This paper presents a new framework for controller robustness verification with respect to F-16 aircraft's closed-loop performance in longitudinal flight. We compare the state regulation performance of a linear quadratic regulator (LQR) and a gain-scheduled linear quadratic regulator (gsLQR), applied to nonlinear open-loop dynamics of F-16, in presence of stochastic initial condition and parametric uncertainties, as well as actuator disturbance. We show that, in presence of initial condition uncertainties alone, both LQR and gsLQR have comparable immediate and asymptotic performances, but the gsLQR exhibits better transient performance at intermediate times. This remains true in the presence of additional actuator disturbance. Also, gsLQR is shown to be more robust than LQR, against parametric uncertainties. The probabilistic framework proposed here, leverages transfer operator based density computation in exact arithmetic and introduces optimal transport theoretic performance validation and verification (V&V) for nonlinear dynamical systems. Numerical results from our proposed method, are in unison with Monte Carlo simulations.
Solving nonlinear model predictive control problems in real time is still an important challenge despite of recent advances in computing hardware, optimization algorithms and tailored implementations. This challenge is even greater when uncertainty is present due to disturbances, unknown parameters or measurement and estimation errors. To enable the application of advanced control schemes to fast systems and on low-cost embedded hardware, we propose to approximate a robust nonlinear model controller using deep learning and to verify its quality using probabilistic validation techniques. We pro…
Leveraging recent developments in black-box risk-aware verification, we provide three algorithms that generate probabilistic guarantees on (1) optimality of solutions, (2) recursive feasibility, and (3) maximum controller runtimes for general nonlinear safety-critical finite-time optimal controllers. These methods forego the usual (perhaps) restrictive assumptions required for typical theoretical guarantees, e.g. terminal set calculation for recursive feasibility in Nonlinear Model Predictive Control, or convexification of optimal controllers to ensure optimality. Furthermore, we show that the…
Permissive Controller Synthesis for Probabilistic Systems
Faculty of Informatics, Masaryk University（马萨里克大学信息学院）；EECS, Queen Mary, University of London（伦敦大学玛丽女王学院电气电子与计算机科学与工程系）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）；School of Computer Science, University of Birmingham（伯明翰大学计算机科学学院）
In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed scheme is based on a notion of so-called $(ε,δ)$-approximate probabilistic relations, allowing one to quantify the similarity between stochastic systems modeled by discrete-time stochastic games and their corresponding finite abstractions. Leveraging this type of relations, the lower bound for the probability of satisfying the desired specifications can be w…
Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of blackbox optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This paper focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provid…
Underwater vehicles are employed in the exploration of dynamic environments where tuning of a specific controller for each task would be time-consuming and unreliable as the controller depends on calculated mathematical coefficients in idealised conditions. For such a case, learning task from experience can be a useful alternative. This paper explores the capability of probabilistic inference learning to control autonomous underwater vehicles that can be used for different tasks without re-programming the controller. Probabilistic inference learning uses a Gaussian process model of the real ve…
This paper contributes to the design of a fractional order (FO) internal model controller (IMC) for a first order plus time delay (FOPTD) process model to satisfy a given set of desired robustness specifications in terms of gain margin (Am) and phase margin (Pm). The highlight of the design is the choice of a fractional order (FO) filter in the IMC structure which has two parameters (lambda and beta) to tune as compared to only one tuning parameter (lambda) for traditionally used integer order (IO) filter. These parameters are evaluated for the controller, so that Am and Pm can be chosen indep…
Safe control of constrained linear systems under both epistemic and aleatory uncertainties is considered. The aleatory uncertainty characterizes random noises and is modeled by a probability distribution function (PDF) and the epistemic uncertainty characterizes the lack of knowledge on the system dynamics. Data-based probabilistic safe controllers are designed for the cases where the noise PDF is 1) zero-mean Gaussian with a known covariance, 2) zero-mean Gaussian with an uncertain covariance, and 3) zero-mean non-Gaussian with an unknown distribution. Easy-to-check model-based conditions for…
We present a full review of PID passivity-based controllers (PBC) applied to power electronic converters, discussing limitations, unprecedented merits and potential improvements in terms of large-signal stability, robustness and performance. We provide four main contributions. The nominal case is first considered and it is shown, under the assumption of perfect knowledge of the system parameters, that the PID-PBC is able to guarantee global exponential stability of a desired operating point for any positive gains. Second, we analyze robustness of the controller to parameters uncertainty for a …
Specification-aware Robustness Margins for Symbolic Controllers
College of Computing, University Mohammed VI Polytechnic（Mohammed VI Polytechnic大学计算学院）；Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes（巴黎萨克雷大学、法国国家科学研究中心、中央理工-高等电力学院、信号与系统实验室）
