Worst-case Uncertainty Research Articles

Hybrid energy system optimization integrated with battery storage in radial distribution networks considering reliability and a robust framework

This research presents a robust optimization of a hybrid photovoltaic-wind-battery (PV/WT/Batt) system in distribution networks to reduce active losses and voltage deviation while also enhancing network customer reliability considering production and network load uncertainties. The best installation position and capacity of the hybrid system (HS) are found via an improved crow search algorithm with an inertia weight technique. The robust optimization issue, taking into account the risk of uncertainty, is described using the gap information decision theory method. The proposed approach is used with 33- and 69-bus networks. The results reveal that the HS optimization in the network reduces active losses and voltage variations, while improving network customer reliability. The robust optimization results show that in the 33-bus network, the system remains resilient to prediction errors under the worst-case uncertainty scenario, with a 44.53% reduction in production and a 22.18% increase in network demand for a 30% uncertainty budget. Similarly, in the 69-bus network, the system withstands a 36.22% reduction in production and a 16.97% increase in load for a 25% uncertainty budget. When comparing stochastic and robust methods, it was found that the stochastic Monte Carlo method could not consistently provide a reliable solution for all objectives under uncertainty, whereas the robust approach successfully managed the maximum uncertainty related to renewable generation and network demand across different uncertainty budgets.

Robust wind power capacity planning under fuel price uncertainty using conic duality theory and piecewise McCormick relaxation

Increasing the proportion of renewable energy sources (RESs) in power generation is crucial due to fossil fuel depletion and rising environmental pollution. In this regard, identifying the most lucrative sites and sizes for installing wind farms, as one of the fastest-growing types of RESs, is imperative. This paper presents a robust profit-oriented wind power capacity planning (WPCP) considering long- and short-term uncertainty. The model forms a two-stage min-max-min hierarchical structure. The first stage minimizes the investment cost plus maximum regret, while the second stage maximizes the profit under the worst-case uncertainty realization. Unlike the existing approaches where uncertainty in fossil fuel prices is neglected, we model fuel price uncertainty using both polyhedral and ellipsoidal uncertainty sets. In this respect, the third level is formulated as a bi-level program, with the upper level being the profit maximization and the lower level being the locational marginal price (LMP) calculation. In the case of the ellipsoidal set, the conic duality theory is employed to dualize the lower level. The piecewise McCormick relaxation (PMR) technique linearizes the bilinear terms. The nested column-and-constraint generation (NCCG) technique solves the formulated problem. A clarifying case study is employed to demonstrate the efficacy of the proposed model.

Coordinated Cyber Security Enhancement for Grid-Transportation Systems With Social Engagement

Effective coordination of energy and transportation systems is fundamental and vital to smart city management. Yet, the deeply intertwined information and communication technologies have exposed smart city management to malicious cyberattacks vastly. This study develops a two-stage mitigation strategy for integrated transportation-energy systems (TESs) by coordinating energy and transportation systems to safeguard against false data injection attacks (FDIAs). Our strategy targets social engagements by electric vehicle (EV) users who can be incentivized to alter their regular EV usage patterns for supporting the energy system via vehicle-to-grid actions. We consider a TES that contains a multi-energy system comprised of power and gas systems as well as an urban transportation system. Integrated system operators can take emergency measures to coordinate important system assets (e.g., traditional generators, renewable generators, EV fleets) in a sensible and intelligent way, and thereby mitigate the consequences of FDIAs. Specifically, we take a two-stage distributionally robust approach to cope with uncertain FDIAs, with which a moment-based ambiguity set is employed to yield the worst-case uncertainty distribution. We leverage constraint generation-based relaxation to solve the problem iteratively. To demonstrate our strategy's value and practical utilities, we use a coupled urban TES to conduct case studies. According to the evaluation results, the optimized EV scheduling and energy dispatch scheme produced by the proposed strategy can contain cyberattacks’ impacts and enhance cyber resilience in smart city management more effectively.

