Extending nonlinear, optimisation to, spaces – part I: optimal control

M.D.S. Aliyu and E.K. Boukas

International Journal of Systems Science, 2011, vol. 42, issue 5, 889-906

Abstract: In this article, we introduce, formulate and solve the W1,2, W1,∞ nonlinear optimal control problems as extensions of ℋ2, ℋ∞ optimal control problems, respectively. As these spaces contain less smooth functions, a larger number of problems could be solved in this framework, and by a suitable choice of weighting functions, additional design objectives could be achieved using the present formulation. Moreover, any solution of the W1, p, p = 2, ∞ problem, is automatically a solution of the corresponding ℋp-problem. Sufficient conditions for the solvability of the problems are given in terms of new Hamilton–Jacobi equations (HJEs). These new HJEs may also be easier to solve because of the additional degrees of freedom offered by the current norms. Both the state-feedback and output-feedback problems are discussed. The results are then specialised to linear systems, in which case the solutions are characterised in terms of new algebraic-Riccati equations.

Date: 2011
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DOI: 10.1080/00207721.2010.488764

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