Extending nonlinearℋ2,ℋ∞optimisation toW1,2,W1,∞spaces – part I: optimal control

Autor:	M. D. S. Aliyu, El-Kébir Boukas
Rok vydání:	2011
Předmět:	Mathematical optimization Nonlinear system Current (mathematics) Design objective Control and Systems Engineering Backstepping Linear system Degrees of freedom (statistics) Optimal control Computer Science Applications Theoretical Computer Science Mathematics Weighting
Zdroj:	International Journal of Systems Science. 42:889-906
ISSN:	1464-5319 0020-7721
DOI:	10.1080/00207721.2010.488764
Popis:	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.
Databáze:	OpenAIRE
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