle. At the DUO state, the average delays of vehicles using the signal phases with positive additional green times (the assigned effective green times minus the minimum effective green times) are equal and maximum. The proposed signal design problem is formulated as a variational inequality (VI) problem. The point queue (PQ) model is applied to represent traffic dynamics and to generate the cumulative traffic flows, which is further used to estimate the average delay of each signal phase. The existence of the solution of the proposed VI problem is proved and a solution algorithm based on the method of successive averages (MSA) is developed to solve the proposed signal design problem. Finally, a sample intersection is used to illustrate the application of the proposed model and the solution algorithm.