Jun Xu

Tsinghua University, Beijing, Beijing Shi, China

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Publications (13)4.18 Total impact

  • [show abstract] [hide abstract]
    ABSTRACT: The model of adaptive hinging hyperplanes (AHH) is used in model predictive control (MPC). The nonlinear dynamic system is approximated by the continuous piecewise affine (CPWA) model AHH and the controller design problem becomes a continuous piecewise quadratic programming. The necessary and sufficient conditions for a point to be locally optimal for such a problem are established, based on which, a descent algorithm is developed to find a local optimum. Issues concerning feasibility and stability are also discussed. Simulations are conducted to confirm the effectiveness of the proposed MPC strategy.
    Journal of Process Control 12/2012; 22(10):1821–1831. · 1.81 Impact Factor
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    ABSTRACT: This paper considers system identification using domain partition based continuous piecewise linear neural network (DP-CPLNN), which is newly proposed. DP-CPLNN has the capability of representing any continuous piecewise linear (CPWL) function, hence its identification performance can be expected. Another attractive feature of DP-CPLNN is the geometrical property of its parameters. Applying this property, this paper proposes an identification method including domain partition and parameter training. In numerical experiments, DP-CPLNN with this method outperforms hinging hyperplanes and high-level canonical piecewise linear representation, which are two widely used CPWL models, showing the flexibility of DP-CPLNN and the effectiveness of the proposed algorithm in nonlinear identification.
    Neurocomputing. 01/2012; 77:167-177.
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    ABSTRACT: This paper describes continuous piecewise linear (CPWL) programming where the objective and constraints are in the form of hinging hyperplane (HH). And HH has received wide attention due to its simplicity and good performance in system identification. When solving a CPWL programming problem, some excellent features inspire us to come up with more efficient algorithms: the two distinguished states of a hinge function reminds us of application of genetic algorithm, while the piecewise linearity and concavity of the problem of minimization of HH naturally lead to the usage of well developed methods for concave programming, such as the cutting plane method. In order to find the global minima, we propose an improved genetic algorithm (GA) incorporating the cutting plane method. The main improvement lies in three aspects. First, it utilizes binary strings that derive local minima as chromosomes, with the proposed local minima locating method. Second, a stopping criterion has been established to ensure the global optimality of GA, with the structure information provided by γ extension of local minima. And third, genetic operations have also been revised to enhance the performance of the algorithm, which is assessed by the computational experiments.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
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    ABSTRACT: In buildings with many elevators, elevator group control algorithm is used to efficiently dispatch the elevators to serve each hall call generated from different floors. Recent researches for energy saving of elevator system have attracted widespread interest, most of which achieve energy saving by minimizing the estimated energy consumption. This paper propose a rule-based algorithm for elevator group control, which focuses on design of dispatching rules for energy saving based on the inner mechanism of the elevator system. As the weights and other parameters for the rules matters a lot to the performance of the algorithm, coarse-to-fine searching strategy is used for optimization. It can overcome the combinatorial explosion of feasible set and the limitation of simulation platform. The proposed algorithm is tested on a very practical simulation platform. The result is reliable, and shows the efficiency of the algorithm on energy saving.
    01/2012;
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    ABSTRACT: This paper studies the problem of minimizing hinging hyperplanes (HH) which is a widely applied nonlinear model. To deal with HH minimization, we transform it into a d.c. (difference of convex functions) programming and a concave minimization on a polyhedron, then some mature techniques are applicable. More importantly, HH is a continuous piecewise linear function and for concave HH, the super-level sets are polyhedra. Inspired by this property, we establish a method which searches on the counter map in order to escape a local optimum. Intuitively, this method bypasses the super-level set and is hence called hill detouring method, following the name of hill climbing. In numerical experiments, the proposed algorithm is compared with CPLEX and a heuristic algorithm showing its effectiveness.
    Computers & OR. 01/2012; 39:1763-1770.
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    ABSTRACT: This paper considers parameter estimation for nonlinear model using median squared error (MSE) criterion, which is limited to linear model in the past. It is shown that applying MSE, the essence of estimating parameters for hinging hyperplanes (HH) and linear model are the same. Motivated by this fact, MSE estimation is discussed for HH. A local optimality condition is given and based on this condition, an algorithm using linear programming technique is proposed. Numerical experiments show the good performance of the proposed estimation strategy and algorithm. KeywordsHinging hyperplane–identification methods–piecewise-linear–robust estimation
    International Journal of Control Automation and Systems 01/2011; 9(4):627-635. · 0.95 Impact Factor