Control of a Seismically Excited Building Using μ-Synthesis

Over the past thirty years, there has been significant progress in protecting structures from earthquakes through structural control, which effectively dissipates energy from dynamic loads. Numerous studies have shown the potential of active control methods in reducing structural responses, leading to improved human safety and seismic structure protection. However, existing control approaches often overlook uncertainties present in real-world scenarios, such as variations in structural coefficients and dynamics. To address this, we aim to employ μ-synthesis, a robust control technique widely used in various fields, which explicitly accounts for these uncertainties during controller design. This paper presents simulations of a three-story building subjected to seismic excitation, with an active bracing system attached to the first floor. We design a robust controller considering both parametric and dynamic uncertainties, demonstrating its effectiveness in significantly reducing structural response amid varying uncertainties. The robustness of the controller is evaluated by testing it under worst-case uncertainty variations.

Toward Trustworthy Decision-Making for Autonomous Vehicles: A Robust Reinforcement Learning Approach with Safety Guarantees

While autonomous vehicles are vital components of intelligent transportation systems, ensuring the trustworthiness of decision-making remains a substantial challenge in realizing autonomous driving. Therefore, we present a novel robust reinforcement learning approach with safety guarantees to attain trustworthy decision-making for autonomous vehicles. The proposed technique ensures decision trustworthiness in terms of policy robustness and collision safety. Specifically, an adversary model is learned online to simulate the worst-case uncertainty by approximating the optimal adversarial perturbations on the observed states and environmental dynamics. In addition, an adversarial robust actor-critic algorithm is developed to enable the agent to learn robust policies against perturbations in observations and dynamics. Moreover, we devise a safety mask to guarantee the collision safety of the autonomous driving agent during both the training and testing processes using an interpretable knowledge model known as the Responsibility-Sensitive Safety Model. Finally, the proposed approach is evaluated through both simulations and experiments. These results indicate that the autonomous driving agent can make trustworthy decisions and drastically reduce the number of collisions through robust safety policies.

Expansion planning of the transmission network with high penetration of renewable generation: A multi-year two-stage adaptive robust optimization approach

This paper addresses the multi-year two-stage expansion planning of the transmission network of a power system with high penetration of renewable generation modeling long-term uncertainty by using adaptive robust optimization. The multi-year nature of the problem is modeled by considering a comprehensive view of the planning horizon. A cardinality-constrained uncertainty set is used to model the future worst-case uncertainty realization of the peak power consumption of loads, along with the capacity and marginal production cost of generating units. Unlike previous works, we model certain features of the operation that are typically ignored in multi-year robust transmission network expansion planning problems, namely, the operational variability of renewable generating units, the operational flexibility of conventional generating units, and the non-convex operational feasibility sets of storage facilities. The solution procedure employed for this multi-year two-stage robust problem, which is formulated as a three-level problem, is based on the combination of the nested column-and-constraint generation algorithm with two exact acceleration techniques. We analyze the performance of the proposed model through the use of the IEEE 24-bus Reliability Test System and the IEEE 118-bus Test System. Numerical results show that the use of the multi-year approach leads to reductions in the total worst-case cost of up to 7% in comparison with the static and sequential static procedures. Moreover, an underestimation of the total worst-case cost of more than 8% is attained when ignoring certain operational constraints of conventional generating units and storage facilities. Lastly, a sensitivity analysis is presented in order to illustrate the impact of the maximum deviations of the uncertain parameters on the total worst-case cost.

Minimax Persistent Monitoring of a network system

We investigate the problem of optimally observing a finite set of targets using a mobile agent over an infinite time horizon. The agent is tasked to move in a network-constrained structure to gather information so as to minimize the worst-case uncertainty about the internal states of the targets. To do this, the agent has to decide its sequence of target-visits and the corresponding dwell-times at each visited target. For a given visiting sequence, we prove that in an optimal dwelling time allocation the peak uncertainty is the same among all the targets. This allows us to formulate the optimization of dwelling times as a resource allocation problem and to solve it using a novel efficient algorithm. Next, we optimize the visiting sequence using a greedy exploration process, using heuristics inspired by others developed in the context of the traveling salesman problem. Numerical results are included to illustrate the contributions.

