A dual-control effect preserving formulation for nonlinear output-feedback stochastic model predictive control with constraints

In this paper we propose a formulation for approximate constrained nonlinear output-feedback stochastic model predictive control. Starting from the ideal but intractable stochastic optimal control problem (OCP), which involves the optimization over output-dependent policies, we use linearization with respect to the uncertainty to derive a tractable approximation which includes knowledge of the output model. This allows us to compute the expected value for the outer functions of the OCP exactly. Crucially, the dual control effect is preserved by this approximation. In consequence, the resulting controller is aware of how the choice of inputs affects the information available in the future which in turn influences subsequent controls. Thus, it can be classified as a form of implicit dual control

Implicit and Explicit Dual Model Predictive Control with an Application to Steel Recycling

We present a formulation for both implicit and explicit dual model predictive control with chance constraints. The formulation is applicable to systems that are affine in the state and disturbances, but possibly nonlinear in the controls. Awareness of uncertainty and dual control effect is achieved by including the covariance of a Kalman Filter state estimate in the predictions. For numerical stability, these predictions are obtained from a square-root Kalman filter update based on a QR decomposition. In the implicit formulation, the incentive for uncertainty reduction is given indirectly via the impact of active constraints on the objective, as large uncertainty leads to large safety backoffs from the constraint set boundary. The explicit formulation additionally uses a heuristic cost term on uncertainty to encourage its active exploration. We evaluate the methods based on numerical simulation of a simplified but representative industrial steel recycling problem. Here, new steel needs to be produced by choosing a combination of several different steel scraps with unknown pollutant content. The pollutant content can only be measured after a scrap combination is molten, allowing for inference on the pollutants in the different scrap heaps. The cost should be minimized while ensuring high quality of the product through constraining the maximum amount of pollutant. The numerical simulations demonstrate the superiority of the two dual formulations with respect to a robustified but non-dual formulation. Specifically we achieve lower cost for the closed-loop trajectories while ensuring constraint satisfaction with a given probability.Comment: Submitted to IEEE Conference on Decision and Control 2022 (CDC 22

An Inverse Optimal Control Approach for Trajectory Prediction of Autonomous Race Cars

This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk smoothness, and which is restricted by constraints. The algorithm predicts a trajectory by solving a parameterized nonlinear program (NLP) which contains path progress and smoothness in cost terms. By observing the actual motion of a vehicle, the parameters of prediction are updated by means of solving an inverse optimal control problem that contains the parameters of the predicting NLP as optimization variables. The algorithm therefore learns to predict the observed vehicle trajectory in a least-squares relation to measurement data and to the presumed structure of the predicting NLP. This work contributes with an algorithm that allows for accurate and interpretable predictions with sparse data. The algorithm is implemented on embedded hardware in an autonomous real-world race car that is competing in the challenge Roborace and analyzed with respect to recorded data.Comment: ECC 202

Survey of sequential convex programming and generalized Gauss-Newton methods*

We provide an overview of a class of iterative convex approximation methods for nonlinear optimization problems with convex-over-nonlinear substructure. These problems are characterized by outer convexities on the one hand, and nonlinear, generally nonconvex, but differentiable functions on the other hand. All methods from this class use only first order derivatives of the nonlinear functions and sequentially solve convex optimization problems. All of them are different generalizations of the classical Gauss-Newton (GN) method. We focus on the smooth constrained case and on three methods to address it: Sequential Convex Programming (SCP), Sequential Convex Quadratic Programming (SCQP), and Sequential Quadratically Constrained Quadratic Programming (SQCQP). While the first two methods were previously known, the last is newly proposed and investigated in this paper. We show under mild assumptions that SCP, SCQP and SQCQP have exactly the same local linear convergence – or divergence – rate. We then discuss the special case in which the solution is fully determined by the active constraints, and show that for this case the KKT conditions are sufficient for local optimality and that SCP, SCQP and SQCQP even converge quadratically. In the context of parameter estimation with symmetric convex loss functions, the possible divergence of the methods can in fact be an advantage that helps them to avoid some undesirable local minima: generalizing existing results, we show that the presented methods converge to a local minimum if and only if this local minimum is stable against a mirroring operation applied to the measurement data of the estimation problem. All results are illustrated by numerical experiments on a tutorial example

