A suboptimal control algorithm for constrained problems using cubic splines

Authors:
C. P. Neuman;A. Sen
Affiliations:
Associate Professor of Electrical Engineering, Carnegie-Mellon University, Department of Electrical Engineering, Schenley Park, Pittsburgh, Pennsylvania 15213 USA;Carnegie-Mellon University, Department of Electrical Engineering, Schenley Park, Pittsburgh, Pennsylvania 15213 USA
Venue:
Automatica (Journal of IFAC)
Year:
1973

Citing 2
Cited 1

Introduction to matrix analysis (2nd ed.)

Introduction to matrix analysis (2nd ed.)
Optimal Control by Mathematical Programming

Optimal Control by Mathematical Programming

Numerical method for a class of optimal control problems subject to nonsmooth functional constraints

Journal of Computational and Applied Mathematics

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Abstract

A suboptimal control algorithm for linear-quadratic regulator problems with state variable inequality constraints (SVIC) is developed. The state and control variables are approximated by cubic splines on an uniform mesh. Through collocation at the knots, the dynamic equations and SVIC are reduced to a set of linear algebraic equations and the suboptimal control is constructed from the solution of a quadratic programming problem with sparse matrices. The number of non-zero storage elements required for these matrices varies linearly with the number of mesh points. Computational experience for specific examples is presented and compared with other approaches described in the literature. Good to excellent accuracy is obtained with modest computational requirements. Memory considerations and on-line implementation are discussed. From both the computational and storage aspects, the approach offers an effective alternative for SVIC problems. Extensions of the algorithm to more general control problems are suggested.