Energy-preserving algorithms, as one of the core research areas in numerical ordinary differential equations, have achieved great success by many methods such as symplectic methods and discrete gradient methods. This ...
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Energy-preserving algorithms, as one of the core research areas in numerical ordinary differential equations, have achieved great success by many methods such as symplectic methods and discrete gradient methods. This paper considers the numerical integration of quasi-bi-Hamiltonian systems, which, as a generalization of bi-Hamiltonian systems, can be expressed in two distinct ways: y=P1(y)del H2(y)=1 rho (y)P2(y)del H1(y). The quasi-bi-Hamiltonian systems have two Hamiltonians H1(y) and H2(y). Conventional discrete gradient methods can only preserve one Hamiltonian at a time. In this paper, based on discrete gradient and projection, new energy-preserving integrators that can preserve the two Hamiltonians simultaneously are proposed. They show better qualitative behaviours than traditional discrete gradient methods do. Numerical integrations of Henon-Heiles type systems and the Korteweg-de Vries (KdV) equation are conducted to show the effectiveness of the new integrators in comparison with traditional discrete gradient methods.
To incorporate the operating constraints of a virtual power plant(VPP)in transmission-level operation and market clearing,the concept of the VPP capability curve(VPP-CC)is proposed which explicitly characterizes the a...
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To incorporate the operating constraints of a virtual power plant(VPP)in transmission-level operation and market clearing,the concept of the VPP capability curve(VPP-CC)is proposed which explicitly characterizes the allowable range of active and reactive power outputs of a VPP.A two-step projection-based calculation framework is proposed to approximate the VPP-CC by the convex hull of critical points on its *** output of the proposed algorithm is concise and can be easily incorporated in the existing system operation and market *** studies based on the IEEE 33 and 123 test feeders show the computational efficiency of the proposed method outperforms existing methods by 4~7 ***,many fewer inequalities are needed to depict the VPP-CC while achieving the comparative approximation accuracy compared to sampling-based methods,which will relieve the communication and computation burden.
The adaptive tracking control problem of the multi-agent system is considered. The dynamics of each agent is of unknown parameter and can only receive different intensities of information from its different neighbors....
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ISBN:
(纸本)9798350334722
The adaptive tracking control problem of the multi-agent system is considered. The dynamics of each agent is of unknown parameter and can only receive different intensities of information from its different neighbors. To identify parameters, the improved projection algorithm is adopted, and based on each parameter estimate update law, the decentralized adaptive controllers are designed. Finally, a numerical example is provided to illustrate that each parameter estimate error is bounded and each agent tracks the desired reference trajectory.
We demonstrate how to evaluate stepwise hedge automata (Shas) with subhedge projection while completely projecting irrelevant subhedges. Since this requires passing finite state information top-down, we introduce the ...
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We demonstrate how to evaluate stepwise hedge automata (Shas) with subhedge projection while completely projecting irrelevant subhedges. Since this requires passing finite state information top-down, we introduce the notion of downward stepwise hedge automata. We use them to define in-memory and streaming evaluators with complete subhedge projection for Shas. We then tune the evaluators so that they can decide on membership at the earliest time point. We apply our algorithms to the problem of answering regular XPath queries on Xml streams. Our experiments show that complete subhedge projection of Shas can indeed speed up earliest query answering on Xml streams so that it becomes competitive with the best existing streaming tools for XPath queries.
In a very interesting paper (SIAM J. Control Optim. 37(3): 765-776, 1999), Solodov and Svaiter introduced an effective projection algorithm with linesearch for finding a solution of a variational inequality problem (V...
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In a very interesting paper (SIAM J. Control Optim. 37(3): 765-776, 1999), Solodov and Svaiter introduced an effective projection algorithm with linesearch for finding a solution of a variational inequality problem (VIP) in Euclidean space. They showed that the iterative sequence generated by their algorithm converges to a solution of (VIP) under the main assumption that the cost mapping is pseudomonotone and continuous. In this paper, we propose to modify this algorithm for solving variational inequality problems in which the cost mapping is not required to be satisfied any pseudomonotonicity. Moreover, we do not use the embedded projection methods as in methods used in literature and the linesearch procedure is not necessary when the cost mapping is Lipschitz. Several numerical examples are also provided to illustrate the efficient of the proposed algorithms.
After re-casting the wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogonality, the Douglas-Rachford algorithm is employed in...
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After re-casting the wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogonality, the Douglas-Rachford algorithm is employed in the search for multi-dimensional, non-separable, compactly supported, smooth, orthogonal, multiresolution wavelets in the case of translations along the integer lattice and isotropic dyadic dilations. An algorithm for the numerical construction of such wavelets is described. By applying the algorithm, new one-dimensional wavelets are produced as well as genuinely non-separable two-dimensional wavelets.
For a type of high⁃order discrete⁃time nonlinear systems(HDNS)whose system models are undefined,a model⁃free predictive control(MFPC)algorithm is proposed in this *** first,an estimation model is given by the improved...
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For a type of high⁃order discrete⁃time nonlinear systems(HDNS)whose system models are undefined,a model⁃free predictive control(MFPC)algorithm is proposed in this *** first,an estimation model is given by the improved projection algorithm to approach the controlled nonlinear ***,on the basis of the estimation model,a predictive controller is designed by solving the finite time domain rolling optimization quadratic function,and the controller’s explicit analytic solution is also ***,the closed⁃loop system's stability can be ***,the results of simulation reveal that the presented control strategy has a faster convergence speed as well as more stable dynamic property compared with the model⁃free sliding mode control(MFSC).
Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection;however, the primary focus of th...
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Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection;however, the primary focus of the literature is on serial algorithms. We present a parallel method that decomposes the input vector and distributes it across multiple processors for local projection. Our method is especially effective when the resulting projection is highly sparse, which is the case, for instance, in large-scale problems with independent and identically distributed (i.i.d.) entries. Moreover, the method can be adapted to parallelize a broad range of serial algorithms from the literature. We fill in theoretical gaps in serial algorithm analysis and develop similar results for our parallel analogues. Numerical experiments conducted on a wide range of large-scale instances, both real world and simulated, demonstrate the practical effectiveness of the method.
This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the lo...
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This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms.
Passengers traveling on transit networks involve two kinds of decision-making strategies: deciding which lines are attractive at an origin or transfer node (denoted line strategy, LS), or deciding which node to transf...
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Passengers traveling on transit networks involve two kinds of decision-making strategies: deciding which lines are attractive at an origin or transfer node (denoted line strategy, LS), or deciding which node to transfer at when riding a line (denoted node strategy, NS). Combining these two strategies, this paper proposes a novel variational inequality formulation for the user equilibrium passenger assignment problem. The inclusion of the NS eliminates the need for passenger assignment on a large augmented graph, reducing the modeling complexity and making it easier to track all passengers' travel routes. Moreover, constraints on the maximal number of transfers-which are crucial in practical decision-making on transit networks-are explicitly included, further drastically reducing the set of passengers' feasible strategies. Furthermore, some extant strategy-based transit assignment models are shown to be a special case of the proposed model when the transfer constraint is removed. Finally, the properties of the proposed model are illustrated on a small network, and the model and algorithm exhibit huge advantages on the chosen transit subnetwork of Beijing.
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