Survey of sequential convex programming and generalized Gauss-Newton methods

We provide an overview of a class of iterative convex approximation methods for nonlinear optimization problems with convex-over-nonlinear substructure. These problems are characterized by outer convexities on the one hand, and nonlinear, generally nonconvex, but differentiable functions on the other hand. All methods from this class use only first order derivatives of the nonlinear functions and sequentially solve convex optimization problems. All of them are different generalizations of the classical Gauss-Newton (GN) method. We focus on the smooth constrained case and on three methods to address it: Sequential Convex Programming (SCP), Sequential Convex Quadratic Programming (SCQP), and Sequential Quadratically Constrained Quadratic Programming (SQCQP). While the first two methods were previously known, the last is newly proposed and investigated in this paper. We show under mild assumptions that SCP, SCQP and SQCQP have exactly the same local linear convergence – or divergence – rate. We then discuss the special case in which the solution is fully determined by the active constraints, and show that for this case the KKT conditions are sufficient for local optimality and that SCP, SCQP and SQCQP even converge quadratically. In the context of parameter estimation with symmetric convex loss functions, the possible divergence of the methods can in fact be an advantage that helps them to avoid some undesirable local minima: generalizing existing results, we show that the presented methods converge to a local minimum if and only if this local minimum is stable against a mirroring operation applied to the measurement data of the estimation problem. All results are illustrated by numerical experiments on a tutorial example

Zero-Order Robust Nonlinear Model Predictive Control with Ellipsoidal Uncertainty Sets

In this paper, we propose an efficient zero-order algorithm that can be used to compute an approximate solution to robust optimal control problems (OCP) and robustified nonconvex programs in general. In particular, we focus on robustified OCPs that make use of ellipsoidal uncertainty sets and show that, with the proposed zero-order method, we can efficiently obtain suboptimal, but robustly feasible solutions. The main idea lies in leveraging an inexact sequential quadratic programming (SQP) algorithm in which an advantageous sparsity structure is enforced. The obtained sparsity allows one to eliminate the variables associated with the propagation of the ellipsoidal uncertainty sets and to solve a reduced problem with the same dimensionality and sparsity structure of a nominal OCP. The inexact algorithm can drastically reduce the computational complexity of the SQP iterations (e.g., in the case where a structure exploiting interior-point method is used to solve the underlying quadratic programs (QPs), from O(N center dot (n(x)(6) + n(u)(3))) to O(N center dot (n(x)(3) + n(u)(3)))). Moreover, standard embedded QP solvers for nominal problems can be leveraged to solve the reduced QP. Copyright (C) 2021 The Authors.ISSN:2405-896

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

Early structural changes of the heart after experimental polytrauma and hemorrhagic shock

<div><p>Evidence is emerging that systemic inflammation after trauma drives structural and functional impairment of cardiomyocytes and leads to cardiac dysfunction, thus worsening the outcome of polytrauma patients. This study investigates the structural and molecular changes in heart tissue 4 h after multiple injuries with additional hemorrhagic shock using a clinically relevant rodent model of polytrauma. We determined mediators of systemic inflammation (keratinocyte chemoattractant, macrophage chemotactic protein 1), activated complement component C3a and cardiac troponin I in plasma and assessed histological specimen of the mouse heart via standard histomorphology and immunohistochemistry for cellular and subcellular damage and ongoing apoptosis. Further we investigated spatial and quantitative changes of connexin 43 by immunohistochemistry and western blotting. Our results show significantly increased plasma levels of both keratinocyte chemoattractant and cardiac troponin I 4 h after polytrauma and 2 h after induction of hypovolemia. Although we could not detect any morphological changes, immunohistochemical evaluation showed increased level of tissue high-mobility group box 1, which is both a damage-associated molecule and actively released as a danger response signal. Additionally, there was marked lateralization of the cardiac gap-junction protein connexin 43 following combined polytrauma and hemorrhagic shock. These results demonstrate a molecular manifestation of remote injury of cardiac muscle cells in the early phase after polytrauma and hemorrhagic shock with marked disruption of the cardiac gap junction. This disruption of an important component of the electrical conduction system of the heart may lead to arrhythmia and consequently to cardiac dysfunction.</p></div