arXiv subjects

Andrea Zanelli

Publications and source records attributed to Andrea Zanelli.

At least 19 recordsLinked to original sources

arXiv2025

On the Effect of Tap Changers and Nonlinear Loads on Voltage Stability

On 21 June 2024, a severe incident happened in the South-Eastern part of the Continental European power system. After a voltage collapse, large parts of Albania, Montenegro, Bosnia and Herzegovina as well as Croatia suffered from a blackout [1]. The initial tripping of two transmission lines resulted in a voltage collapse in these countries. Investigations have shown that a) transformers with on-load tap changers (OLTC) and b) nonlinear loads, in particular air conditioning systems, played a significant role in this event. Motivated by this, we carry out an assessment of the effect of OLTC on voltage stability in the presence of nonlinear loads. By doing this we hope to further shed some light on the potential instability mechanisms that can be triggered in scenarios like the above-mentioned blackout.

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arXiv2025

Robust Nonlinear Optimal Control via System Level Synthesis

This paper addresses the problem of finite horizon constrained robust optimal control for nonlinear systems subject to norm-bounded disturbances. To this end, the underlying uncertain nonlinear system is decomposed based on a first-order Taylor series expansion into a nominal system and an error (deviation) described as an uncertain linear time-varying system. This decomposition allows us to leverage system level synthesis to jointly optimize an affine error feedback, a nominal nonlinear trajectory, and, most importantly, a dynamic linearization error over-bound used to ensure robust constraint satisfaction for the nonlinear system. The proposed approach thereby results in less conservative planning compared with state-of-the-art techniques. We demonstrate the benefits of the proposed approach to control the rotational motion of a rigid body subject to state and input constraints.

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arXiv2024

A Stiffness-Oriented Model Order Reduction Method for Low-Inertia Power Systems

This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power systems, posing challenges for time-domain simulations and control design. Our approach involves rotation of the coordinate system of a linearized system using a transformation matrix derived from the real Jordan canonical form, leading to mode decoupling. The fast modes are then truncated in the rotated coordinate system to obtain a lower-order model with reduced stiffness. Applying the same transformation to the original nonlinear system results in an approximate separation of slow and fast states, which can be truncated to reduce the stiffness. The resulting reduced-order model demonstrates an accurate time-domain performance, the slow eigenvalues of the linearized system are correctly preserved, and a reduction in the model stiffness is achieved, allowing for accurate integration with increased step size. Our methodology is assessed in detail for a 3-bus system with generation units involving grid-forming/following converters and synchronous machines, where it allows for a computational speed-up of up to 100x compared to the original system. Several standard larger test systems are also considered.

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arXiv2024

Predictive stability filters for nonlinear dynamical systems affected by disturbances

Predictive safety filters provide a way of projecting potentially unsafe inputs, proposed, e.g. by a human or learning-based controller, onto the set of inputs that guarantee recursive state and input constraint satisfaction by leveraging model predictive control techniques. In this paper, we extend this framework such that in addition, robust asymptotic stability of the closed-loop system can be guaranteed by enforcing a decrease of an implicit Lyapunov function which is constructed using a predicted system trajectory. Differently from previous results, we show robust asymptotic stability with respect to a predefined disturbance set on an extended state consisting of the system state and a warmstart input sequence. The proposed strategy is applied to an automotive lane keeping example in simulation.

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arXiv2024

Inherently robust suboptimal MPC for autonomous racing with anytime feasible SQP

In recent years, the increasing need for high-performance controllers in applications like autonomous driving has motivated the development of optimization routines tailored to specific control problems. In this paper, we propose an efficient inexact model predictive control (MPC) strategy for autonomous miniature racing with inherent robustness properties. We rely on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility. In this way, we provide a strategy that computes suboptimal and yet feasible solutions with a computational footprint that is much lower than state-of-the-art methods based on the computation of locally optimal solutions. Under suitable assumptions on the terminal set and on the controllability properties of the system, we can state that, for any sufficiently small disturbance affecting the system's dynamics, recursive feasibility can be guaranteed. We validate the effectiveness of the proposed strategy in simulation and by deploying it onto a physical experiment with autonomous miniature race cars. Both the simulation and experimental results demonstrate that, using the feasible SQP method, a feasible solution can be obtained with moderate additional computational effort compared to strategies that resort to early termination without providing a feasible solution. At the same time, the proposed method is significantly faster than the state-of-the-art solver Ipopt.

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arXiv2023

Zero-Order Optimization for Gaussian Process-based Model Predictive Control

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to i) the increased number of augmented states in the optimization problem, as well as ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach, and combine it with ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension $n_x$ for each SQP iteration from $\mathcal{O}(n_x^6)$ to $\mathcal{O}(n_x^3)$, and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.

