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Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish a robustness property of the feedback relative to(More)
A standard finite dimensional nonlinear control system is considered, along with a state constraint set S and a target set Σ. It is proven that open loop S-constrained controllability to Σ implies closed loop Sconstrained controllability to the closed δ-neighborhood of Σ, for any specified δ > 0. When the target set Σ satisfies a small time S-constrained(More)
An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given ε > 0, produces ε-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes(More)
Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given.
Exocrine pancreatic function was evaluated in 13 dogs, using the chymotrypsin-labile peptide N-benzoyl-L-tyrosyl-p-aminobenzoic acid (BT-PABA). This peptide releases p-aminobenzoic acid (PABA) in the presence of pancreatic chymotrypsin. The amount of PABA in blood or urine after BT-PABA administration then served as an index of pancreatic function.(More)