Algorithm for Optimal Mode Scheduling in Switched Systems

This paper considers the problem of computing the schedule of modes in a switched dynamical system, that minimizes a cost functional defined on the trajectory of the system's continuous state variable. A recent approach to such optimal control problems consists of algorithms that alternate between computing the optimal switching times between modes in a given sequence, and updating the mode-sequence by inserting to it a finite number of new modes. These algorithms have an inherent inefficiency due to their sparse update of the mode-sequences, while spending most of the computing times on optimizing with respect to the switching times for a given mode-sequence. This paper proposes an algorithm that operates directly in the schedule space without resorting to the timing optimization problem. It is based on the Armijo step size along certain Gateaux derivatives of the performance functional, thereby avoiding some of the computational difficulties associated with discrete scheduling parameters. Its convergence to local minima as well as its rate of convergence are proved, and a simulation example on a nonlinear system exhibits quite a fast convergence

Congestion management in traffic-light intersections via Infinitesimal Perturbation Analysis

We present a flow-control technique in traffic-light intersections, aiming at regulating queue lengths to given reference setpoints. The technique is based on multivariable integrators with adaptive gains, computed at each control cycle by assessing the IPA gradients of the plant functions. Moreover, the IPA gradients are computable on-line despite the absence of detailed models of the traffic flows. The technique is applied to a two-intersection system where it exhibits robustness with respect to modeling uncertainties and computing errors, thereby permitting us to simplify the on-line computations perhaps at the expense of accuracy while achieving the desired tracking. We compare, by simulation, the performance of a centralized, joint two-intersection control with distributed control of each intersection separately, and show similar performance of the two control schemes for a range of parameters

Approximate IPA: Trading Unbiasedness for Simplicity

When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to be unbiased, the complexity of its estimators often does not scale with the system's size. The purpose of this paper is to suggest an alternative approach to optimization which balances precision with computing efforts by trading off complicated, unbiased PA estimators for simple, biased approximate estimators. Furthermore, we provide guidelines for developing such estimators, that are largely based on the Stochastic Flow Modeling framework. We suggest that if the relative error (or bias) is not too large, then optimization algorithms such as stochastic approximation converge to a (local) minimum just like in the case where no approximation is used. We apply this approach to an example of balancing loss with buffer-cost in a finite-buffer queue, and prove a crucial upper bound on the relative error. This paper presents the initial study of the proposed approach, and we believe that if the idea gains traction then it may lead to a significant expansion of the scope of PA in optimization of discrete event systems.Comment: 8 pages, 8 figure

Temperature Regulation in Multicore Processors Using Adjustable-Gain Integral Controllers

This paper considers the problem of temperature regulation in multicore processors by dynamic voltage-frequency scaling. We propose a feedback law that is based on an integral controller with adjustable gain, designed for fast tracking convergence in the face of model uncertainties, time-varying plants, and tight computing-timing constraints. Moreover, unlike prior works we consider a nonlinear, time-varying plant model that trades off precision for simple and efficient on-line computations. Cycle-level, full system simulator implementation and evaluation illustrates fast and accurate tracking of given temperature reference values, and compares favorably with fixed-gain controllers.Comment: 8 pages, 6 figures, IEEE Conference on Control Applications 2015, Accepted Versio

BEYOND THE CONSTRUCTION OF OPTIMAL SWITCHING SURFACES FOR AUTONOMOUS HYBRID SYSTEMS

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