搜索结果：Systems

Vehicle-to-building (V2B) systems integrate physical infrastructures, such as smart buildings and electric vehicles (EVs) connected to chargers at the building, with digital control mechanisms to manage energy use. By utilizing EVs as flexible energy reservoirs, buildings can dynamically charge and discharge them to optimize energy use and cut costs under time-variable pricing and demand charge policies. This setup leads to the V2B optimization problem, where buildings coordinate EV charging and discharging to minimize total electricity costs while meeting users' charging requirements. However, the V2B optimization problem is challenging because of: (1) fluctuating electricity pricing, which includes both energy charges ($/kWh) and demand charges ($/kW); (2) long planning horizons (typically over 30 days); (3) heterogeneous chargers with varying charging rates, controllability, and directionality (i.e., unidirectional or bidirectional); and (4) user-specific battery levels at departure to ensure user requirements are met. In contrast to existing approaches that often model this setting as a single-shot combinatorial optimization problem, we highlight critical limitations in prior w

Extreme events such as earthquakes pose significant threats to integrated electricity-gas distribution systems (IEGDS) by causing widespread damage. Existing restoration approaches typically assume full awareness of damage, which may not be true if monitoring and communication infrastructures are impaired. In such circumstances, field inspection is necessary. This paper presents a novel adaptive restoration framework for IEGDS, considering dynamic damage assessment and repair. The restoration problem is formulated as a partially observable Markov decision process (POMDP), capturing the gradually revealed contingency and the evolving impact of field crew actions. To address the computational challenges of POMDPs in real-time applications, an advanced belief tree search (BTS) algorithm is introduced. This algorithm enables crew members to continuously update their actions based on evolving belief states, leveraging comprehensive simulations to evaluate potential future trajectories and identify optimal inspection and repair strategies. Based on the BTS algorithm, a unified real-time decision-making framework is developed for IEGDS restoration. Case studies on two distinct IEGDS syste

This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework transforms such dynamical systems into equivalent infinite-dimensional linear dynamical systems. In this paper, we establish the exponential convergence of the primary block in the finite-section approximation of this linearized system to the state vector of the original nonlinear system. To showcase the efficacy of our approach, we apply it to the Kuramoto model, a prominent model for coupled oscillators. The results demonstrate promising accuracy in approximating the original system's behavior.

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of stochastic systems, methods based on discrete, finite Markov approximations -- abstractions -- thereof have surged in recent years. These are found in contexts where: either a) one only has partial, discrete observations of the underlying continuous stochastic process, or b) the original system is too complex to analyze, so one partitions the continuous state-space of the original system to construct a handleable, finite-state model thereof. In both cases, the abstraction is an approximation of the discrete stochastic process that arises precisely from the discretization of the underlying continuous process. The fact that the abstraction is Markov and the discrete process is not (even though the original one is) leads to approximation errors. Towards accounting for non-Markovianity, we introduce memory-dependent abstractions for stochastic systems, capturing dynamics with memory effects. Our contribution is twofold. First, we provide a formalism for memo

This paper addresses the fundamental problem of non-uniform area coverage in multi-agent systems, where different regions require varying levels of attention due to mission-dependent priorities. Existing uniform coverage strategies are insufficient for realistic applications, and many non-uniform approaches either lack optimality guarantees or fail to incorporate crucial real-world constraints such as agent dynamics, limited operation time, the number of agents, and decentralized execution. To resolve these limitations, we propose a novel framework called Density-Driven Optimal Control (D2OC). The central idea of D2OC is the integration of optimal transport theory with multi-agent coverage control, enabling each agent to continuously adjust its trajectory to match a mission-specific reference density map. The proposed formulation establishes optimality by solving a constrained optimization problem that explicitly incorporates physical and operational constraints. The resulting control input is analytically derived from the Lagrangian of the objective function, yielding closed-form optimal solutions for linear systems and a generalizable structure for nonlinear systems. Furthermore,

Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered mean field limits for deterministic discrete-time systems, which are relevant for the analysis and control of large-scale discrete-time multiagent system. We prove existence results for the mean field limit of very general discrete-time control systems, for which we utilize kernel mean embeddings. These results are then applied in a typical optimal control setup, where we establish the mean field limit of the relaxed dynamic programming principle. Our results can serve as a rigorous foundation for many applications of mean field approaches for discrete-time dynamical systems.