Decentralized Energy Management System in Microgrid Considering Uncertainty and Demand Response

Smart energy management and control systems can improve the efficient use of electricity and maintain the balance between supply and demand. This paper proposes the modeling of a decentralized energy management system (EMS) to reduce system operation costs under renewable generation and load uncertainties. There are three stages of the proposed strategy. First, this paper applies an autoregressive moving average (ARMA) model for forecasting PV and wind generations as well as power demand. Second, an optimal generation scheduling process is designed to minimize system operating costs. The well-known algorithm of particle swarm optimization (PSO) is applied to provide optimal generation scheduling among PV and WT generation systems, fuel-based generation units, and the required power from the main grid. Third, a demand response (DR) program is introduced to shift flexible load in the microgrid system to achieve an active management system. Simulation results demonstrate the performance of the proposed method using forecast data for hourly PV and WT generations and a load profile. The simulation results show that the optimal generation scheduling can minimize the operating cost under the worst-case uncertainty. The load-shifting demand response reduced peak load by 4.3% and filled the valley load by 5% in the microgrid system. The proposed optimal scheduling system provides the minimum total operation cost with a load-shifting demand response framework.

Set-Based Intent-Expressive Trajectory Planning and Intent Estimation

This letter proposes a novel approach to intent-expressive motion planning and intent estimation for agents/robots with uncertain discrete-time affine dynamics. In contrast to the more commonly considered stochastic settings, our intent-expressive trajectory planning approach is set-based and leverages the active model discrimination framework for designing optimal inputs to attain certain target/goal states, while allowing an observer/teammate to clearly infer the intended goal based only on observations of a partial trajectory before it has reached its target/goal state, despite worst-case uncertainties. Further, in tandem with the planning algorithm, we also propose an intent estimation algorithm that can be used by the observer/teammate to determine the intended goal from observations of a noisy, partial trajectory.

Safe Control Synthesis With Uncertain Dynamics and Constraints

This paper considers safe control synthesis for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and the safety constraints. We formulate novel probabilistic and robust (worst-case) control Lyapunov function (CLF) and control barrier function (CBF) constraints that take into account the effect of uncertainty in either case. We show that either the probabilistic or the robust (worst-case) formulation leads to a second-order cone program (SOCP), which enables efficient safe and stable control synthesis. We evaluate our approach in PyBullet simulations of an autonomous robot navigating in unknown environments and compare the performance with a baseline CLF-CBF quadratic programming approach.

Risk-averse decision under worst-case continuous and discrete uncertainties in transmission system with the support of active distribution systems

Nowadays, risk-averse management is a principal concern for transmission system (TS) operator that involve different types of uncertainty including continuous uncertainties (e.g., wind energy uncertainty) and discrete uncertainties (e.g., generator/line outages). In this condition, risk-averse decision making for managing these uncertainties are extremely complex, and the complexity is more amplified by the worst-case uncertainties. Accordingly, in this study a novel contingency-constrained information gap decision theory (CC-IGDT) approach has been proposed to cope with worst-case continuous and discrete uncertainties. Also, active distribution systems (ADSs) with distributed energy resources are important components in a TS, and can play an important role in addressing the issue of risk-averse management for TS operator. Therefore, in this study a coupled operation model for the TS & ADSs with the CC-IGDT approach has been proposed. But, solve proposed coupled operation model is problematic, thus, to solve this problem a new four-level hierarchical optimization technique has been proposed. Finally, the IEEE 30-bus transmission and IEEE 33-bus distribution systems have been analyzed to show the effectiveness of the proposed CC-IGDT approach and the co-operation of TS & ADSs.

Robust Control Based Stability Analysis and Trajectory Tracking of Triple Link Robot Manipulator

In this paper the stability and tracking control for robot manipulator subjected to known parameters is proposed using robust control technique. The modelling of robot manipulator is obtained using Euler- Lagrange technique. Three link manipulators have been taken for the study of robust control techniques. Lyapunov based approach is used for stability analysis of triple link robot manipulator. The Ultimate upper bound parameter (UUBP) is estimated by the worst-case uncertainties subject to bounded conditions. The proposed robust control is also compared with computer torque control to show the superiority of the proposed control law.

