We introduce River, a novel Condorcet-consistent voting method that is based on pairwise majority margins and can be seen as a simplified variation of Tideman's Ranked Pairs method. River is simple to explain, simple to compute even 'by hand', and gives rise to an easy-to-interpret certificate in the form of a directed tree. Like Ranked Pairs and Schulze's Beat Path method, River is a refinement of the Split Cycle method and shares with those many desirable properties, including independence of clones. Unlike the other three methods, River satisfies a strong form of resistance to agenda-manipulation that is known as independence of Pareto-dominated alternatives.
Flooding is the most devastating phenomenon occurring globally, particularly in mountainous regions, risk dramatically increases due to complex terrains and extreme climate changes. These situations are damaging livelihoods, agriculture, infrastructure, and human lives. This study uses the Kabul River between Pakistan and Afghanistan as a case study to reflect the complications of flood forecasting in transboundary basins. The challenges in obtaining upstream data impede the efficacy of flood control measures and early warning systems, a common global problem in similar basins. Utilizing satellite-based climatic data, this study applied numerous advanced machine-learning and deep learning models, such as Support Vector Machines (SVM), XGBoost, and Artificial Neural Networks (ANN), Long Short-Term Memory (LSTM) networks, and Gated Recurrent Units (GRU) to predict daily and multi-step river flow. The LSTM network outperformed other models, achieving the highest R2 value of 0.96 and the lowest RMSE value of 140.96 m3/sec. The time series LSTM and GRU network models, utilized for short-term forecasts of up to five days, performed significantly. However, the accuracy declined beyond the fourth day, highlighting the need for longer-term historical datasets for reliable long-term flood predictions. The results of the study are directly aligned with Sustainable Development Goals 6, 11, 13, and 15, facilitating disaster and water management, timely evacuations, improved preparedness, and effective early warning.
The theory of optimal control on positive cones has recently identified several new problem classes where the Bellman equation can be solved explicitly, in analogy with classical linear quadratic control. In this paper, the idea is extended to minimax adaptive control, yielding exact solutions to instances of the Bellman equation for dual control. In particular, this allows for optimization of the fundamental tradeoff between exploration and exploitation.
The operation of hydraulic projects within plain river networks to mitigate floods can alter river network connectivity patterns, subsequently affecting flood processes. This study employed the MIKE 11 model to simulate flood processes under three different river network connectivity scenarios. Based on the simulations, we propose a method to evaluate flood intensity severity by integrating three flood characteristic indices: Slope of the Flow Duration Curve (SFDC), Rising Climb Index (RCI), and Flashiness Index (FI). These indices assess the overall magnitude of change, the rate of rise, and process fluctuations, respectively. Results indicate that changes in river network connectivity significantly impact RCI and SFDC, more than FI. Compared to the natural river network connectivity mode, changes in urban or watershed river network connectivity resulted in a significant decrease in RCI values by 3–37% or 18–38% across various return periods, with the rate of change in RCI values increasing as the return period lengthened. The impact of urban river network connectivity changes on SFDC within the Changzhou urban area was more pronounced under high-magnitude storm conditions, causing a 61% reduction. Furthermore, changes in watershed river network connectivity had a larger effect on SFDC under low-magnitude storm conditions than under high-intensity storms. Over 80% of the rivers under natural connectivity conditions exhibited flood intensity severity of Level III or higher, particularly in the Chenshu–Qingyang area. The alterations in connectivity significantly decreased flood intensity severity, with 85% to 91% of rivers showing the lowest flood intensity severity of Level I. Under a 100-year rainstorm scenario, flood risk shifted from within the flood protection envelope to outside it in the Changzhou urban area. The results will provide an important scientific basis for regional flood management in plains with dense rivers.
In this study, we propose a novel gap-constraint-based reformulation for optimal control problems with equilibrium constraints (OCPECs). We show that the proposed reformulation generates a new constraint system equivalent to the original one but more concise and with favorable differentiability. Moreover, constraint regularity can be recovered by a relaxation strategy. We show that the gap constraint and its gradient can be evaluated efficiently. We then propose a successive gap constraint linearization method to solve the discretized OCPEC. We also provide an intuitive geometric interpretation of the gap constraint. Numerical experiments validate the effectiveness of the proposed reformulation and solution method.
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a previously proposed local reduction method to consider those with existence constraints on the uncountable variables. We also consider the possibility of non-unique trajectories that satisfy equality and inequality constraints. Crucially, we show that the problems of interest can be cast into a standard semi-infinite program and demonstrate how to generate optimal uncertainty scenario sets in order to obtain numerical solutions. We also include examples on model predictive control for obstacle avoidance with logical conditions, control with input saturation affected by uncertainty, and optimal parameter estimation to highlight the need for the proposed extension. Our method solves each of the examples considered, producing violation-free and locally optimal solutions.
