Comparisons of practical hierarchical control methods for interconnected dynamical systems

A discrete dynamic model of multidimensional high-order difference equations is described for the dynamics of biochemical oxygen demand (BOD) and dissolved oxygen (DO) in a multiple-reach river system. The high-order difference equations represent the distributed transport delays between the adjacent reaches in the river to allow for the effects of dispersion of BOD and DO. A hierarchical optimization technique, which is based on duality and decomposition, is applied to the high-order discrete dynamic model having state and control constraints for minimizing the deviation of water quality from the desired level. It is shown that the distributed delay model is the most realistic one by comparing the responses for no delay, pure delay, and distributed delay models. By solving a 4-reach problem it is also shown that the hierarchical optimization technique is a powerful tool for optimizing fairly large dimensional discrete dynamic systems having distributed transport delays and state and control constraints.

A Discrete Dynamic Model with Distributed Transport Delays and Its Hierarchical Optimization for Preserving Stream Quality

The data-based mechanistic approach to the modelling, forecasting and control of environmental systems

A method is developed for providing the optimal feedback gain matrix for high-order linear quadratic problems by a decentralized computational procedure. All the calculations in this approach are done off-line. The resulting gains are optimal for all initial conditions so that the eventual on-line computation is minimal. The method is applicable to both the regulator and the servomechanism problems and is particularly attractive to use for the infinite time case where even the off-line computation is small. A 22nd-order numerical example is used to illustrate the approach. The system here is the practical one of river pollution control based on some data from the river Cam near Cambridge, England. For this case, the optimal feedback matrix is calculated using the new approach.

Multilevel Feedback Control for Interconnected Dynamical Systems Using the Prediction Principle

A method isdeveloped forproviding theoptimal feedback thesystem, since inthetimeittakes todothecalculation, gainmatrix forhigh-order linear quadratic problems byadecentralized thestate ofthesystemmayhavechangedsubstantially. computational procedure. Allthecalculations inthis approach aredone Ifeverydisturbance weretobring thesystem tothesame off-line. Theresulting gains areoptimal forallinitial conditions sothat theeventual on-line computation isminimal. Themethodisapplicable state, itwouldbepossible totreat thisstate astheinitial toboththeregulator andtheservomechanism problems andispar-condition andperform thedynamic optimization calculation ticularly attractive tousefortheinfinite timecasewhere eventheoff-line off-line. Thisis, however, notrealistic, anditisnecessary to computation issmall. A 22nd-order numerical example isusedtoillus- determine acontrol lawwhichprovides closed-loop control trate theapproach. Thesystem hereisthepractical oneofriver pollution valid foranyinitial condition. Itisparticularly attractive to control based onsomedatafromtheriver CamnearCambridge, England. Forthis case, theoptimal feedback matrix iscalculated using thenew haveaconstant feedback matrixsince thenimplementation

http://ieeexplore.ieee.org/iel5/21/5408770/05408774.pdf

Multilevel Feedback Control forInterconnected Dynamical Systems Using thePrediction Principle

The modelling and control of pollution in a river system

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The modelling and control of pollution in a river system