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arXiv2023

Asynchronous Computation of Tube-based Model Predictive Control

Tube-based model predictive control (MPC) methods bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. While techniques that compute the tubes online reduce conservativeness and increase performance, they suffer from high and potentially prohibitive computational complexity. This paper presents an asynchronous computation mechanism for system level tube-MPC (SLTMPC), a recently proposed tube-based MPC method which optimizes over both the nominal trajectory and the tubes. Computations are split into a primary and a secondary process, computing the nominal trajectory and the tubes, respectively. This enables running the primary process at a high frequency and moving the computationally complex tube computations to the secondary process. We show that the secondary process can continuously update the tubes, while retaining recursive feasibility of the primary process.

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arXiv2022

A Feasible Sequential Linear Programming Algorithm with Application to Time-Optimal Path Planning Problems

In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to time-optimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear constraints which arise in motion planning of mechatronic systems. The algorithm applies a trust-region globalization strategy ensuring global convergence. For fully determined problems our algorithm provides locally quadratic convergence. Moreover, the algorithm keeps all iterates feasible enabling early termination at suboptimal, feasible solutions. This additional feasibility is achieved by an efficient iterative strategy using evaluations of constraints, i.e., zero-order information. Convergence of the feasibility iterations can be enforced by reduction of the trust-region radius. These feasibility iterations maintain feasibility for general Nonlinear Programs (NLP). Therefore, the algorithm is applicable to general NLPs. We demonstrate our algorithm's efficiency and the feasibility update strategy on a TOCP of an overhead crane motion planning simulation case.

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arXiv2022

Inexact GMRES Policy Iteration for Large-Scale Markov Decision Processes

Policy iteration enjoys a local quadratic rate of contraction, but its iterations are computationally expensive for Markov decision processes (MDPs) with a large number of states. In light of the connection between policy iteration and the semismooth Newton method and taking inspiration from the inexact variants of the latter, we propose \textit{inexact policy iteration}, a new class of methods for large-scale finite MDPs with local contraction guarantees. We then design an instance based on the deployment of GMRES for the approximate policy evaluation step, which we call inexact GMRES policy iteration. Finally, we demonstrate the superior practical performance of inexact GMRES policy iteration on an MDP with 10000 states, where it achieves a $\times 5.8$ and $\times 2.2$ speedup with respect to policy iteration and optimistic policy iteration, respectively.

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arXiv2022

Dynamic Programming Through the Lens of Semismooth Newton-Type Methods (Extended Version)

Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to solve the Bellman equation. In particular, we prove that policy iteration is equivalent to the exact semismooth Newton method and enjoys local quadratic convergence rate. This finding is corroborated by extensive numerical evidence in the fields of control and operations research, which confirms that policy iteration generally requires few iterations to achieve convergence even when the number of policies is vast. We then show that value iteration is an instance of the fixed-point iteration method. In this spirit, we develop a novel locally accelerated version of value iteration with global convergence guarantees and negligible extra computational costs.

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arXiv2022

PAGE-PG: A Simple and Loopless Variance-Reduced Policy Gradient Method with Probabilistic Gradient Estimation

Despite their success, policy gradient methods suffer from high variance of the gradient estimate, which can result in unsatisfactory sample complexity. Recently, numerous variance-reduced extensions of policy gradient methods with provably better sample complexity and competitive numerical performance have been proposed. After a compact survey on some of the main variance-reduced REINFORCE-type methods, we propose ProbAbilistic Gradient Estimation for Policy Gradient (PAGE-PG), a novel loopless variance-reduced policy gradient method based on a probabilistic switch between two types of updates. Our method is inspired by the PAGE estimator for supervised learning and leverages importance sampling to obtain an unbiased gradient estimator. We show that PAGE-PG enjoys a $\mathcal{O}\left( ε^{-3} \right)$ average sample complexity to reach an $ε$-stationary solution, which matches the sample complexity of its most competitive counterparts under the same setting. A numerical evaluation confirms the competitive performance of our method on classical control tasks.

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arXiv2021

Introducing the quadratically-constrained quadratic programming framework in HPIPM

This paper introduces the quadratically-constrained quadratic programming (QCQP) framework recently added in HPIPM alongside the original quadratic-programming (QP) framework. The aim of the new framework is unchanged, namely providing the building blocks to efficiently and reliably solve (more general classes of) optimal control problems (OCP). The newly introduced QCQP framework provides full features parity with the original QP framework: three types of QCQPs (dense, optimal control and tree-structured optimal control QCQPs) and interior point method (IPM) solvers as well as (partial) condensing and other pre-processing routines. Leveraging the modular structure of HPIPM, the new QCQP framework builds on the QP building blocks and similarly provides fast and reliable IPM solvers.