Moritz Heinlein, Sankaranarayanan Subramanian, Sergio Lucia
Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between conservatism and computational complexity. Monotone systems facilitate the efficient computation of reachable sets and thus the straightforward formulation of a robust model predictive control approach optimizing over open-loop predictions. We present an approach based on the division of reachable sets to incorporate feedback in the predictions, resulting in less conservative strategies. The concept of mixed-monotonicity enables an extension of our methodology to non-monotone systems. The potential of the proposed approaches is demonstrated through a nonlinear high-dimensional chemical tank reactor cascade case study.
Fundamental limitations or performance trade-offs/limits are important properties and constraints of both control and filtering systems. Among various trade-off metrics, total information rate that characterizes the sensitivity trade-offs and time-averaged performance of control and filtering systems was conventionally studied by using the differential entropy rate and Kolmogorov-Bode formula. In this paper, by extending the famous I-MMSE (mutual information -- minimum mean-square error) relationships to the discrete-time additive white Gaussian channels with and without feedback, a new paradigm is introduced to estimate and analyze total information rate as a control and filtering trade-off metric. Under this framework, we explore the trade-off properties of total information rate for a variety of the discrete-time control and filtering systems, e.g., LTI, LTV, and nonlinear, and propose an alternative approach to investigate total information rate via optimal estimation.
Distributed Parameter Systems (DPSs), modelled by partial differential equations (PDEs), are increasingly vulnerable to disturbances arising from various sources. Although detection of disturbances in PDE systems have received considerable attention in existing literature, safety control of PDEs under disturbances remains significantly under-explored. In this context, we explore a practical input-to-state safety (pISSf) based control design approach for a class of DPSs modelled by linear Parabolic PDEs. Specifically, we develop a control design framework for this class of system with both safety and stability guarantees based on control Lyapunov functional and control barrier functional. To illustrate our methodology, we apply our strategy to design a thermal control system for battery modules under disturbance. Several simulation studies are done to show the efficacy of our method.
This paper studies impulsive stabilization of nonlinear systems. We propose two types of event-triggering algorithms to update the impulsive control signals with actuation delays. The first algorithm is based on continuous event detection, while the second type makes decision about updating the impulsive control inputs according to periodic event detection. Sufficient conditions are derived to ensure asymptotic stability of the impulsive control systems with the designed event-triggering algorithms. Lower bounds of the time period between two consecutive events are also obtained, so that the closed-loop impulsive systems are free of Zeno behavior. That is to say that the pulse phenomena are excluded from the event-triggered impulsive control systems, in the community of impulsive differential equations. An illustrative example demonstrates effectiveness of the proposed algorithms and our theoretical results.
This paper proposes a reinforcement learning-based approach for optimal transient frequency control in power systems with stability and safety guarantees. Building on Lyapunov stability theory and safety-critical control, we derive sufficient conditions on the distributed controller design that ensure the stability and transient frequency safety of the closed-loop system. Our idea of distributed dynamic budget assignment makes these conditions less conservative than those in recent literature, so that they can impose less stringent restrictions on the search space of control policies. We construct neural network controllers that parameterize such control policies and use reinforcement learning to train an optimal one. Simulations on the IEEE 39-bus network illustrate the guaranteed stability and safety properties of the controller along with its significantly improved optimality.
This paper proposes a decentralised secondary voltage control strategy that has several benefits over the existing centralised strategies. For that, a new structure for the control is proposed in terms of an inner and outer loops for each generator. The individual generators of a particular zone participate in the secondary voltage control by aligning their reactive powers with respect to the pilot point voltage reference. The decentralised nature of the proposed control strategy enables plug and play operation: run with different numbers of generators without any need of regulators reconfiguration, resilience in case of generator failure. This allows one to use such control to integrate renewable generators to existing secondary regulations alongside with the classic generators. The proposed control strategy is implemented using a model-free control scheme that does not require a higher order complex model of the power grid. The deployment of a discrete-time intelligent proportional controller simplifies the tuning of the controller gains. The proposed strategy is validated on a four generator power system model in MATLAB/ Simulink/Simelectrical environment. Simulation results are presented to show the effectiveness of the proposed strategy along with different case studies such as load perturbation, transmission line perturbation, generator disconnection and delay in pilot point voltage measurement to highlight its robustness.
This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this paper, we propose a model that combines the Hammerstein-Wiener model with input convex neural networks, which have recently been proposed in the field of machine learning. An important feature of the proposed model is that resulting optimal control problems are effectively solvable exploiting their convexity and partial linearity while retaining flexible modeling ability. The practical usefulness of the method is examined through its application to the modeling and control of an engine airpath system.