This chapter addresses the increasing vulnerability of coastal regions to typhoons and the consequent power outages, emphasizing the critical role of power transmission systems in disaster resilience. It introduces a framework for assessing and enhancing the resilience of these systems against typhoon impacts. The approach integrates a hybrid-driven model for system failure analysis and resilience assessment, employing both data-driven and model-driven techniques. It includes a unique method to identify system vulnerabilities and optimal strategies for resilience enhancement, considering cost-effectiveness. The efficacy of this method is demonstrated through simulations on the IEEE RTS-79 system under realistic typhoon scenarios, showcasing its potential to guide planners in making informed decisions for disaster resilience.

Certifying the safety of nonlinear systems, through the lens of set invariance and control barrier functions (CBFs), offers a powerful method for controller synthesis, provided a CBF can be constructed. This paper draws connections between partial feedback linearization and CBF synthesis. We illustrate that when a control affine system is input-output linearizable with respect to a smooth output function, then, under mild regularity conditions, one may extend any safety constraint defined on the output to a CBF for the full-order dynamics. These more general results are specialized to robotic systems where the conditions required to synthesize CBFs simplify. The CBFs constructed from our approach are applied and verified in simulation and hardware experiments on a quadrotor.

Many modern engineering structures exhibit nonlinear vibration. Characterizing such vibrations efficiently is critical to optimizing designs for reliability and performance. For linear systems, steady-state vibration occurs only at the forcing frequencies. However, nonlinearities (e.g., contact, friction, large deformation, etc.) can result in nonlinear vibration behavior including superharmonics - responses at integer multiples of the forcing frequency. When the forcing frequency is near an integer fraction of the natural frequency, superharmonic resonance occurs, and the magnitude of the superharmonics can exceed that of the fundamental harmonic that is externally forced. Characterizing such superharmonic resonances is critical to improving engineering designs. The present work extends the concept of phase resonance nonlinear modes (PRNM) to be applicable to general nonlinearities, and is demonstrated for eight different nonlinear forces. The considered forces include stiffening, softening, contact, damping, and frictional nonlinearities that have not been previously considered with PRNM. The proposed variable phase resonance nonlinear modes (VPRNM) method can accurately track su

Modern engineering structures exhibit nonlinear vibration behavior as designs are pushed to reduce weight and energy consumption. Of specific interest here, joints in assembled structures introduce friction, hysteresis, and unilateral contact resulting in nonlinear vibration effects. In many cases, it is impractical to remove jointed connections necessitating, the understanding of these behaviors. This work focuses on superharmonic and internal resonances in hysteretic and jointed systems. Superharmonic resonances occur when a nonlinear system is forced at an integer fraction of a natural frequency resulting in a large (locally maximal) response at an integer multiple of the forcing frequency. When a second vibration mode simultaneously responds in resonance at the forcing frequency, the combined phenomena is termed an internal resonance. First, variable phase resonance nonlinear modes (VPRNM) is extended to track superharmonic resonances in multiple degree of freedom systems exhibiting hysteresis. Then a novel reduced order model based on VPRNM (VPRNM ROM) is proposed to reconstruct frequency response curves faster than utilizing the harmonic balance method (HBM). The VPRNM ROM is

This paper introduces a framework for studying the interactions of autonomous system components and the design of the connectivity structure in Systems of Systems (SoSs). This framework, which uses complex network models, is also used to study the connectivity structure's impact on resource management. We discuss resource sharing as a mechanism that adds a level of flexibility to distributed systems and describe the connectivity structures that enhance components' access to the resources available within the system. The framework introduced in this paper explicitly incorporates costs of connection and the benefits that are received by direct and indirect access to resources and provides measures of the optimality of connectivity structures. We discuss central and a distributed schemes that, respectively, represent systems in which a central planner determines the connectivity structure and systems in which distributed components are allowed to add and sever connections to improve their own resource access. Furthermore, we identify optimal connectivity structures for systems with various heterogeneity conditions.

