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Register a new userWhen Distributed Formation Control Is Feasible under Hard Constraints on Energy and Time?
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This paper studies distributed optimal formation control with hard constraints on energy levels and termination time, in which the formation error is to be minimized jointly with the energy cost. The main contributions include a globally optimal distributed formation control law and a comprehensive analysis of the resulting closed-loop system under those hard constraints. It is revealed that the energy levels, the task termination time, the steady-state error tolerance, as well as the network topology impose inherent limitations in achieving the formation control mission. Most notably, the lower bounds on the achievable termination time and the required minimum energy levels are derived, which are given in terms of the initial formation error, the steady-state error tolerance, and the largest eigenvalue of the Laplacian matrix. These lower bounds can be employed to assert whether an energy and time constrained formation task is achievable and how to accomplish such a task. Furthermore, the monotonicity of those lower bounds in relation to the control parameters is revealed. A simulation example is finally given to illustrate the obtained results.
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In this paper, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.
We study how to design a secure observer-based distributed controller such that a group of vehicles can achieve accurate state estimates and formation control even if the measurements of a subset of vehicle sensors are compromised by a malicious attacker. We propose an architecture consisting of a resilient observer, an attack detector, and an observer-based distributed controller. The distributed detector is able to update three sets of vehicle sensors: the ones surely under attack, surely attack-free, and suspected to be under attack. The adaptive observer saturates the measurement innovation through a preset static or time-varying threshold, such that the potentially compromised measurements have limited influence on the estimation. Essential properties of the proposed architecture include: 1) The detector is fault-free, and the attacked and attack-free vehicle sensors can be identified in finite time; 2) The observer guarantees both real-time error bounds and asymptotic error bounds, with tighter bounds when more attacked or attack-free vehicle sensors are identified by the detector; 3) The distributed controller ensures closed-loop stability. The effectiveness of the proposed methods is evaluated through simulations by an application to vehicle platooning.
In this paper, we present a data-driven secondary controller for regulating to some desired values several variables of interest in a power system, namely, electrical frequency, voltage magnitudes at critical buses, and active power flows through critical lines. The power generation system is based on distributed energy resources (DERs) interfaced with either grid-forming (GFM) or grid-following (GFL) inverters. The secondary controller is based on online feedback optimization leveraging the learned sensitivities of the changes in the system frequency, voltage magnitudes at critical buses, and active power flows through critical lines to the changes in inverter active and reactive power setpoints. To learn the sensitivities accurately from data, the feedback optimization has a built-in mechanism for keeping the secondary control inputs persistently exciting without degrading its performance. The feedback optimization also utilizes the learned power-voltage characteristics of photovoltaic (PV) arrays to compute DC-link voltage setpoints so as to allow the PV arrays to track the power setpoints. To learn the power-voltage characteristics, we separately execute a data-driven approach that fits a concave polynomial to the collected power-voltage measurements by solving a sum-of-squares (SoS) optimization. We showcase the secondary controller using the modified IEEE-14 bus test system, in which conventional energy sources are replaced with inverter-interfaced DERs.
One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface. Here, dynamics becomes completely independent of the model parameters and can be tuned accordingly to the desired target. In this paper we study this problem when the feedback law is subject to strong structural constraints. In particular, we assume that the control input may take values only over two bounded and disjoint sets. Such sets could be also non perfectly known a priori. An example is a control input allowed to switch only between two values. Under these peculiarities, we derive the necessary and sufficient conditions that guarantee sliding-mode control effectiveness for a class of time-varying continuous-time linear systems that includes all the stationary state-space linear models. Our analysis covers several scientific fields. It is only apparently confined to the linear setting and allows also to study an important set of nonlinear models. We describe fundamental examples related to epidemiology where the control input is the level of contact rate among people and the sliding surface permits to control the number of infected. For popular epidemiological models we prove the global convergence of control schemes based on the introduction of severe restrictions, like lockdowns, to contain epidemic. This greatly generalizes previous results obtained in the literature by casting them within a general sliding-mode theory.
The security of mobile robotic networks (MRNs) has been an active research topic in recent years. This paper demonstrates that the observable interaction process of MRNs under formation control will present increasingly severe threats. Specifically, we find that an external attack robot, who has only partial observation over MRNs while not knowing the system dynamics or access, can learn the interaction rules from observations and utilize them to replace a target robot, destroying the cooperation performance of MRNs. We call this novel attack as sneak, which endows the attacker with the intelligence of learning knowledge and is hard to be tackled by traditional defense techniques. The key insight is to separately reveal the internal interaction structure within robots and the external interaction mechanism with the environment, from the coupled state evolution influenced by the model-unknown rules and unobservable part of the MRN. To address this issue, we first provide general interaction process modeling and prove the learnability of the interaction rules. Then, with the learned rules, we design an Evaluate-Cut-Restore (ECR) attack strategy considering the partial interaction structure and geometric pattern. We also establish the sufficient conditions for a successful sneak with maximum control impacts over the MRN. Extensive simulations illustrate the feasibility and effectiveness of the proposed attack.
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