Convex operator-theoretic methods in stochastic control

This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and Hamilton-Jacobi-Bellman (HJB) equations for nonlinear systems in an ergodic Hilbert-Sobolev space. In detail, a generalized Bakry-Emery condition is introduced under which one can establish the global exponential stabilizability of a large class of nonlinear systems. It is shown that this condition is sufficient to ensure the existence of solutions of the ergodic HJB for stochastic optimal control problems on infinite time horizons. Moreover, a novel dynamic programming recursion for bounded linear operators is introduced, which can be used to numerically solve HJB equations by a Galerkin projection

Intrinsic Separation Principles

This paper is about output-feedback control problems for general linear systems in the presence of given state-, control-, disturbance-, and measurement error constraints. Because the traditional separation theorem in stochastic control is inapplicable to such constrained systems, a novel information-theoretic framework is proposed. It leads to an intrinsic separation principle that can be used to break the dual control problem for constrained linear systems into a meta-learning problem that minimizes an intrinsic information measure and a robust control problem that minimizes an extrinsic risk measure. The theoretical results in this paper can be applied in combination with modern polytopic computing methods in order to approximate a large class of dual control problems by finite-dimensional convex optimization problems

Approximations for Optimal Experimental Design in Power System Parameter Estimation

This paper is about computationally tractable methods for power system parameter estimation and Optimal Experiment Design (OED). Here, the main motivation is that OED has the potential to significantly increase the accuracy of power system parameter estimates, for example, if only a few batches of data are available. The problem is, however, that solving the exact OED problem for larger power grids turns out to be computationally expensive and, in many cases, even computationally intractable. Therefore, the present paper proposes three numerical approximation techniques, which increase the computational tractability of OED for power systems. These approximation techniques are bench-marked on a 5-bus and a 14-bus case studies