How scaling of the disturbance set affects robust positively invariant sets for linear systems

This paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature

Error bounds for maxout neural network approximations of model predictive control

Neural network (NN) approximations of model predictive control (MPC) are a versatile approach if the online solution of the underlying optimal control problem (OCP) is too demanding and if an exact computation of the explicit MPC law is intractable. The drawback of such approximations is that they typically do not preserve stability and performance guarantees of the original MPC. However, such guarantees can be recovered if the maximum error with respect to the optimal control law and the Lipschitz constant of that error are known. We show in this work how to compute both values exactly when the control law is approximated by a maxout NN. We build upon related results for ReLU NN approximations and derive mixed-integer (MI) linear constraints that allow a computation of the output and the local gain of a maxout NN by solving an MI feasibility problem. Furthermore, we show theoretically and experimentally that maxout NN exist for which the maximum error is zero.Comment: 8 pages, 2 tables, to be published in the proceedings of the 22nd World Congress of the International Federation of Automatic Control (2023

Implicit predictors in regularized data-driven predictive control

We introduce the notion of implicit predictors, which characterize the input-(state)-output prediction behavior underlying a predictive control scheme, even if it is not explicitly enforced as an equality constraint (as in traditional model or subspace predictive control). To demonstrate this concept, we derive and analyze implicit predictors for some basic data-driven predictive control (DPC) schemes, which offers a new perspective on this popular approach that may form the basis for modified DPC schemes and further theoretical insights.Comment: This paper is a reprint of a contribution to the IEEE Control Systems Letters. 6 pages, 2 figure

Tailored neural networks for learning optimal value functions in MPC

Learning-based predictive control is a promising alternative to optimization-based MPC. However, efficiently learning the optimal control policy, the optimal value function, or the Q-function requires suitable function approximators. Often, artificial neural networks (ANN) are considered but choosing a suitable topology is also non-trivial. Against this background, it has recently been shown that tailored ANN allow, in principle, to exactly describe the optimal control policy in linear MPC by exploiting its piecewise affine structure. In this paper, we provide a similar result for representing the optimal value function and the Q-function that are both known to be piecewise quadratic for linear MPC.Comment: 7 pages, 2 figures, 1 tabl

Cryptanalysis of Random Affine Transformations for Encrypted Control

Cloud-based and distributed computations are of growing interest in modern control systems. However, these technologies require performing computations on not necessarily trustworthy platforms and, thus, put the confidentiality of sensitive control-related data at risk. Encrypted control has dealt with this issue by utilizing modern cryptosystems with homomorphic properties, which allow a secure evaluation at the cost of an increased computation or communication effort (among others). Recently, a cipher based on a random affine transformation gained attention in the encrypted control community. Its appeal stems from the possibility to construct security providing homomorphisms that do not suffer from the restrictions of ``conventional'' approaches. This paper provides a cryptanalysis of random affine transformations in the context of encrypted control. To this end, a deterministic and probabilistic variant of the cipher over real numbers are analyzed in a generalized setup, where we use cryptographic definitions for security and attacker models. It is shown that the deterministic cipher breaks under a known-plaintext attack, and unavoidably leaks information of the closed-loop, which opens another angle of attack. For the probabilistic variant, statistical indistinguishability of ciphertexts can be achieved, which makes successful attacks unlikely. We complete our analysis by investigating a floating point realization of the probabilistic random affine transformation cipher, which unfortunately suggests the impracticality of the scheme if a security guarantee is needed.Comment: 8 pages, 2 figures, to be published in the proceedings of the 22nd World Congress of the International Federation of Automatic Control (2023

Energetische Wohngebäudesanierung mit Faktor 10 : Analyse von Passivhaus-Konzepten und deren Anwendung auf die Sanierung

[no abstract

Consumer preferences for electric vehicles in Germany

Purpose. Analyze the preference for battery electric vehicles (BEVs) as opposed to hybrid electric vehicles (HEVs) or normal combustible vehicles (NCVs) in Germany. Design. Survey of 400 respondents who stated their preference for one of the three vehicles and considered purchase price, driving range, fuel costs, emissions, refueling availability, refueling time, acceleration and policy incentives. Binary and multinomial choice logit models are applied. Main findings. We find strong evidence that previous experience of driving a BEV and car sharing are significant factors to state a preference for electric cars. Other factors such as driving range, purchase price, gender, ecological awareness and incentives such as tax exemptions also influence the choice. Originality. The preference for BEVs among German customers would increase if granted the opportunity of a driving experience and, more intensely when combined with car sharing opportunities. Increasing the availability of car sharing of electric vehicles seems an excellent way to penetrate the market