Biologically consistent dose accumulation using daily patient imaging

BackgroundThis work addresses a basic inconsistency in the way dose is accumulated in radiotherapy when predicting the biological effect based on the linear quadratic model (LQM). To overcome this inconsistency, we introduce and evaluate the concept of the total biological dose, bEQDd.MethodsDaily computed tomography imaging of nine patients treated for prostate carcinoma with intensity-modulated radiotherapy was used to compute the delivered deformed dose on the basis of deformable image registration (DIR). We compared conventional dose accumulation (DA) with the newly introduced bEQDd, a new method of accumulating biological dose that considers each fraction dose and tissue radiobiology. We investigated the impact of the applied fractionation scheme (conventional/hypofractionated), uncertainties induced by the DIR and by the assigned α/β-value.ResultsbEQDd was systematically higher than the conventionally accumulated dose with difference hot spots of 3.3–4.9 Gy detected in six out of nine patients in regions of high dose gradient in the bladder and rectum. For hypofractionation, differences are up to 8.4 Gy. The difference amplitude was found to be in a similar range to worst-case uncertainties induced by DIR and was higher than that induced by α/β. ConclusionUsing bEQDd for dose accumulation overcomes a potential systematic inaccuracy in biological effect prediction based on accumulated dose. Highest impact is found for serial-type late responding organs at risk in dose gradient regions and for hypofractionation. Although hot spot differences are in the order of several Gray, in dose-volume parameters there is little difference compared with using conventional or biological DA. However, when local dose information is used, e.g. dose surface maps, difference hot spots can potentially change outcomes of dose-response modelling and adaptive treatment strategies.

Optimal design of controlled environment agricultural systems under market uncertainty

We present a novel methodology for the simultaneous robust design and scheduling of controlled environment agricultural (CEA) systems under multi-period risk. This problem is formulated as a semi-infinite program with several semi-infinite constraints pertaining to mean-variance risk exposure with uncertain covariance over each period in the planning horizon. The general model enables robust optimization of CEA systems for cultivation of any crop portfolio under any number of cultivation modes, with a solution that represents an optimal design and operating schedule that is robust to worst-case uncertainty. Therefore, this methodology provides a conservative basis for engineering and investment decision-making and represents, to our knowledge, the first robust optimization approach to CEA systems. Our approach effectively increases the robustness of CEA systems to market uncertainty, improves the long-term economics of CEA systems over naïve operating strategies, and validates the economic viability of single and multi-mode CEA production of distinct crop portfolios.

Fortification Against Cascade Propagation Under Uncertainty

Network cascades represent a number of real-life applications: social influence, electrical grid failures, viral spread, and so on. The commonality between these phenomena is that they begin from a set of seed nodes and spread to other regions of the network. We consider a variant of a critical node detection problem dubbed the robust critical node fortification problem, wherein the decision maker wishes to fortify nodes (within a budget) to limit the spread of cascading behavior under uncertain conditions. In particular, the arc weights—how much influence one node has on another in the cascade process—are uncertain but are known to lie in some range bounded by a worst-case budget uncertainty. This problem is shown to be [Formula: see text]-hard even in the deterministic case. We formulate a mixed-integer program (MIP) to solve the deterministic problem and improve its continuous relaxation via nonlinear constraints and convexification. The robust problem is computationally more difficult, and we present an MIP-based expand-and-cut exact solution algorithm, in which the expansion is enhanced by cutting planes, which are themselves tied to the expansion process. Insights from these exact solutions motivate two novel (interrelated) centrality measures, and a centrality-based heuristic that obtains high-quality solutions within a few seconds. Finally, extensive computational results are given to validate our theoretical developments as well as provide insights into structural properties of the robust problem and its solution.

COVID-19 Epidemic and Opening of the Schools: Artificial Intelligence-Based Long-Term Adaptive Policy Making to Control the Pandemic Diseases

Even though the COVID-19 pandemic has endured to be a serious threat for the societies, the state authorities have been seeking policies to re-open the schools and universities. It is clear that opening of the schools will cause more COVID-19 casualties, but the key question is how many students should attend the schools daily while keeping the casualties under control. In this paper, an artificial intelligence based long-term policy making algorithm has been developed to generate time varying policies for opening of the schools part-by-part. The key aim of the algorithm is to produce policies which maximize the number of the students attending the schools while minimizing the pandemic casualties under the worst-case uncertainties. The proposed algorithm consists of a multi-input-multi-output, uncertain, and adaptive background parametric model which is externally manipulated by the produced adaptive policy. Its long-term predictor assesses the possible future casualties under the current policy and its policy maker generates alternative solutions that minimize the future casualties. The results confirm that the proposed algorithm is able to generate effective policies which minimize the COVID-19 casualties while maximize the number of the students attending the schools under the worst-case uncertainties.

Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks

Scenario-based model predictive control (MPC) methods introduce recourse into optimal control and can thus reduce the conservativeness inherent to open-loop robust MPC. However, the uncertainty scenarios are often generated offline using worst-case uncertainty bounds quantified a priori, limiting the potential gains in control performance. This paper presents a learning-based multistage MPC (msMPC) for systems with hard-to-model dynamics and time-varying plant-model mismatch. Gaussian Processes (GP) are used to learn state- and input-dependent plant-model mismatch in real-time and accordingly adapt the scenario tree online. Due to the increased computational complexity associated with incorporating the GP predictions into the optimal control problem, the learning-based msMPC (LB-msMPC) law is approximated by a deep neural network (DNN) that is cheap-to-evaluate online and has a small memory footprint, which makes it suitable for embedded applications. In addition, we present a novel algorithm for training the DNN-based controller that uses a GP description of the plant-model mismatch to generate closed-loop simulation data, which ensures the LB-msMPC law is evaluated in regions of the state space most relevant to closed-loop operation. The proposed LB-msMPC strategy is demonstrated on a cold atmospheric plasma jet with applications in (bio)materials processing. The simulation results indicate the promise of the approximate LB-msMPC strategy for control of hard-to-model systems with fast dynamics on millisecond timescales.

Continuous-time reinforcement learning for robust control under worst-case uncertainty

ABSTRACT Reinforcement learning (RL) is an effective method to design a robust controller for unknown nonlinear systems. Uncertainty in the worst case requires a large state-action space. Hence, it is natural to use continuous-time RL methods rather than the discretisation of the spaces. In this paper, we propose a novel continuous-time RL using neural network approximation. Our method uses worst-case uncertainty to train the continuous-time RL algorithm. The backward Euler approximation is used to approximate the time derivative of the value function. Compared with the actor–critic (AC) algorithm, our method finds the robust control policy in the presence of worst-case uncertainty by taking into account the applied actions. It is shown that the AC algorithm finds the robust controller in less episodes, but its robustness is less than the results presented by our approach. The convergence of the proposed algorithm is analysed using the contraction property and differential equation techniques. The experiments show that our approach is more robust than the model-based LQR method and the well-known AC method.

Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming

We present a motion planning algorithm with probabilistic guarantees for limbed robots with stochastic gripping forces. Planners based on deterministic models with a worst-case uncertainty can be conservative and inflexible to consider the stochastic behavior of the contact, especially when a gripper is installed. Our proposed planner enables the robot to simultaneously plan its pose and contact force trajectories while considering the risk associated with the gripping forces. Our planner is formulated as a nonlinear programming problem with chance constraints, which allows the robot to generate a variety of motions based on different risk bounds. To model the gripping forces as random variables, we employ Gaussian Process regression. We validate our proposed motion planning algorithm on an 11.5 kg six-limbed robot for two-wall climbing. Our results show that our proposed planner generates various trajectories (e.g., avoiding low friction terrain under the low risk bound, choosing an unstable but faster gait under the high risk bound) by changing the probability of risk based on various specifications.

Uncertainty Estimation in Extremum Seeking Control of Unknown Static Maps

This letter proposes a design of extremum seeking controllers that guarantees precise convergence of the control system to the unknown optimizer of a measured unknown cost function. The approach introduces an uncertainty estimation technique that provides an estimate of the worst case uncertainty associated with the unknown optimizer. An uncertainty set update algorithm is proposed to reduce the radius of the uncertain set as new data is received. The radius of the uncertainty set is used to reduce the required dither amplitude. The convergence to the unknown optimum and the removal of the dither signal are achieved simultaneously. Asymptotic convergence of the extremum seeking control system to the unknown minimizer is achieved in the absence of measurement noise. A simulation example is provided to demonstrate the effectiveness of the approach.