Extending nonlinear H2, H∞ optimisation to W1,2, W1,∞ spaces - part I: optimal control

Author: Aliyu M. D. S.   Boukas E. K.  

Publisher: Taylor & Francis Ltd

ISSN: 1464-5319

Source: International Journal of Systems Science, Vol.42, Iss.5, 2011-05, pp. : 889-906

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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.