1,720,980 research outputs found
Incremental stability of planar Filippov systems
No full textWe study the problem of proving incremental stability of a planar Filippov system. In particular, referring to systems that present an attractive sliding region on their discontinuity boundary, we will give a differential condition on such region able to guarantee incremental exponential stability of sliding mode trajectories. We will then derive conditions for the incremental stability of the whole system. The approach is based on using tools from contraction theory, extending their applicability to include discontinuous dynamical systems
Contraction Analysis for a Class of NonDifferentiable Systems with Applications to Stability and Network Synchronization
No full textIn this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched nondifferentiable systems satisfying Carathéodory conditions for the existence and uniqueness of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched systems
Convergence and synchronization in heterogeneous networks of smooth and piecewise smooth systems
No full textThis paper presents a framework for the study of convergence in networks where the nodes’ dynamics may be both piecewise smooth and/or nonidentical. Sufficient conditions are derived for global convergence of all node trajectories towards the same bounded region in the synchronization error space. The analysis is based on the use of set-valued Lyapunov functions and bounds are derived on the minimum coupling strength required to make all nodes in the network converge towards each other. We also provide an estimate of the asymptotic bound on the mismatch between the node state trajectories. The analysis is performed both for linear and nonlinear coupling protocols. The theoretical analysis is extensively illustrated and validated via its application to a set of representative numerical examples.</p
Price Management in Resource Allocation Problem with Approximate Dynamic Programming
No full textThe problem of managing the price for resource allocation arises in several applications, such as purchasing plane tickets, reserving a parking slot, booking a hotel room or renting SW/HW resources on a cloud. In this paper, we model a price management resource allocation problem with parallel Birth-Death stochastic Processes (BDPs) to account for the fact that the same resource can be possibly purchased by customers at different prices. In addition, customers can hold the resource at the purchase price to the necessary extent. The maximization of the revenue in both the finite and infinite time horizon cases is addressed in this paper with Stochastic Dynamic Programming (DP) approaches. To overcome the difficulty in solving the corresponding optimization problem due to the state space explosion, Approximate Dynamic Programming (ADP) techniques (in particular, the Least Square Temporal Difference method along with Monte Carlo simulations) are adopted. Furthermore, a MATLAB Toolbox is developed with the aim of solving stochastic DP/ADP problems and supporting probabilistic analysis. Extensive simulations are performed to show the effectiveness of the proposed model and the optimization approach
Hierarchical model predictive control for islanded and grid-connected microgrids with wind generation and hydrogen energy storage systems
No full textThis paper presents a novel energy management strategy (EMS) to control a wind-hydrogen microgrid which includes a wind turbine paired with a hydrogen-based energy storage system (HESS), i.e., hydrogen production, storage and re-electrification facilities, and a local load. This complies with the mini-grid use case as per the IEA-HIA Task 24 Final Report, where three different use cases and configurations of wind farms paired with HESS are proposed in order to promote the integration of wind energy into the grid. Hydrogen production surpluses by wind generation are stored and used to provide a demand-side management solution for energy supply to the local and contractual loads, both in the grid-islanded and connected modes, with corresponding different control objectives. The EMS is based on a hierarchical model predictive control (MPC) in which long-term and short-term operations are addressed. The long-term operations are managed by a high-level MPC, in which power production by wind generation and load demand forecasts are considered in combination with day-ahead market participation. Accordingly, the hydrogen production and re-electrification are scheduled so as to jointly track the load demand, maximize the revenue through electricity market participation and minimize the HESS operating costs. Instead, the management of the short-term operations is entrusted to a low-level MPC, which compensates for any deviations of the actual conditions from the forecasts and refines the power production so as to address the real-time market participation and the short time-scale equipment dynamics and constraints. Both levels also take into account operation requirements and devices’ operating ranges through appropriate constraints. The mathematical modeling relies on the mixed-logic dynamic (MLD) framework so that the various logic states and corresponding continuous dynamics of the HESS are considered. This results in a mixed-integer linear program which is solved numerically. The effectiveness of the controller is analyzed by simulations which are carried out using wind forecasts and spot prices of a wind farm in center-south of Italy
Emergence and Control of Synchronization in Networks with Directed Many-Body Interactions
No full text: The emergence of collective behaviors in networks of dynamical units in pairwise interaction has been explained as the effect of diffusive coupling. How does the presence of higher-order interaction impact the onset of spontaneous or induced synchronous behavior? Inspired by actuation and measurement constraints typical of physical and engineered systems, we propose a diffusion mechanism over hypergraphs that explains the onset of synchronization through a clarifying analogy with signed graphs. Our findings are mathematically backed by general conditions for convergence to the synchronous state
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