The optimal open loop control of systems described by a set of linear partial differential equations is investigated. The performance index is of quadratic type and the mean square error is considered as a special case. Energy type inequality constraints are imposed on the control inputs. The problem is formulated as a minimization problem in Hilbert space. The necessary and sufficient conditions for a minimum are obtained and it is proved that these conditions yield the global minimum. It is shown how the solution to the constrained problem can be obtained from the solution of the unconstrained problem. The optimal control functions satisfy Fredholm integral equations with symmetric kernels. The paper presents an example where the solution is obtained by eigenfunction expansion.
Optimal Control of Linear Distributed Parameter Systems With Constrained Inputs
W. A. Weigand,
W. A. Weigand
School of Chemical Engineering, Purdue University, Lafayette, Ind.
A. F. D’Souza
Department of Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, Ill.
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Weigand, W. A., and D’Souza, A. F. (June 1, 1969). "Optimal Control of Linear Distributed Parameter Systems With Constrained Inputs." ASME. J. Basic Eng. June 1969; 91(2): 161–167. https://doi.org/10.1115/1.3571052
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