The increasing penetration of inverter-based resources into the power grid, with often only black-box models available, challenges long-standing frequency control methods. Most recent works take a decentralized approach without online device coordination via communication. This paper considers both dynamic behavior and communication within secondary frequency control on an intermediate timescale. We develop a distributed data-driven approach that utilizes peer-to-peer communication between inverters to avoid the need for a central control center. To enable a trade off between communication network requirements and control performance, we present a framework to guide communication topology design for secondary frequency regulation. Following design of the inter-agent information exchange scheme, we design a controller that is structured according to the communication topology with a closed-loop stability guarantee. Case studies on the IEEE 39-bus system validate the framework and illustrate the trade-off between communication requirements and control performance that is enabled by our approach.
Nicolae Marcoie, Șerban Chihaia, Tomi Alexăndrel Hrăniciuc
et al.
This work analyzed the nutrient dynamics (2011–2022) and discharge (2005–2022) for the Bahlui River at four distinctive locations: Parcovaci—a dam-protected area that has been untouched by agriculture or urbanization; Belcesti—a primarily agricultural area, also dam-protected; Podu Iloaiei—a region influenced by agriculture and urbanization; and Holboca—placed after a heavily urbanized area. The analysis focused on determining a series of statistical indicators using the Minitab 21.2 software. Two drought intervals and one flood interval were analyzed to highlight daily discharge evolution during the selected period, showing that the constructed reservoirs successfully control the streamflow. For the entire period, the evolution of mean and median values of the streamflow is consistent, considering the locations’ positions from the source to the river’s end. The total nitrogen and total phosphorus were selected as representative quality indicators. The study follows the influence of the analyzed areas’ characteristics and reservoirs’ presence on nutrient dynamics. The results showed that the most influential factor that impacts nutrient dynamics is the reservoirs’ presence, which controls the discharge, creates wetlands and swamps, and implicitly impacts nutrient concentration.
This paper studies viability and control synthesis for a delayed SIR epidemic. The model integrates a constant delay representing an incubation/latency time. The control inputs model non-pharmaceutical interventions, while an intensive care unit (ICU) state-constraint is introduced to reflect the healthcare system's capacity. The arising delayed control system is analyzed via functional viability tools, providing insights into fulfilling the ICU constraint through feedback control maps. In particular, we consider two scenarios: first, we consider the case of general continuous initial conditions. Then, as a further refinement of our analysis, we assume that the initial conditions satisfy a Lipschitz continuity property, consistent with the considered model. The study compares the (in general, sub-optimal) obtained control policies with the optimal ones for the delay-free case, emphasizing the impact of the delay parameter. The obtained results are supported and illustrated, in a concluding section, by numerical examples.
Emilija Krantić, Ivana Jovanović, Selena Pavličević
et al.
Collaboration among local self-government units within the Skrapež River basin (municipalities of Čačak, Sevojno, Valjevo, Užice, Bajina Bašta, Požega, Gornji Milanovac, and Kosjerić) represents a crucial factor in controlling soil erosion and actively defending against floods in the area. The Skrapež River basin, characterized by a fan-shaped and symmetrical form, is situated within the microregion of Srpska Crna Gora within the Western Morava region. It features a specific topography ranging from a minimum elevation of 305 m to a maximum elevation of 1347 m. Hilly-mountainous terrain occupies 46.63% of the surveyed area, with an average river basin slope of 18.36 m/km. Most of the basin is covered by metamorphic rocks (206.52 km²). The climatic parameters of the basin, with an average annual temperature of 9.55 °C and precipitation of 644.16 mm, influence erosion processes and hydrological characteristics of the basin. Using the Gavrilović method, the average yearly sediment yield was calculated at 249,650.24 m³/year, with the identification of 127 erosive channels. Maximum flows occur in May and June, with the most significant variations in the basin observed in September, May, and August. To prevent the destructive effects of major floods, it is necessary to establish collaboration and coordination among the mentioned local self-government units to prevent stream siltation, implement preventive anti-erosion measures, and carry out biotechnical protective works.
The largest economic center in Vietnam - Ho Chi Minh City, is facing increasingly serious riverbank erosion, one of the main reasons being the flow. Therefore, in this study, the flow velocity field on the Saigon River section is accurately analyzed in different time intervals with the help of MIKE 11 and MIKE 21 models. The simulation results show that The number of flow velocities in the middle of the river is 3-4 times greater than that of the two banks. However, between high tide and low tide, the flow on both sides of the river is faster than the main flow, especially in the upper part of the winding banks, such as the section from Ben Nghe sluice to Tan Thuan, sewer and river section from An Loi Dong Ward police station to Thu Thiem Bridge 2. The velocity value on the studied river section, in most cases, exceeds the allowable value of the non-erosion velocity of the bed material particles. , riverbanks, as well as suspended sediment particles. Therefore, the erosion process on both sides of the river will occur regularly and continuously, so urgent measures are needed to protect the riverbank. During the operation of the anti-flood sluice, the flow velocity will decrease slightly before sluices also appear as whirlpools. The flow velocity on the Saigon River has a complex distribution and changes from time to time depending on the flood discharge from Dau Tieng Lake and the tidal currents of the East Sea.
