A robust controller is specified, and the stability bounds of the uncertain closed-loop system are determined using the small gain, circle, positive real, and Popov criteria. A graphical approach is employed in order to demonstrate the ease with which the above robustness tests can be carried out on a problem of practical interest. A significant improvement in stability bounds is observed as the analysis moves from the small gain test to the circle, positive real, and Popov tests. In particular, small gain analysis results in the most conservative robust stability bounds, while Popov analysis yields significantly less conservative bounds. This is because traditional small gain type tests allow the uncertainty to be arbitrarily time-varying, whereas Popov analysis restricts the uncertainty to be constant, real parametric uncertainty. Therefore, the results reported here indicate the conservatism associated with small gain analysis, and the effectiveness of Popov analysis, in gauging robust stability in the presence of constant, real parametric uncertainty.
Mission planners for aircraft that operate in radar detection environments are often concerned the probability of detection. The probability of detection is a nonlinear function of the aircraft pose and radar position. Current path planning techniques for this application assume that the aircraft pose is deterministic. In practice, however, the aircraft pose is estimated using a navigation filter and therefore contains uncertainty. The uncertainty in the aircraft pose induces uncertainty in the probability of detection, but this phenomenon is generally not considered when path planning. This p…
Mission planners for aircraft operating under threat of detection by ground-based radar systems are concerned with the probability of detection. Current path planning methods for such scenarios consider the aircraft pose, radar position, and radar parameters to be deterministic and known. This paper presents a framework for incorporating uncertainty in these quantities into a radar detection model that is used by a path planner. The developed path planner evaluates the radar detection risk in the presence of uncertainties and uses linear covariance analysis to efficiently generate error budget…
The accurate online estimation of the road-friction coefficient is an essential feature for any advanced brake control system. In this study, a data-driven scheme based on a MLP Neural Net is proposed to estimate the optimum friction coefficient as a function of windowed slip-friction measurements. A stochastic NN weights drop-out mechanism is used to online estimate the confidence interval of the estimated best friction coefficient thus providing a characterization of the epistemic uncertainty associated to the NN block. Open loop and closed loop simulations of the landing phase of an aircraf…
The performance of model-based control techniques strongly depends on the quality of the employed dynamics model. If strong guarantees are desired, it is therefore common to robustly treat all possible sources of uncertainty, such as model inaccuracies or external disturbances. This, however, can result in overly conservative control strategies. In this paper, we present a stochastic model predictive control approach for discrete-time LTI systems subject to bounded parametric uncertainty and potentially unbounded stochastic additive noise. The proposed scheme makes use of homothetic tubes alon…
Mission planners for aircraft operating under threat of detection from ground-based radar systems are often concerned with the probability of detection. Current approaches to path planning in such environments consider the radar state (i.e. radar position and parameters) to be deterministic and known. In practice, there is uncertainty in the radar state which induces uncertainty in the probability of detection. This paper presents a method to incorporate the uncertainty of the radar state in a single-pulse radar detection model. The method linearizes the radar detection model with respect to t…
We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-lo…
Interval Prediction for Continuous-Time Systems with Parametric Uncertainties
Renault（雷诺）；Inria, Univ. Lille, CNRS, UMR 9189 - CRIStAL（法国国家信息与自动化研究所，里尔大学，法国国家科学研究中心，联合研究实验室9189）；ITMO University（信息技术、机械与光学大学）；Conservatoire National des Arts et Métiers (CNAM)（国立工艺学院）；Centrale Lille, CNRS, UMR 9189 - CRIStAL（里尔中央理工学院，法国国家科学研究中心，联合研究实验室9189）
We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-appr…
Robust Parametric Microgrid Dispatch Under Endogenous Uncertainty of Operation- and Temperature-Dependent Battery Degradation
State Key Laboratory of Environmental Adaptability for Industrial Products, China National Electric Apparatus Research Institute Co., Ltd.（工业产品环境适应性国家重点实验室，中国电器科学研究院有限公司）；Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong（香港中文大学机械与自动化工程学系）
We present a novel technique for solving the problem of safe control for a general class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS), we introduce a parameter adaptation law which guarantees convergence of the estimates of unknown parameters in the system dynamics to their true values within a fixed-time independent of the initial parameter estimation error. We then synthesize the adaptation law with a robust, adaptive control barrier function (RaCBF) based quadratic program to compute sa…
We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the general min-max model predictive control. The invariance property of the proposed tube holds for any arbitrary scaling. It yields a second-order cone programming problem which is less computationally expensive than standard semi-definite programming problems. We also present a numerical example with a comparative study among the proposed approach, an open-loop gu…
MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems
Water Research Institute (NEWRI), Nanyang Technological University, Singapore（新跃大学水研究 institute（NEWRI））；School of Chemistry, Chemical Engineering and Biotechnology, Nanyang Technological University, Singapore（新跃大学化学、化工与生物技术学院）；Soft Robotics Lab, ETH Zurich, Switzerland（苏黎世联邦理工学院软机器人实验室）；Department of Civil and Environmental Engineering, National University of Singapore, Singapore（新加坡国立大学土木与环境工程系）
In this paper, two types of linear estimators are considered for three related estimation problems involving set-theoretic uncertainty pertaining to $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ balls of frequency-responses. The problems at stake correspond to robust $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ in the face of non-parametric "channel-model" uncertainty and to a nominal $\mathcal{H}_{\infty}$ estimation problem. The estimators considered here are defined by minimizing the worst-case squared estimation error over the "uncertainty set" and by minimizing an average cost under the co…
