A survey of optimal control of distributed-parameter systems

Abstract. Optimal modal feedback control laws are synthesized from the modal equations which are obtained by eigenfunction expansion of the diffusion equation systems with space-independent control, boundary control, and distributed control. Comparison between the modal feedback control laws and distributed feedback control laws are discussed. The results also indicate proper quadrature performance criteria for the synthesis of the distributed feedback control laws.

show abstract

“…The usual method to generate the distributed feedback control law is to use the quadratic performance criterion 1 1 …”

Section: (5)mentioning

confidence: 99%

On optimal feedback control of a class of linear distributed systems

Shih

Chu

1975

J Optim Theory Appl

View full text Add to dashboard Cite

show abstract

“…Essentially, thc distributed systctn is i~pproximatcd by A lumped system, which can be attacked by existing techniqucs. Robinson (1971) discusses a number of ways of performing this approximation. 'I'lie system of PDE's may be quantized in either the spatial or the temporal variablc, lcaving a set of ODE'S in the remaining continuous vnrit~ble.…”

Section: Early Approachesmentioning

confidence: 99%

New optimal control synthesis techniques for distributed systems

Vermeychuk

Lapidus

1973

International Journal of Systems Science

View full text Add to dashboard Cite

Two ncw techniques for the synthesis of open-loop optimal controls in distributed systems are presented and apphod to a number of test problems. Rosults thus obtaincd sre cornparod with the results obtainorl via application of existing techniques to tho tcst problems.Necessary conditions for optimality in the form of a two-point boundary-value problem nro found to be preferable from the computational point of view for the solrrtion of distributed optimal control problems.

show abstract

“…Although optimal control of DPSs, i.e., systems governed by partial differential equations (PDEs), has been under development since 1960s, optimal control of nonlinear SDPSs subject to stochastic disturbances has been rarely addressed, [6], [40], [39], [36], [27], [25], [5], [10], [23]. The optimal control methods of the DPSs can be roughly classified into two main approaches.…”

Section: Introductionmentioning

confidence: 99%

Hamilton-Jacobi equation for optimal control of nonlinear stochastic distributed parameter systems applied to air pollution process

Duc¹

2014

ams

View full text Add to dashboard Cite

This paper derives Hamilton-Jacobi equation (HJE) in Hilbert space for optimal control of stochastic distributed parameter systems (SDPSs) governed by partial differential equations (SPDEs) subject to both state-dependent and additive stochastic disturbances. First, nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equations (SODEs) in Hilbert space, using functional analysis. Second, the Hamilton-Jacobi equation (HJE), of which the solution results in an optimal control law, is derived. Third, a problem of optimal control of linear SDPSs, which include the air pollution process, with a quadratic cost functional is addressed as an application of the HJE. After, the control design is done, the SESs are transformed back to Euclidean space for implementation.

show abstract

A survey of optimal control of distributed-parameter systems

Cited by 84 publications

References 107 publications

On optimal feedback control of a class of linear distributed systems

On optimal feedback control of a class of linear distributed systems

New optimal control synthesis techniques for distributed systems

Hamilton-Jacobi equation for optimal control of nonlinear stochastic distributed parameter systems applied to air pollution process

Contact Info

Product

Resources

About