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Register a new userConvex Parameterization and Optimization for Robust Tracking of a Magnetically Levitated Planar Positioning System
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Magnetic levitation positioning technology has attracted considerable research efforts and dedicated attention due to its extremely attractive features. The technology offers high-precision, contactless, dust/lubricant-free, multi-axis, and large-stroke positioning. In this work, we focus on the accurate and smooth tracking problem of a multi-axis magnetically levitated (maglev) planar positioning system for a specific S-curve reference trajectory. The floating characteristics and the multi-axis coupling make accurate identification of the system dynamics difficult, which lead to a challenge to design a high performance control system. Here, the tracking task is achieved by a 2-Degree of Freedom (DoF) controller consisting of a feedforward controller and a robust stabilizing feedback controller with a prescribed sparsity pattern. The approach proposed in this paper utilizes the basis of an H-infinity controller formulation and a suitably established convex inner approximation. Particularly, a subset of robust stabilizable controllers with prescribed structural constraints is characterized in the parameter space, and so thus the re-formulated convex optimization problem can be easily solved by several powerful numerical algorithms and solvers. With this approach, the robust stability of the overall system is ensured with a satisfactory system performance despite the presence of parametric uncertainties. Furthermore, experimental results clearly demonstrate the effectiveness of the proposed approach.
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The outbreak of coronavirus disease 2019 (COVID-19) has led to significant challenges for schools, workplaces and communities to return to operations during the pandemic, while policymakers need to balance between individuals safety and operational efficiency. In this paper, we present a mixed-integer programming model for redesigning routes and bus schedules for the University of Michigan (UM)s campus bus system, to prepare for students return in the 2020 Fall semester. To ensure less than 15-minute travel time for all routes and to enforce social distancing among passengers, we propose a hub-and-spoke design and utilize real data of student activities to identify hub locations and reduce the number of bus stops used in the new routes. The new bus routes, although using only 50% or even fewer seats in each bus, can still satisfy peak-hour demand in regular semesters at UM. We sample a variety of scenarios that cover variations of peak demand, social-distancing requirements, broken-down buses or no-shows of drivers, to demonstrate the system resiliency of the new routes and schedules via simulation. Our approach can be generalized to redesign public transit systems with social distancing requirement during the pandemic, to reduce passengers infection risk.
Reusable decoys offer a cost-effective alternative to the single-use hardware commonly applied to protect surface assets from threats. Such decoys portray fake assets to lure threats away from the true asset. To deceive a threat, a decoy first has to position itself such that it can break the radar lock. Considering multiple simultaneous threats, this paper introduces an approach for controlling multiple decoys to minimise the time required to break the locks of all the threats. The method includes the optimal allocation of one decoy to every threat with an assignment procedure that provides local position constraints to guarantee collision avoidance and thereby decouples the control of the decoys. A crude model of a decoy with uncertainty is considered for motion planning. The task of a decoy reaching a state in which the lock of the assigned threat can be broken is formulated as a temporal logic specification. To this end, the requirements to complete the task are modelled as time-varying set-membership constraints. The temporal and logical combination of the constraints is encoded in a mixed-integer optimisation problem. To demonstrate the results a simulated case study is provided.
We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is NP-hard in general and motivates the development of tractable approximations. We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity pattern. For sparsity constraints, the approach of SI goes beyond the notion of Quadratic Invariance (QI): 1) the SI approach always yields a convex restriction; 2) the solution via the SI approach is guaranteed to be globally optimal when QI holds and performs at least as well as considering a nearest QI subset. Moreover, the notion of SI naturally applies to designing structured static controllers, while QI is not utilizable. Numerical examples show that even for non-QI cases, SI can recover solutions that are 1) globally optimal and 2) strictly more performing than previous methods.
We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter a novel and unifying disturbance description is employed. While large parts of the paper focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.
In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimzation over directed networks that preserves differential privacy, which is a strong notion that protects agents privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is kept private. That is to say, only one substate is visible to an adversary, protecting the privacy from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.
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