Showing papers by "John B. Moore published in 1973"

The Application of Optimal Linear Regulator Theory to a Problem in Water Pollution

Abstract: At present, many metropolitan sewer systems do not meet existing and proposed standards on water pollution. Existing systems were designed to overflow at prescribed locations in order to protect the sewage treatment plants whenever severe overload conditions exist (usually during storms). This discharge of untreated overflows into natural receiving waters is of growing concern to water pollution control authorities. The model considered in this paper is representative of the combined storm-sewer systems in cities such as Minneapolis-St. Paul, Minn., Seattle, Wash., and San Francisco, Calif. The objective is to utilize the total storage capacity available in the system in such a manner as to minimize the water pollution resulting from overflows at individual points within the system. In addition, it is required that no abrupt changes in control be admitted, as this is likely to lead to undesirable surges. The nonlinear model is shown to fit within the framework of an optimal regulator problem with derivative constraints. The optimal feedback control law is derived and compared with the optimal bang-bang controller. The solution technique that is presented may be applied to many combined storm-sewer systems in which the flows through the systems to the treatment plants may be controlled. It may be used by city engineers to determine necessary modifications to existing systems in order to meet the new standards regarding water pollution.

Fixed-Lag Smoothing Results for Linear Dynamical Systems *

Abstract: Recent results in the smoothing oj’signals ji-om linear s~.s[ems~i~h gaussian input and nleasurement noise hate provided new perspectives on receiuer design. The particular new results and fierspectioes discussed in this paper are [hose concernilz,qthe importa?z[ class of’ ‘on line’>jil~ers known as filters with delq, lag-jilters, or)xedIOLT smoothers. Fixed-lag smoothers are now su$cient(y developed to be strong competitors qf the wide(y used Wiener and Kalrnan Jilters for some applications, and the paper disrusres the various trade-offs be[ween, f’ilter pe)forrncrnce, permissible delgy, filter contjrlexi~y, and design dz$crdp.

Solution of the Stochastic control problem in unbounded domains

Abstract: Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.

Optimal demodulation of PAM signals

Abstract: Kalman filtering theory is applied to yield an optimal causal demodulator for pulse-amplitude-modulated (PAM) signals in the presence of white Gaussian noise. The discrete-time data (or sampled continuous-time data) are assumed to be either a stationary or non-stationary Gaussian stochastic process, in general nonwhite. Optimal demodulation with delay is also achieved by application of Kalman filtering theory. The resulting demodulators (fixed-lag smoothers) are readily constructed and their performance represents in many cases a significant improvement over that for the optimal demodulator without delay. The fixed-lag smoothing results are in contrast to those for amplitude-modulated signals (AM) where only approximate fixed-lag smoothing is possible, and this with considerable design effort. The performance of the optimal PAM demodulator is shown to be equivalent to that of an optimal discrete filter for the discrete data.

The ApplicationofOptimal Linear Regulator Theorytoa Problem inWater Pollution

Abstract: At present, manymetropolitan sewer systems donotmeet existing andproposed standards onwater pollution. Existing systems were designed tooverflow atprescribed locations inorder toprotect thesewage treatment plants whenever severe overload conditions exist (usually during storms). Thisdischarge ofuntreated overflows intonatural receiving waters isofgrowing concern towater pollution control authorities. The model considered inthis paper isrepresentative ofthecombined storm- sewersystems incities suchasMinneapolis-St. Paul, Minn., Seattle, Wash., andSanFrancisco, Calif. Theobjective istoutilize thetotal storage capacity available inthesystem insuchamanner astominimize thewaterpollution resulting fromoverflows atindividual points within thesystem. Inaddition, itisrequired that noabrupt changes incontrol be admitted, asthis islikely tolead toundesirable surges. Thenonlinear model isshowntofit within theframework ofanoptimal regulator problem withderivative constraints. Theoptimal feedback control lawisderived andcompared withtheoptimal bang-bang con- troller. Thesolution technique that ispresented maybeapplied tomany combined storm-sewer systems inwhich theflows through thesystems to thetreatment plants maybecontrolled. Itmaybeusedbycity engineers todetermine necessary modifications toexisting systems inorder tomeet thenewstandards regarding water pollution. I.INTRODUCTION A MAJORPROBLEMpresently existing inmanyurban areas isthat ofwater pollution caused bydirect over- flowfromcombined storm-sewer systems tonatural re- ceiving waters. Combined storm-sewer systems aresewer systems inwhich bothsanitary waste andstormrunoff are handled simultaneously. Theoriginal design ofsuchsystems wassuchthat notallofthestormrunoff could becarried inaddition tothenormal sanitary flow. Theexcess flow was diverted toreceiving waters atnumerous points throughout thesystem. Itwasconsidered that thestormwater wasclean andwouldsufficiently dilute thesanitary wastesothat there wouldbenopollution problems associated withthe direct discharge oftheexcess flow intoreceiving waters. Thepractice inthepasthasbeentoincrease thenumber ofoverflow locations asthetotal loadonthesystem has increased duetogrowth intheurban area. Thisprinciple mayhavebeenappropriate whenthetotal seweroverflow andtheoverflow locations didnotcontribute seriously to waterpollution. Recent studies (1)haveshown, however,