This paper builds the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville operators and control occupation kernels are introduced to separate the drift dynamics from the input dynamics. A given feedback controller is represented through a multiplication operator and a composition of the control Liouville operator and the multiplication operator is used to express the nonlinear closed-loop system as a linear total derivative operator on RKHSs. A spectral decomposition of a finite-rank representation of the total derivative operator yields a DMD of the closed-loop system. The DMD generates a model that can be used to predict the trajectories of the closed-loop system. For a large class of systems, the total derivative operator is shown to be compact provided the domain and the range RKHSs are selected appropriately. The sequence of models, resulting from increasing-rank finite-rank representations of the compact total derivative operator, are shown to converge to the true system dynamics, provided sufficiently rich data are available. Numerical experiments are included to demonstrate the efficacy of the developed technique.
We consider the Linear Quadratic Regulation for the boundary control of the one dimensional linear wave equation under both Dirichlet and Neumann activation. For each activation we present a Riccati partial differential equation that we explicitly solve. The derivation the Riccati partial differential equations is by the simple and explicit technique of completing the square.
In the present work a new controller called Particle Swarm Optimization based state feedback gain controller has been proposed for frequency regulation of a two area system and then its performance is compared with earlier designed controllers such as Linear Quadratic Regulator Proportional Integral controller and Integral controller. The performance comparison has been done for the power system network comprising of two thermal power plants which are tie line connected. For using the optimal control based method such as LQR PI controller and computationally intelligent method such as PSO based state feedback gain controller, the state space modeling of the system has been done. Transfer function model for the system is used for finding the response of Integral controller. In an effective generation control scheme the change in frequency should be minimum during the load variation. The proposed PSO based state feedback gain controller technique has been found most effective for improving the frequency response.
Konaweeha watershed is the largest watershed in Southeast Sulawesi with Konaweeha River as the main river. The main issues in Konaweeha Watershed is floods that occur caused damage to infrastructure and public facilities, lowering agricultural production, and cause fatalities. One of the government's efforts to cope with the flooding problem in Konaweeha Watershed is planning the construction of multi-purpose dams in the upstream of Konaweeha Watershed that is Pelosika Dam and Ameroso Dam. Necessary to study the flood control performance of the two dams. Analyses were performed with hydrologic-hydraulic modeling using HEC-HMS software (Hydrologic Modelling System) version 4.0 and HEC-RAS (River Analysis System) version 4.1. The design rainfalls that were used as input to the model were 2 year, 5-year, 10-year and 25 year. Scenarios used in this study are: (1) Existing Scenario (2) Pelosika Dam Scenario; (3) Ameroro Dam Scenario; (4) Pelosika and Ameroro Dams Scenario. The results showed the maximum water surface elevation along the downstream of Konaweeha River in Scenario (2) and (4) were almost the same in the 2 and 5 years return period design flood. However, in case of 10 and 25 years return period, the difference of maximum water surface elevation at downstream of Konaweeha River was slightly significant. Furthermore, the damping efficiency of the peak discharge (at Probably Maximum Flood or PMF) was found to be 71.70% and 18.18% for the individual Pelosika Dam and Ameroro Dam respectively. Further discussion suggests the development of Pelosika Dam as the higher priority rather than that of the Ameroro Dam.
In this paper, we study the distributed control of networked cyber-physical systems when a much more energy-efficient distributed communication management strategy is proposed to solve the well-studied consensus problem. In contrast to the existing potential-based network topology control method, the proposed topology control method is based on the variation of communication ranges such that each agent can control its ad hoc communication range. The proposed network topology control technique can not only guarantee network connectivity but also reduce the communication energy. We apply the new network topology control technique, based on variable communication ranges, in a well-studied consensus problem, where the communication range for each agent is designed locally along with a new bounded control algorithm. Theoretical analysis is then provided to show that the proposed network topology control technique can guarantee consensus with bounded communication energy consumption. Finally, simulation examples are provided to show the effectiveness of the proposed energy-efficient distributed topology control technique.
Martin Andreasson, Emma Tegling, Henrik Sandberg
et al.
In this paper, we compare the transient performance of a multi-terminal high-voltage DC (MTDC) grid equipped with a slack bus for voltage control to that of two distributed control schemes: a standard droop controller and a distributed averaging proportional-integral (DAPI) controller. We evaluate performance in terms of an H2 metric that quantifies expected deviations from nominal voltages, and show that the transient performance of a droop or DAPI controlled MTDC grid is always superior to that of an MTDC grid with a slack bus. In particular, by studying systems built up over lattice networks, we show that the H2 norm of a slack bus controlled system may scale unboundedly with network size, while the norm remains uniformly bounded with droop or DAPI control. We simulate the control strategies on radial MTDC networks to demonstrate that the transient performance for the slack bus controlled system deteriorates significantly as the network grows, which is not the case with the distributed control strategies.