We consider a simply-supported Euler-Bernoulli beam with viscous and Kelvin--Voigt damping. Our objective is to attenuate the effect of an unknown distributed disturbance using one piezoelectric actuator. We show how to design a suitable $H_\infty$ state-feedback controller based on a finite number of dominating modes. If the remaining (infinitely many) modes are ignored, the calculated $L^2$ gain is wrong. This happens because of the spillover phenomenon that occurs when the effect of the control on truncated modes is not accounted for in the feedback design. We propose a simple modification of the $H_\infty$ cost that prevents spillover. The key idea is to treat the control as a disturbance in the truncated modes and find the corresponding $L^2$ gains using the bounded real lemma. These $L^2$ gains are added to the control weight in the $H_\infty$ cost for the dominating modes, which prevents spillover. A numerical simulation of an aluminum beam with realistic parameters demonstrates the effectiveness of the proposed method. The presented approach is applicable to other types of PDEs, such as the heat, wave, and Kuramoto-Sivashinsky equations, as well as their semilinear versions. While this work focuses on $H_\infty$ control, the same methodology can be applied to guaranteed cost control, regional stability analysis, input-to-state stability, and systems with time-varying delays, including sampled-data systems.
This paper introduces an approach for synthesizing feasible safety indices to derive safe control laws under state-dependent control spaces. The problem, referred to as Safety Index Synthesis (SIS), is challenging because it requires the existence of feasible control input in all states and leads to an infinite number of constraints. The proposed method leverages Positivstellensatz to formulate SIS as a nonlinear programming (NP) problem. We formally prove that the NP solutions yield safe control laws with two imperative guarantees: forward invariance within user-defined safe regions and finite-time convergence to those regions. A numerical study validates the effectiveness of our approach.
Inverse Optimal Control (IOC) is a powerful framework for learning a behaviour from observations of experts. The framework aims to identify the underlying cost function that the observed optimal trajectories (the experts' behaviour) are optimal with respect to. In this work, we considered the case of identifying the cost and the feedback law from observed trajectories generated by an ``average cost per stage" linear quadratic regulator. We show that identifying the cost is in general an ill-posed problem, and give necessary and sufficient conditions for non-identifiability. Moreover, despite the fact that the problem is in general ill-posed, we construct an estimator for the cost function and show that the control gain corresponding to this estimator is a statistically consistent estimator for the true underlying control gain. In fact, the constructed estimator is based on convex optimization, and hence the proved statistical consistency is also observed in practice. We illustrate the latter by applying the method on a simulation example from rehabilitation robotics.
Mohammad Alsalti, Victor G. Lopez, Matthias A. Müller
In the context of data-driven control, persistence of excitation (PE) of an input sequence is defined in terms of a rank condition on the Hankel matrix of the input data. For nonlinear systems, recent results employed rank conditions involving collected input and state/output data, for which no guidelines are available on how to satisfy them a priori. In this paper, we first show that a set of discrete impulses is guaranteed to be persistently exciting for any controllable LTI system. Based on this result, for certain classes of nonlinear systems, we guarantee persistence of excitation of sequences of basis functions a priori, by design of the physical input only.
Filiberto Fele, Antonio De Paola, David Angeli
et al.
A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary conditions are derived for convergence of a receding horizon map to a periodic equilibrium of the aggregative game. This result is achieved for any (feasible) initial condition, thus ensuring implicit adaptivity of the proposed control framework to real-time variations in the number and parameters of players. Design and implementation of the proposed control strategy are discussed and an example of distributed control for data routing is presented, evaluating its performance in simulation.
Nikolaus Vertovec, Sina Ober-Blöbaum, Kostas Margellos
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.
This paper presents a strategy for control of a spacecraft docking with a non-maneuvering target in the presence of safety constraints and bounded disturbances. The presence of disturbances prevents convergence to a unique docking state, so in our formulation, docking is defined as occurring within a set constructed using prescribed tolerances. Safety is ensured via application of Robust Control Barrier Functions to render a designated safe set forward invariant for any allowable disturbance. However, this safety strategy necessarily presumes a worst-case disturbance, and thus restricts trajectories to a subset of the safe set when a worst-case disturbance is not present. The presented controller accounts for this restriction, and guarantees that the spacecraft both remains safe and achieves docking in finite time for any allowable disturbance. The controller is then validated in simulation for a spacecraft landing on an asteroid, and two spacecraft docking in low Earth orbit.
We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.
We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints. We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller.
In this paper, we address the problem of closed-loop control of nonlinear dynamical systems subjected to probabilistic uncertainties. More precisely, we design time-varying polynomial feedback controllers to follow the given nominal trajectory and also, for safety purposes, remain in the tube around the nominal trajectory, despite all uncertainties. We formulate this problem as a chance optimization problem where we maximize the probability of achieving control objectives. To address control problems with long planning horizons, we formulate the single large chance optimization problem as a sequence of smaller chance optimization problems. To solve the obtained chance optimization problems, we leverage the theory of measures and moments and obtain convex relaxations in the form of semidefinite programs. We provide numerical examples on stabilizing controller design and motion planning of uncertain nonlinear systems to illustrate the performance of the proposed approach.
Luca Furieri, Yang Zheng, Antonis Papachristodoulou
et al.
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.
With the rising importance of large-scale network control, the problem of actuator placement has received increasing attention. Our goal in this paper is to find a set of actuators minimizing the metric that measures the average energy consumption of the control inputs while ensuring structural controllability of the network. As this problem is intractable, greedy algorithm can be used to obtain an approximate solution. To provide a performance guarantee for this approach, we first define the submodularity ratio for the metric under consideration and then reformulate the structural controllability constraint as a matroid constraint. This shows that the problem under study can be characterized by a matroid optimization involving a weakly submodular objective function. Then, we derive a novel performance guarantee for the greedy algorithm applied to this class of optimization problems. Finally, we show that the matroid feasibility check for the greedy algorithm can be cast as a maximum matching problem in a certain auxiliary bipartite graph related to the network graph.
In this paper we prove that the Ball-Marsden-Slemrod controllability obstruction also holds for nonlinear equations, with integrable bilinear controls. We first show an abstract result and then we apply it to nonlinear wave equations. The first application to the Sine-Gordon equation directly follows from the abstract result, and the second application concerns the cubic wave/Klein-Gordon equation and needs some additional work.