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    ABSTRACT: Centrifugal chiller plants (CCP) are widely used in air conditioning systems, its operation optimization can save lots of energy and has great significance in environmental protection. The optimization is a large-scale nonlinear problem and there is no practical algorithm until now. This paper proposes a new method to do this operation optimization using continuous piecewise linear programming (CPWLP). The main idea is transforming the nonlinear problem into a series of linear programmings by approximating the original system using piecewise linear representation. For CPWLP, some properties are discussed and an algorithm is given. Using CPWLP, CCP system is optimized and its energy performance is improved significantly.
    Systems Man and Cybernetics (SMC), 2010 IEEE International Conference on; 11/2010
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    ABSTRACT: In this paper, planar continuous piecewise linear (PCPWL) systems composed of more than two linear subsystems are investigated. Instead of using Lyapunov method, we study the behavior of the PCPWL system directly to give the stability analysis. When there exist eigenvectors for the PCPWL system, the subsystem stability ensures the global stability. If there are no eigenvectors, the one-circle-gain determines the global stability. Besides, we claim that PCPWL system with three stable subsystems is always globally stable if each subsystem has distinct real eigenvalues. Simulation results illustrate the proposed stability tests.
    Proceedings of the American Control Conference 01/2010;
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    ABSTRACT: Standard continuous piecewise linear neural network (SCPLNN) is a new continuous piecewise linear (CPL) model. It can represent all the CPL functions and approximate any continuous nonlinear function with arbitrary precision. Moreover, the parameters of SCPLNN are directly related to the expression of the subregions, in each of which SCPLNN equals to a linear function. Based on this property, this paper proposes an identification algorithm for SCPLNN, including domain partition and parameters optimization. In numerical experiments, SCPLNN with this algorithm outperforms hinging hyperplanes which is a widely used CPL model, showing the power and flexibility of SCPLNN in approximation.
    Proceedings of the American Control Conference 01/2010;
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    ABSTRACT: This paper deals with the problem of nonlinear model predictive control using a piecewise linear predictive model: the adaptive hinging hyperplanes (AHH). The AHH model is adaptive and efficient, thus depicts the relationship of the nonlinear system very well. Thanks to the piecewise linear property of the predictive model, a series of convex quadratic programming are constructed in the controller design step. The existence of a global optimum is guaranteed and a descent search algorithm is performed to get a reasonable control sequence within the sampling interval. Simulation results are also presented to illustrate the potential of the proposed methodologies.
    Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, combined withe the 28th Chinese Control Conference, December 16-18, 2009, Shanghai, China; 01/2009
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    ABSTRACT: The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subregion. The AHH model is actually a special case of the GHH model, which has a universal representation capability for continuous piecewise linear functions. The approximation ability of the AHH model is proved. The AHH algorithm is developed similar to the MARS algorithm. It is adaptive and can be executed efficiently, hence has power and flexibility to model unknown relationships. The AHH procedure is applied to identifying two dynamic systems and its potential is illustrated.
    Automatica. 01/2009;
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    ABSTRACT: In this paper, after a review of traffic forecasting methods and the development of piecewise linear functions, a new traffic flow forecasting model based on adaptive hinging hyperplanes was proposed. Adaptive hinging hyperplanes (AHH) is a kind of piecewise linear models which can decide its division of the domain and the parameters adaptively. Acceptable results (forecasting error is smaller than 15%) were obtained in the test of the real traffic data in Beijing. After comparison with the results of prediction model base on MARS, the following conclusions can be drawn. First, the two methods have almost the same performance in prediction precision. Second, AHH will be a little more stable and cost less computing time. Thus, AHH model may be more applicable in practical engineering.
    Artificial Intelligence and Computational Intelligence, International Conference, AICI 2009, Shanghai, China, November 7-8, 2009. Proceedings; 01/2009
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    ABSTRACT: Utilizing compact representations for continuous piecewise linear functions, this paper discusses some theoretical properties for nonseparable continuous piecewise linear programming. The existence of exact penalty for continuous piecewise linear programming is proved, which allows us to concentrate on unconstrained problems. For unconstrained problems, we give a sufficient and necessary local optimality condition, which is based on a model with universal representation capability and hence applicable to arbitrary continuous piecewise linear programming. From the gained optimality condition, an algorithm is proposed and evaluated by numerical experiments, where the theoretical properties are illustrated as well.
    Journal of Optimization Theory and Applications 155(1). · 1.42 Impact Factor