Download Optimal control, stabilization and nonsmooth analysis by Marcio S. de Queiroz, Michael Malisoff, Peter Wolenski PDF

By Marcio S. de Queiroz, Michael Malisoff, Peter Wolenski

This edited ebook includes chosen papers awarded on the Louisiana convention on Mathematical regulate conception (MCT'03), which introduced jointly over 35 in demand international specialists in mathematical keep watch over idea and its purposes. The publication kinds a well-integrated exploration of these parts of mathematical keep watch over idea during which nonsmooth research is having a big impression. those contain valuable and adequate stipulations in optimum control, Lyapunov characterizations of balance, input-to-state balance, the development of suggestions mechanisms, viscosity options of Hamilton-Jacobi equations, invariance, approximation concept, impulsive structures, computational matters for nonlinear platforms, and different themes of curiosity to mathematicians and regulate engineers. The ebook has a robust interdisciplinary part and used to be designed to facilitate the interplay among major mathematical specialists in nonsmooth research and engineers who're more and more utilizing nonsmooth analytic instruments.

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Additional resources for Optimal control, stabilization and nonsmooth analysis

Example text

So (12) is false and, in this case, the claim is true. Case 2: 0 < T ∗ < +∞. Take Ti ↑ T ∗ and a sequence {(vi , xi )} in D∗ such that vi |[0,Ti ] = v¯|[0,Ti ] , for each i. Define x ¯ ∈ ACloc ([0, ∞); IRn ) according to x ¯(t) = xi (t), where i is any index value such that Ti > t. e. e. It v, x follows that (¯ ¯) ∈ S. By (12), (¯ v, x ¯) ∈ / D∗ . Define D := D∗ ∪ {(¯ v, x ¯)}. We show that D ∈ Q. To this end, take any T > 0 and distinct elements (v, x), (v x ) ∈ D such that v|[0,T ] = v |[0,T ] .

Such control laws cannot be regarded as classical feedback control strategies because the associated state trajectories are not unique. We provide full details of the proofs of recently announced general theorems that interpret discontinuous state feedback laws as non-anticipative feedback strategies. An application to flow control illustrates the relevance of the theory to process systems engineering. Keywords: Differential Games, Differential Inclusions, Feedback Control. M. de Queiroz et al.

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