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A subset X of a real Hilbert space H is said to be proximally smooth provided that the function d X : H ! R (the distance to X) is continuously diierentiable on an open tube U around X. It is proven that this property is equivalent to d X having a nonempty proximal subgradient at every point of U, and that the (G^ ateaux = Fr echet) derivative is locally… (More)

- Francis H. Clarke, Yuri S. Ledyaev, L. Rifford, R. J. Stern
- SIAM J. Control and Optimization
- 2000

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)

- Francis H. Clarke, R. J. Stern
- SIAM J. Control and Optimization
- 2003

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)

- R. J. Stern
- Systems & Control Letters
- 2002

- Francis H. Clarke, R. J. Stern
- Systems & Control Letters
- 2005

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.

- R. J. Stern
- 2010

This paper presents the first estimate of United States military cost for Persian Gulf force (CPGfp) derived entirely by a quantitative method. An activity-based cost (ABC) model uses geographic distribution of aircraft carriers as a proxy allocator of Department of Defense (DoD) baseline cost to regional operations. Allocation follows simply from DoD data… (More)

- Roger P. Stradley, R. J. Stern, N B Heinhold
- American journal of veterinary research
- 1979

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)

- R. J. Stern
- SIAM J. Control and Optimization
- 2004