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arXiv2021

A Lyapunov Function for the Combined System-Optimizer Dynamics in Inexact Model Predictive Control

In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is derived for the setting where a limited number of iterations of the optimizer are carried out per sampling time. Under the assumption of Lipschitz continuity of the solution, we explicitly construct a Lyapunov function for the combined system-optimizer dynamics, which shows that asymptotic stability can be obtained if the sampling time is sufficiently short. The results constitute an extension to existing attractivity results which hold in the simplified setting where inequality constraints are either not present or inactive in the region of attraction considered. Moreover, with respect to the established results on robust asymptotic stability of suboptimal model predictive control, we develop a framework that takes into account the optimizer's dynamics and does not require decrease of the objective function across iterates. By extending these results, the gap between theory and practice of the standard real-time iteration strategy is bridged and asymptotic stability for a broader class of methods is guaranteed.

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arXiv2021

System Level Disturbance Reachable Sets and their Application to Tube-based MPC

Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube-based MPC formulation based on system level disturbance reachable sets (SL-DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL-DRS. This allows us to formulate a system level tube-MPC (SLTMPC) method using the SL-DRS as tubes, which enables concurrent optimization of the nominal trajectory and the tubes, while using a positively invariant terminal set. Finally, we show that the SL-DRS tubes can also be computed offline.

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arXiv2020

acados: a modular open-source framework for fast embedded optimal control

This paper presents the acados software package, a collection of solvers for fast embedded optimization intended for fast embedded applications. Its interfaces to higher-level languages make it useful for quickly designing an optimization-based control algorithm by putting together different algorithmic components that can be readily connected and interchanged. Since the core of acados is written on top of a high-performance linear algebra library, we do not sacrifice computational performance. Thus, we aim to provide both flexibility and performance through modularity, without the need to rely on automatic code generation, which facilitates maintainability and extensibility. The main features of acados are: efficient optimal control algorithms targeting embedded devices implemented in C, linear algebra based on the high-performance BLASFEO library, user-friendly interfaces to Matlab and Python, and compatibility with the modeling language of CasADi. acados is free and open-source software released under the permissive BSD 2-Clause license.

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arXiv2020

Convergence Analysis of Homotopy-SGD for non-convex optimization

First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning models. Their inexpensive iterations generally come together with slow global convergence rate (mostly sublinear), leading to the necessity of carrying out a very high number of iterations before the iterates reach a neighborhood of a minimizer. In this work, we present a first-order stochastic algorithm based on a combination of homotopy methods and SGD, called Homotopy-Stochastic Gradient Descent (H-SGD), which finds interesting connections with some proposed heuristics in the literature, e.g. optimization by Gaussian continuation, training by diffusion, mollifying networks. Under some mild assumptions on the problem structure, we conduct a theoretical analysis of the proposed algorithm. Our analysis shows that, with a specifically designed scheme for the homotopy parameter, H-SGD enjoys a global linear rate of convergence to a neighborhood of a minimum while maintaining fast and inexpensive iterations. Experimental evaluations confirm the theoretical results and show that H-SGD can outperform standard SGD.

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arXiv2020

An Efficient Real-Time NMPC for Quadrotor Position Control under Communication Time-Delay

The advances in computer processor technology have enabled the application of nonlinear model predictive control (NMPC) to agile systems, such as quadrotors. These systems are characterized by their underactuation, nonlinearities, bounded inputs, and time-delays. Classical control solutions fall short in overcoming these difficulties and fully exploiting the capabilities offered by such platforms. This paper presents the design and implementation of an efficient position controller for quadrotors based on real-time NMPC with time-delay compensation and bounds enforcement on the actuators. To deal with the limited computational resources onboard, an offboard control architecture is proposed. It is implemented using the high-performance software package acados, which solves optimal control problems and implements a real-time iteration (RTI) variant of a sequential quadratic programming (SQP) scheme with Gauss-Newton Hessian approximation. The quadratic subproblems (QP) in the SQP scheme are solved with HPIPM, an interior-point method solver, built on top of the linear algebra library BLASFEO, finely tuned for multiple CPU architectures. Solution times are further reduced by reformulating the QPs using the efficient partial condensing algorithm implemented in HPIPM. We demonstrate the capabilities of our architecture using the Crazyflie 2.1 nano-quadrotor.

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arXiv2020

Continuous Control Set Nonlinear Model Predictive Control of Reluctance Synchronous Machines

In this paper we describe the design and implementation of a current controller for a reluctance synchronous machine based on continuous set nonlinear model predictive control. A computationally efficient grey box model of the flux linkage map is employed in a tracking formulation which is implemented using the high-performance framework for nonlinear model predictive control acados. The resulting controller is validated in simulation and deployed on a dSPACE real-time system connected to a physical reluctance synchronous machine. Experimental results are presented where the proposed implementation can reach sampling times in the range typical for electrical drives and can achieve large improvements in terms of control performance with respect to state-of-the-art classical control strategies.

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