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In this paper, continuous piecewise affine (PWA) functions are realized using the lattice PWA representations on convex projection regions. Detailed proof for the realization is given. Compared with previous methods that develop lattice PWA representations based on base regions, the computational burden can be largely decreased for the current representation. Based on the result, continuous PWA functions can be more efficiently studied and used in modelling as well as approximation of nonlinear systems.

This paper presents a descent algorithm for the continuous convex piecewise linear network flow problem (CCPWLNFP). The CCPWLNFP can be reformulated as a linear programming problem and directly solved by mature algorithms. However, reformulation methods not only greatly increase the problem scale but also destroy the excellent structure of the constraint matrix. The sequential simplex algorithm (SSA) makes use of the linearity of the cost function on each segment and transforms the CCPWLNFP to a series of linear network flow problems with the original constraint matrix. The mature bounded network simplex algorithm can be applied to solve these linear network flow problems efficiently. In numerical experiments, the SSA is compared with two reformulation methods and shows its superior optimization efficiency.

As a measure of risks, value at risk (VaR) has been widely used in financial industry, while its optimization is still popular and attracting. In this paper, we will formulate the minimization of VaR as a piecewise linear (PWL) function, i.e. the k-th maximum function, and transform it into a PWL DC problem. In order to address the redundancy and nondifferentiability in the transformed problem, we propose a domain contraction algorithm which solves a series of linear programming problems and converges to a local optimum of the transformed problem. Further, considering that the equivalent problem is concave and multimodal, we carefully design an improved genetic algorithm for global search. Numerical experiments on the datasets collected from the Dow Jones Index confirm the global search capability and efficiency of the proposed algorithms.

In this work, we concentrate on the Nonconvex Piecewise Linear Network Flow Problems (NPLNFP) with discontinuous piecewise linear cost functions. Based on the piecewise linearity and discontinuity of the cost functions, we equivalently transform the NPLNFP into a range of linear Minimum Cost Network Flow Problem (MCNFP) in subdomains, and propose an approach based on a network simplex method (NSM) and a Dynamic Domain Contraction (DDC) technique. Experiment results show that the proposed approach has higher optimization efficiency compared with the other relevant algorithms.

This paper works on a descent algorithm for continuous piecewise linear (CPWL) minimization problems. CPWL minimization is a widely applied nonlinear programming, which can be equivalently transformed into a difference of convex functions (DC) programming, and then, a concave optimization over a polyhedron. By utilizing the concavity of the objective function, the sequential global linear programming (SGLP) algorithm is proposed. The SGLP algorithm makes use of global information of the polyhedral feasible domain to gain superior optimizing capacity, while applies the mature linear programming technique to insure a rapid algorithm speed. In the numerical experiments, SGLP is compared with two other algorithms of DCA and DALPT, and shows its superior optimization efficiency.

This paper considers the global optimization of hinging hyperplanes (HH), which is a widely applied nonlinear model. HH minimization can be equivalently transformed into difference of convex functions (D.C.) programming, and further, concave optimization over a polyhedron. Motivated by a novel algorithm called Hill Detouring (HD), we present a modified hill detouring (MHD) algorithm. The proposed algorithm escapes local optima efficiently with a new search strategy, and establishes an exact stopping criterion for global optimality based on the theory of γ valid cut. In the numerical experiments, MHD is compared with mixed integer programming (MIP) and HD, which shows its superior performance on the numerical efficiency and the global search capability.

Cost effectiveness analysis is to select the best alternative based on the value of effectiveness, which can be obtained by the life cycle cost. Inspired by the thought of cost as an independent variable (CAIV), this paper attempts to turn the evaluation and decision problem into a programming problem. We estabilish the system effectiveness model with the logarithm method and the cost model with the logistic curve. Then according to the cost effectiveness decision-making criteria, we estabilish cost effectiveness model of the weapon system, which can be approximated by a continuous piecewise linear (CPWL) surrogate model. To solve the obtained problem, we utilize CPWL programming methods. The feasibility of model and optimization is validated by an example of cost effectiveness model of armed helicopter.

This paper presents an energy-saving algorithm for elevator group control system (EGCS) with cameras. The cameras installed at each floor provide the information of the number of passengers waiting for service. With processing of the camera information, the number of passengers corresponding to each hall call is estimated. Then the total number of passengers assigned to be served by each elevator can be calculated. By analyzing the impact of the number of passengers on the performance of EGCS, new dispatching rules are designed. With fusion of rules and optimization of parameters, an energy-saving algorithm for EGCS with cameras is proposed. In both cases that camera provides accurate and fuzzy information, the performance of the proposed algorithm in down-peak traffic mode is presented. Compared with the existing algorithm, the proposed algorithm can achieve about 20% energy-saving without degradation of service performance.

We consider the optimal scheduling problem of the omnidirectional relay scheme in wireless networks. In a half-duplex model, we first present an optimal operation scheme that can achieve the maximum rate for the all-source all-cast problem for both one-dimensional and two-dimensional regular networks. Then, we show that the same rate can also be achieved with the greedy scheme. In the full-duplex model, the maximum rate is achieved with a simpler proof compared to the previous result. Some discussions are presented on more general networks.

