arXiv subjects

Boris Houska

Publications and source records attributed to Boris Houska.

At least 37 records · Page 2Linked to original sources

arXiv2022

Distributed MPC with ALADIN -- A Tutorial

This paper consists of a tutorial on the Augmented Lagrangian based Alternating Direction Inexact Newton method (ALADIN) and its application to distributed model predictive control (MPC). The focus is - for simplicity of presentation - on convex quadratic programming (QP) formulations of MPC. It is explained how ALADIN can be used to synthesize sparse QP solvers for large-scale linear-quadratic optimal control by combining ideas from augmented Lagrangian methods, sequential quadratic programming, as well as barrier or interior point methods. The highlight of this tutorial is a real-time ALADIN variant that can be implemented with a few lines of code yet arriving at a sparse QP solver that can compete with mature open-source and commercial QP solvers in terms of both run-time as well as numerical accuracy. It is discussed why this observation could have far reaching consequences on the future of algorithm and software development in the field of large-scale optimization and MPC.

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arXiv2021

ALADIN-$α$ -- An open-source MATLAB toolbox for distributed non-convex optimization

This paper introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-$α$. ALADIN-$α$ is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Its user interface is convenient for rapid prototyping of non-convex distributed optimization algorithms. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization with reduced information exchange. A collection of examples from different applications fields including chemical engineering, robotics, and power systems underpins the potential of ALADIN-$α$.

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arXiv2021

Online power system parameter estimation and optimal operation

The integration of renewables into electrical grids calls for optimization-based control schemes requiring reliable grid models. Classically, parameter estimation and optimization-based control is often decoupled, which leads to high system operation cost in the estimation procedure. The present work proposes a method for simultaneously minimizing grid operation cost and optimally estimating line parameters based on methods for the optimal design of experiments. This method leads to a substantial reduction in cost for optimal estimation and in higher accuracy in the parameters compared with standard Optimal Power Flow and maximum-likelihood estimation. We illustrate the performance of the proposed method on a benchmark system.

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arXiv2021

Distributed Multi-Building Coordination for Demand Response

This paper presents a distributed optimization algorithm tailored for solving optimal control problems arising in multi-building coordination. The buildings coordinated by a grid operator, join a demand response program to balance the voltage surge by using an energy cost defined criterion. In order to model the hierarchical structure of the building network, we formulate a distributed convex optimization problem with separable objectives and coupled affine equality constraints. A variant of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method for solving the considered class of problems is then presented along with a convergence guarantee. To illustrate the effectiveness of the proposed method, we compare it to the Alternating Direction Method of Multipliers (ADMM) by running both an ALADIN and an ADMM based model predictive controller on a benchmark case study.

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arXiv2020

Decentralized Optimization over Tree Graphs

This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication protocol. In contrast to existing parallelizable optimization algorithms for non-convex optimization the nodes of the network are neither synchronized nor assign any central entity. None of the nodes needs to know the whole topology of the network, but all nodes know that the network is tree-structured. We discuss conditions under which locally quadratic convergence rates can be achieved. The method is illustrated by running the decentralized asynchronous multi-sweep protocol on a radial AC power network case study.

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arXiv2020

Distributed Optimization for Massive Connectivity

Massive device connectivity in Internet of Thing (IoT) networks with sporadic traffic poses significant communication challenges. To overcome this challenge, the serving base station is required to detect the active devices and estimate the corresponding channel state information during each coherence block. The corresponding joint activity detection and channel estimation problem can be formulated as a group sparse estimation problem, also known under the name "Group Lasso". This letter presents a fast and efficient distributed algorithm to solve such Group Lasso problems, which alternates between solving small-scaled problems in parallel and dealing with a linear equation for consensus. Numerical results demonstrate the speedup of this algorithm compared with the state-of-the-art methods in terms of convergence speed and computation time.

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arXiv2020

Optimal Experiment Design for AC Power Systems Admittance Estimation

The integration of renewables into electrical grids calls for the development of tailored control schemes which in turn require reliable grid models. In many cases, the grid topology is known but the actual parameters are not exactly known. This paper proposes a new approach for online parameter estimation in power systems based on optimal experimental design using multiple measurement snapshots. In contrast to conventional methods, our method computes optimal excitations extracting the maximum information in each estimation step to accelerate convergence. The performance of the proposed method is illustrated on a case study.

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arXiv2020

A set-theoretic generalization of dissipativity with applications in Tube MPC

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept of dissipativity of systems that are affected by external disturbances. The corresponding theoretical developments build upon set based analysis methods and lay a general theoretical foundation for a rigorous stability analysis of economic tube model predictive controllers. Besides, we discuss practical prodecures for verifying set-dissipativity of constrained linear control systems with convex stage costs.

