Towards Distributed OPF using ALADIN

The present paper discusses the application of the recently proposed Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method to non-convex AC Optimal Power Flow Problems (OPF) in a distributed fashion. In contrast to the often used Alternating Direction of Multipliers Method (ADMM), ALADIN guarantees locally quadratic convergence for AC OPF. Numerical results for 5 to 300 bus test cases indicate that ALADIN is able to outperform ADMM and to reduce the number of iterations by about one order of magnitude. We compare ALADIN to numerical results for ADMM documented in the literature. The improved convergence speed comes at the cost of increasing the communication effort per iteration. Therefore, we propose a variant of ALADIN that uses inexact Hessians to reduce communication. Additionally, we provide a detailed comparison of these ALADIN variants to ADMM from an algorithmic and communication perspective. Moreover, we prove that ALADIN converges locally at quadratic rate even for the relevant case of suboptimally solved local NLPs

Distributed State Estimation for AC Power Systems using Gauss-Newton ALADIN

This paper proposes a structure exploiting algorithm for solving non-convex power system state estimation problems in distributed fashion. Because the power flow equations in large electrical grid networks are non-convex equality constraints, we develop a tailored state estimator based on Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method, which can handle the nonlinearities efficiently. Here, our focus is on using Gauss-Newton Hessian approximations within ALADIN in order to arrive at at an efficient (computationally and communicationally) variant of ALADIN for network maximum likelihood estimation problems. Analyzing the IEEE 30-Bus system we illustrate how the proposed algorithm can be used to solve highly non-trivial network state estimation problems. We also compare the method with existing distributed parameter estimation codes in order to illustrate its performance

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

Backward-Forward Reachable Set Splitting for State-Constrained Differential Games

This paper is about a set-based computing method for solving a general class of two-player zero-sum Stackelberg differential games. We assume that the game is modeled by a set of coupled nonlinear differential equations, which can be influenced by the control inputs of the players. Here, each of the players has to satisfy their respective state and control constraints or loses the game. The main contribution is a backward-forward reachable set splitting scheme, which can be used to derive numerically tractable conservative approximations of such two player games. In detail, we introduce a novel class of differential inequalities that can be used to find convex outer approximations of these backward and forward reachable sets. This approach is worked out in detail for ellipsoidal set parameterizations. Our numerical examples illustrate not only the effectiveness of the approach, but also the subtle differences between standard robust optimal control problems and more general constrained two-player zero-sum Stackelberg differential games