Richard B. Vinter

Measurement Placement in Distribution System State Estimation

This paper introduces a technique for meter placement for the purpose of improving the quality of voltage and angle estimates across a network. The proposed technique is based on the sequential improvement of a bivariate probability index governing relative errors in voltage and angle at each bus. The meter placement problem is simplified by transforming it into a probability bound reduction problem, with the help of the two sided-Chebyshev inequality. A straightforward solution technique is proposed for the latter problem, based on the consideration of 2-sigma error ellipses. The benefits of the proposed technique are revealed by Monte Carlo simulations on a 95-bus UKGDS network model.

A maximum principle for optimal processes with discontinuous trajectories

A Maximum Principle is proved which governs solutions to dynamic optimization problems in which the controls driving the system may be impulsive and give rise to discontinuous trajectories. The approach, which involves approximating the problem by a conventional one and using Ekeland’s theorem, is new. It permits us to weaken very considerably the hypotheses under which Maximum Principles for such problems have previously been proved.

Existence of neighbouring feasible trajectories: applications to dynamic programming for state constrained optimal control problems

In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.

Degenerate Optimal Control Problems with State Constraints

Standard necessary conditions for optimal control problems with pathwise state constraints supply no useful information about minimizers in a number of cases of interest, e.g., when the left endpoint of state trajectories is fixed at x0 and x0 lies in the boundary of the state constraint set; in these cases a nonzero, but nevertheless trivial, set of multipliers exists. We give conditions for the existence of nontrivial multipliers. A feature of these conditions is that they allow nonconvex velocity sets and measurably time-dependent data. The proof techniques are based on refined estimates of the distance of a given state trajectory from the set of state trajectories satisfying the state constraint, originating in the dynamic programming literature.

Convex duality and nonlinear optimal control

Problems in nonlinear optimal control can be reformulated as convex optimization problems over a vector space of linear functionals. In this way, methods of convex analysis can be brought to bear on the task of characterizing solutions to such problems. The result is a necessary and sufficient condition of optimality that generalizes well-known sufficient conditions, referred to as verification theorems, in dynamic programming; as a byproduct, we obtain a representation of the minimum cost in terms of the upper envelope of subsolutions to the Hamilton–Jacobi equation. It is a striking illustration of the wide range of problems to which convex analysis, and, in particular, convex duality, is applicable. The approach, applied to parametric problems in the calculus of variations, was pioneered by L. C. Young [Lectures on the Calculus of Variations and Optimal Control Theory, W. B. Saunders, Philadelphia, PA, 1969]. As recent work has shown, however, it is equally fruitful when applied in optimal control. Thi...

Local Optimality Conditions and Lipschitzian Solutions to the Hamilton–Jacobi Equation

We consider an optimal control problem with end-constraints formulated in terms of a differential inclusion. A sufficient condition for local optimality of a trajectory is given, involving a Lipschitzian function

Meter Placement for Distribution System State Estimation: An Ordinal Optimization Approach

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Applications of optimal multiprocesses

which is a generalized solution to the Hamilton–Jacobi equation. It is shown that the weakest hypothesis under which the condition is also necessary is that the problem be locally calm. It is further proved that local calmness is implied by strong normality. We thereby establish that the Caratheodory approach, modified to permit Lipschitzian functions

Lipschitz Continuity of Optimal Controls for State Constrained Problems

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A Necessary and Sufficient Condition for Optimality of Dynamic Programming Type, Making No a Priori Assumptions on the Controls

, is applicable in principle when the first order optimality conditions yield nontrivial information.