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arXiv2020

Distributed Optimization using ALADIN for MPC in Smart Grids

This paper presents a distributed optimization algorithm tailored to solve optimization problems arising in smart grids. In detail, we propose a variant of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method, which comes along with global convergence guarantees for the considered class of linear-quadratic optimization problems. We establish local quadratic convergence of the proposed scheme and elaborate its advantages compared to the Alternating Direction Method of Multipliers (ADMM). In particular, we show that, at the cost of more communication, ALADIN requires fewer iterations to achieve the desired accuracy. Furthermore, it is numerically demonstrated that the number of iterations is independent of the number of subsystems. The effectiveness of the proposed scheme is illustrated by running both an ALADIN and an ADMM based model predictive controller on a benchmark case study.

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arXiv2020

Towards Global Optimal Control via Koopman Lifts

This paper introduces a framework for solving time-autonomous nonlinear infinite horizon optimal control problems, under the assumption that all minimizers satisfy Pontryagin's necessary optimality conditions. In detail, we use methods from the field of symplectic geometry to analyze the eigenvalues of a Koopman operator that lifts Pontryagin's differential equation into a suitably defined infinite dimensional symplectic space. This has the advantage that methods from the field of spectral analysis can be used to characterize globally optimal control laws. A numerical method for constructing optimal feedback laws for nonlinear systems is then obtained by computing the eigenvalues and eigenvectors of a matrix that is obtained by projecting the Pontryagin-Koopman operator onto a finite dimensional space. We illustrate the effectiveness of this approach by computing accurate approximations of the optimal nonlinear feedback law for a Van der Pol control system, which cannot be stabilized by a linear control law.

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arXiv2020

Distributed Control Enforcing Group Sparsity in Smart Grids

In modern smart grids, charging of local energy storage devices is coordinated on a residential level to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which reduces their lifetime. We enforce group sparsity by using an $\ell_{p,q}$-regularization on the control to counteract this phenomenon. This leads to a non-smooth convex optimization problem, for which we propose a tailored Alternating Direction Method of Multipliers algorithm. We elaborate further how to embed it in a Model Predictive Control framework. We show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving by numerical simulations.

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arXiv2019

Partially Distributed Outer Approximation

This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming (MICP) problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads.

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arXiv2019

Parallel Explicit Tube Model Predictive Control

This paper is about a parallel algorithm for tube-based model predictive control. The proposed control algorithm solves robust model predictive control problems suboptimally, while exploiting their structure. This is achieved by implementing a real-time algorithm that iterates between the evaluation of piecewise affine functions, corresponding to the parametric solution of small-scale robust MPC problems, and the online solution of structured equality constrained QPs. The performance of the associated real-time robust MPC controllers is illustrated by a numerical case study.

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arXiv2019

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.

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arXiv2019

Decomposition of non-convex optimization via bi-level distributed ALADIN

Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems. In case of constrained non-convex optimization only a few algorithms are currently are available; often their performance is limited, or they lack convergence guarantees. This paper proposes a framework for decentralized non-convex optimization via bi-level distribution of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Bi-level distribution means that the outer ALADIN structure is combined with an inner distribution/decentralization level solving a condensed variant of ALADIN's convex coordination QP by decentralized algorithms. We prove sufficient conditions ensuring local convergence while allowing for inexact decentralized/distributed solutions of the coordination QP. Moreover, we show how a decentralized variant of conjugate gradient or decentralized ADMM schemes can be employed at the inner level. We draw upon case studies from power systems and robotics to illustrate the performance of the proposed framework.

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arXiv2019

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.

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arXiv2019

Parallel Explicit Model Predictive Control

This paper is about a real-time model predictive control (MPC) algorithm for large-scale, structured linear systems with polytopic state and control constraints. The proposed controller receives the current state measurement as an input and computes a sub-optimal control reaction by evaluating a finite number of piecewise affine functions that correspond to the explicit solution maps of small-scale parametric quadratic programming (QP) problems. We provide recursive feasibility and asymptotic stability guarantees, which can both be verified offline. The feedback controller is suboptimal on purpose because we are enforcing real-time requirements assuming that it is impossible to solve the given large-scale QP in the given amount of time. In this context, a key contribution of this paper is that we provide a bound on the sub-optimality of the controller. Our numerical simulations illustrate that the proposed explicit real-time scheme easily scales up to systems with hundreds of states and long control horizons, system sizes that are completely out of the scope of existing, non-suboptimal Explicit MPC controllers.

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arXiv2018

Interval Superposition Arithmetic for Guaranteed Parameter Estimation

The problem of guaranteed parameter estimation (GPE) consists in enclosing the set of all possible parameter values, such that the model predictions match the corresponding measurements within prescribed error bounds. One of the bottlenecks in GPE algorithms is the construction of enclosures for the image-set of factorable functions. In this paper, we introduce a novel set-based computing method called interval superposition arithmetics (ISA) for the construction of enclosures of such image sets and its use in GPE algorithms. The main benefits of using ISA in the context of GPE lie in the improvement of enclosure accuracy and in the implied reduction of number set-membership tests of the set-inversion algorithm.

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