This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate Boolean functions with probability distributions that govern the activation frequency of each Boolean function. Owing to the stochasticity, the uniform state feedback controller, independent of switching signal, might be out of work, and in this case, the non-uniform state feedback controller is required. Subsequently, a criterion is derived to determine whether …
This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system…
Design and implementation of an optimal and robust single-loop voltage controller is proposed for single-phase grid forming voltage source inverter (VSI). The objective of the proposed controller is to have good reference tracking and disturbance rejection. Uncertain nature of loads can significantly alter system's behavior, especially during heavily loaded conditions, and impose an uncertainty in the dynamic model. This deteriorates the robustness of the controller severely. H-Infinity-based controller design is proposed in this article to address this issue. The required objectives of the op…
In the realm of supervised learning, Bayesian learning has shown robust predictive capabilities under input and parameter perturbations. Inspired by these findings, we demonstrate the robustness properties of Bayesian learning in the control search task. We seek to find a linear controller that stabilizes a one-dimensional open-loop unstable stochastic system. We compare two methods to deduce the controller: the first (deterministic) one assumes perfect knowledge of system parameter and state, the second takes into account uncertainties in both and employs Bayesian learning to compute a poster…
RWTH Aachen University（亚琛工业大学）；Ingenieurgesellschaft Auto und Verkehr (IAV)（IAV汽车与交通工程公司）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties into a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning method's posterior distribution i…
This paper presents three types of sliding mode controllers for a magnetic levitation system. First, a proportional-integral sliding mode controller (PI-SMC) is designed using a new switching surface and a proportional plus power rate reaching law. The PI-SMC is more robust than a feedback linearization controller in the presence of mismatched uncertainties and outperforms the SMC schemes reported recently in the literature in terms of the convergence rate and settling time. Next, to reduce the chattering phenomenon in the PI-SMC, a state feedback-based discrete-time SMC algorithm is developed…
While $\mathcal{H}_\infty$ methods can introduce robustness against worst-case perturbations, their nominal performance under conventional stochastic disturbances is often drastically reduced. Though this fundamental tradeoff between nominal performance and robustness is known to exist, it is not well-characterized in quantitative terms. Toward addressing this issue, we borrow from the increasingly ubiquitous notion of adversarial training from machine learning to construct a class of controllers which are optimized for disturbances consisting of mixed stochastic and worst-case components. We …
Adaptive control architectures often make use of Lyapunov functions to design adaptive laws. We are specifically interested in adaptive control methods, such as the well-known L1 adaptive architecture, which employ a parameter observer for this purpose. In such architectures, the observation error plays a critical role in determining analytical bounds on the tracking error as well as robustness. In this paper, we show how the non-existence of coercive Lyapunov operators can impact the analytical bounds, and with it the performance and the robustness of such adaptive systems.
Probabilistic Plan Synthesis for Coupled Multi-Agent Systems
ACCESS Linnaeus Center, School of Electrical Engineering and KTH Center for Autonomous Systems, KTH Royal Institute of Technology（ACCESS林奈中心、电气工程学院和KTH自主系统中心，KTH皇家理工学院）；School of Computer Science and Communication, KTH Royal Institute of Technology（计算机科学与通信学院，KTH皇家理工学院）
This paper aims to synthesize a reachability controller for an unknown dynamical system. We first learn the unknown system using Gaussian processes and the (probabilistic) guarantee on the learned model. Then we use the funnel-based controller synthesis approach using this approximated dynamical system to design the controller for a reachability specification. Finally, the merits of the proposed method are shown using a numerical example.
In this research we propose a new compound Fractional Order Sliding Mode Controller (FOSMC) and SuperTwisting Controller (FOSMC+STC) to control of a MEMS gyroscope. A new sliding mode surface has been defined to design the proposed new sliding mode controller. The main advantages of a FOSMC is its high tracking performance and robustness against external perturbation, but it is susceptible to chattering. By augmenting a STC with a FOSMC, the chattering phenomenon is eliminated, singularity problem is solved and systems robustness has significatnetly improved. Simulation results validate the ef…
A Passivity-Based Design for Stability and Robustness in Event-Triggered Networked Control Systems with Communication Delays, Signal Quantizations and Packet Dropouts
University of Pennsylvania（宾夕法尼亚大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Motivated by the fragility of neural network (NN) controllers in safety-critical applications, we present a data-driven framework for verifying the risk of stochastic dynamical systems with NN controllers. Given a stochastic control system, an NN controller, and a specification equipped with a notion of trace robustness (e.g., constraint functions or signal temporal logic), we collect trajectories from the system that may or may not satisfy the specification. In particular, each of the trajectories produces a robustness value that indicates how well (severely) the specification is satisfied (v…
