An effective and user-friendly method to control a large portion of input-affine nonlinear systems is proposed. This method works based on transforming the nonlinear control problem to a linear programming (LP) in unk...
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An effective and user-friendly method to control a large portion of input-affine nonlinear systems is proposed. This method works based on transforming the nonlinear control problem to a linear programming (LP) in unknown controls, the state variables of plant, and possibly the constraints imposed on the controls and state variables. The solution of this LP provides the control to be applied to the plant. The main advantages of the proposed method are: simplicity of applying to multi-input multi-output systems, taking into account the actuator saturation and constraints on states, and robustness to uncertainties in the model. Two numerical examples are presented to verify the effectiveness of the proposed method. These are output voltage regulation of a two-input two-output dc-dc boost converter with actuator saturation and position control of a magnetic levitation system with a constraint on the speed of ball.
Tropical geometry has been recently used to obtain new complexity results in convex optimization and game theory. In this paper, we present an application of this approach to a famous class of algorithms for linear pr...
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Tropical geometry has been recently used to obtain new complexity results in convex optimization and game theory. In this paper, we present an application of this approach to a famous class of algorithms for linear programming, i.e., log-barrier interior point methods. We show that these methods are not strongly polynomial by constructing a family of linear programs with 3r + 1 inequalities in dimension 2r for which the number of iterations performed is in Omega(2(r)). The total curvature of the central path of these linear programs is also exponential in r, disproving a continuous analogue of the Hirsch conjecture proposed by Deza, Terlaky, and Zinchenko. These results are obtained by analyzing the tropical central path, which is the piecewise linear limit of the central paths of parameterized families of classical linear programs viewed through "logarithmic glasses."" This allows us to provide combinatorial lower bounds for the number of iterations and the total curvature in a general setting.
Given a graph, we wish to find a maximum number of vertex-disjoint paths of length 2. We propose a series of local improvement algorithms for this problem, and present a linear-programming based method for analyzing t...
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Given a graph, we wish to find a maximum number of vertex-disjoint paths of length 2. We propose a series of local improvement algorithms for this problem, and present a linear-programming based method for analyzing their performance. (c) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional...
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Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L 1 -gain and H 1 -norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.
In this article, we present a fault diagnosis approach for discrete event systems using labeled Petri nets. In contrast to the existing works, a new fault class containing all the fault transitions is additionally int...
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In this article, we present a fault diagnosis approach for discrete event systems using labeled Petri nets. In contrast to the existing works, a new fault class containing all the fault transitions is additionally introduced in the diagnosis function, leading to a more informative and precise diagnosis result. An integer linear programming (ILP) problem is built according to an observed word. By specifying different objective functions to the ILP problem, the diagnosis result is obtained without enumerating all observable transition sequences consistent with the observed word, which is more efficient in comparison with the existing ILP-based approaches.
Facility layout problems (FLPs) in hospitals are typically to arrange facilities or rooms along both sides of a corridor to minimize some objectives. In a hospital, very often there are center-islands to decrease the ...
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Facility layout problems (FLPs) in hospitals are typically to arrange facilities or rooms along both sides of a corridor to minimize some objectives. In a hospital, very often there are center-islands to decrease the flow cost among facilities or rooms. However, these islands have not been considered before. In this article, we propose an FLP with center-islands that involves two parallel rows and center-islands. A mixed-integer program formulation is established for modeling it. A methodology for combining a multiobjective evolutionary algorithm based on decomposition (MOEA/D) and linear program is proposed to solve this problem. MOEA/D optimizes the sequence of facilities on two rows and center-islands while the linear program is embedded into MOEA/D to optimize the exact locations of center-islands. A tabu search with a local search is also integrated into MOEA/D to enhance its search capability. Experiments show that our proposed methodology can effectively solve the problem.
In real world problems, the parameters of the solid transportation (ST) problems (supply, demand and capacity of vehicles) are not always accurate. Therefore, in dealing with these problems due to the existence of unc...
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Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that ...
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Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.
A longstanding open problem in coding theory is to determine the best (asymptotic) rate R2(δ) of binary codes with minimum constant (relative) distance δ. An existential lower bound was given by Gilbert and Varshamo...
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The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear op...
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