With the emergence of communication services with stringent requirements such as autonomous driving or on-flight Internet, the sixth-generation (6G) wireless network is envisaged to become an enabling technology for future transportation systems. In this paper, two ways of interactions between 6G networks and transportation are extensively investigated. On one hand, the new usage scenarios and capabilities of 6G over existing cellular networks are firstly highlighted. Then, its potential in seamless and ubiquitous connectivity across the heterogeneous space-air-ground transportation systems is demonstrated, where railways, airplanes, high-altitude platforms and satellites are investigated. On the other hand, we reveal that the introduction of 6G guarantees a more intelligent, efficient and secure transportation system. Specifically, technical analysis on how 6G can empower future transportation is provided, based on the latest research and standardization progresses in localization, integrated sensing and communications, and security. The technical challenges and insights for a road ahead are also summarized for possible inspirations on 6G enabled advanced transportation.

Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side. Such a transformation unveils new variables and model structures that facilitate model analysis, simulation, and control and offers a convenient parameterization for data-driven approaches. Quadratization techniques have found applications in diverse fields, including systems theory, fluid mechanics, chemical reaction modeling, and mathematical analysis. In this study, we focus on quadratizations that preserve the stability properties of the original model, specifically dissipativity at given equilibria. This preservation is desirable in many applications of quadratization including reachability analysis and synthetic biology. We establish the existence of dissipativity-preserving quadratizations, develop an algorithm for their computation, and demonstrate it in several case studies.

We present a multi-rate control architecture that leverages fundamental properties of differential flatness to synthesize controllers for safety-critical nonlinear dynamical systems. We propose a two-layer architecture, where the high-level generates reference trajectories using a linear Model Predictive Controller, and the low-level tracks this reference using a feedback controller. The novelty lies in how we couple these layers, to achieve formal guarantees on recursive feasibility of the MPC problem, and safety of the nonlinear system. Furthermore, using differential flatness, we provide a constructive means to synthesize the multi-rate controller, thereby removing the need to search for suitable Lyapunov or barrier functions, or to approximately linearize/discretize nonlinear dynamics. We show the synthesized controller is a convex optimization problem, making it amenable to real-time implementations. The method is demonstrated experimentally on a ground rover and a quadruped robotic system.

Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a Lagrangian function, with a cyclic variable, the degrees of freedom for the corresponding hybrid Lagrangian system can be reduced by means of a method known as \textit{hybrid Routhian reduction}. In this paper we study sufficient conditions for the existence of periodic orbits in hybrid Routhian systems which also exhibit time-reversal symmetry. Likewise, we explore some stability aspects of such orbits through the characterization of the eigenvalues for the corresponding linearized Poincaré map. Finally, we apply the results to find periodic solutions in underactuated hybrid Routhian control systems.

Cloud computing and distributed computing are becoming ubiquitous in many modern control systems such as smart grids, building automation, robot swarms or intelligent transportation systems. Compared to "isolated" control systems, the advantages of cloud-based and distributed control systems are, in particular, resource pooling and outsourcing, rapid scalability, and high performance. However, these capabilities do not come without risks. In fact, the involved communication and processing of sensitive data via public networks and on third-party platforms promote, among other cyberthreats, eavesdropping and manipulation of data. Encrypted control addresses this security gap and provides confidentiality of the processed data in the entire control loop. This paper presents a tutorial-style introduction to this young but emerging field in the framework of secure control for networked dynamical systems.

In this paper we consider the problem of mixed-criticality (MC) scheduling of implicit-deadline sporadic task systems on a homogenous multiprocessor platform. Focusing on dual-criticality systems, algorithms based on the fluid scheduling model have been proposed in the past. These algorithms use a dual-rate execution model for each high-criticality task depending on the system mode. Once the system switches to the high-criticality mode, the execution rates of such tasks are increased to meet their increased demand. Although these algorithms are speed-up optimal, they are unable to schedule several feasible dual-criticality task systems. This is because a single fixed execution rate for each high-criticality task after the mode switch is not efficient to handle the high variability in demand during the transition period immediately following the mode switch. This demand variability exists as long as the carry-over jobs of high-criticality tasks, that is jobs released before the mode switch, have not completed. Addressing this shortcoming, we propose a multi-rate fluid execution model for dual-criticality task systems in this paper. Under this model, high-criticality tasks are alloca

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial conditions. The class of systems for which the method is applicable is identified via two assumptions related to the transformability of the system into a suitable cascaded form and our ability to estimate the unknown parameters. The first condition involves the solvability of a partial differential equation while the second one requires some persistency of excitation--like conditions. The proposed observer is shown to be applicable to position estimation of a class of electromechanical systems, for the reconstruction of the state of power converters and for speed observation of a class of mechanical systems.