In this paper, the charge pump efficiency is discussed, and a charge pump with continuous frequency charge sharing scheme is presented. The proposed charge sharing clock generator is able to recover the charge from parasitic-capacitor charging and discharging, so that the dynamic power loss is reduced by half. Furthermore, the proposed frequency regulation structure is able to keep the efficiency of charge pump at the theoretical maximum value without effect of load current. The simulation results show a maximum 10% efficiency increase and the efficiency is kept around 68% when load current decreases, while efficiency of conventional charge pump drops to 23% when load current is 10uA.

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.

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.

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.

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.

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.

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.

The main difficulty for standard continuous piecewise linear neural networks (SCPLNN) approximation is how to partition the definitional domain into several simplices, which is called a triangulation. In this paper, we firstly propose a method of triangulation to perform SCPLNN approximation. Our scheme starts with an initial, coarse triangulation of the given data and subdivides simplex until the error of the SCPLNN approximation is smaller than some tolerance. Then SCPLNN based on triangulation is identified. The proposed method involving triangulation and identification of SCPLNN is shown to be useful in approximating nonlinear systems. In addition, for each simplex, the local inverse model can easily be calculated for each local model of SCPLNN is linear. From control perspective, we exploit the advantage of the piecewise linear property of SCPLNN and design controllers for each approximate model. The validity of this control scheme using inverse of the local linear model is tested by using a NARX model.

It is common to transfer large scale nonlinear circuit equations into piecewise-linear equations to find the approximate solutions. In this paper an efficient algorithm is proposed for finding all solutions of piecewise-linear resistive circuits. This algorithm is based on a reformed algorithm mixed by sign test algorithm and linear programming algorithm to check the existence of a solution to a system of piecewise-linear equations in a super region. The proposed algorithm is more efficient than the conventional sign test algorithm and linear programming algorithm and can find all solutions of large scale circuits.

Approximation and control of nonlinear systems is a very important field of research for systems analysis and design. Although there is a growing interest in modeling and compact representation of piecewise linear functions as seen in the recent research, however only limited applications exist in the literature. In this paper a systematic procedure is outlined for modeling a nonlinear system with continuous piecewise linear function. The scheme is applied to approximate the nonlinear vehicle following model, where a third-order nonlinear system is considered to model the vehicle and power train dynamics. It is shown that without facing the problem of curse of dimensionality in linear models, the approximated model is compact, captures essential vehicle dynamics and is suitable for further control by linear methods. The control is implemented on local linear models based on gain scheduling technique. Simulation examples show that the designed system not only guarantees asymptotic tracking of the desired trajectories, but also ensures safety and ride comfort under the constraints of physical limitations inherent in the system. Various issues of vehicle following e.g. convergence of error in the inter-vehicle spacing, velocity following and control saturation are addressed in this paper. The performance analysis reveals that the new strategy yields valid results

The problem of regression within an application region is studied in this paper. The model errors are regarded as unknown but bounded. A concept of optimal forecasting parameter is introduced. The criterion and algorithm for determining this parameter are proposed. It is shown by a practical application that the forecasting accuracy can be improved by the new approach as compared with an ordinary parameter estimation method.

In this paper we consider how to determine route traffic flows for traffic assignment problem (TAP). A new approach is proposed for this purpose. It determines the route traffic flows indirectly. It solves the problem based on the solution of the link based model for the user equilibrium TAP given by LeBlanc but without enumerating all routes of the concerned traffic network explicitly. In this approach a modified Frank-Wolfe algorithm is first applied to obtain link traffic flows with different destinations for TAP, which are then used to determine the route traffic flows by a new algorithm. A simple numerical example is given to illustrate the availability of the new approach. A comparison between the new approach and the other algorithms are made.

The concept of network system equilibrium is defined in this paper, based on which the traffic assignment problem is modeled as a nonlinear complementary problem. It is proven that the solution of this model can be obtained by solving a mathematical programming and there is a unique solution to the related mathematical programming. Two examples are studied to verify the new approach, which shows that more reasonable results can be obtained in this way.

A multi-model adaptive control approach is proposed to improve the performance of adaptive control of discrete time invariant plant or time variant plant with jumping parameters and bounded disturbances. Multiple models of the plant are set up to cover the uncertainties of the plant dynamics. The localization method is used to reduce the computation burden of the multiple model algorithm. It is proved that the closed loop system is stable when multi-model pole assignment controller is used to a linear time-invariant plant with unknown parameters. The simulation results are given to show the usefulness of the proposed method.

© 2018 IEEE. This paper proposes a fast algorithm for the training of adaptive hinging hyperplanes (AHH), which is a popular and effective continuous piecewise affine (CPWA) model consisting of a linear combination of basis functions. The original AHH incrementally generates new basis functions by simply traversing all the existing basis functions in each dimension with the pre-given knots. Meanwhile, it also incorporates a backward procedure to delete redundant basis functions, which avoids over-fitting. In this paper, we accelerate the procedure of AHH in generating new basis functions, and the backward deletion is replaced with Lasso regularization, which is robust, requires less computation, and manages to prevent over-fitting. Besides, the selection of the splitting knots based on training data is also discussed. Numerical experiments show that the proposed algorithm significantly improves the efficiency of the existing AHH algorithm even with higher accuracy and it also enhances robustness in the given benchmark problems. ispartof: pages:1482-1487 ispartof: Proc. CDC 2018 vol:2018-December pages:1482-1487 ispartof: 2018 IEEE Conference on Decision and Control (CDC 2018) location:Miami Beach, USA date:17 Dec - 19 Dec 2018 status: published