In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min-max model predictive control problem that can be solved using a single linear progr...
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In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min-max model predictive control problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the optimal control law is piecewise affine and can be explicitly pre-computed so that the linear program does not have to be solved on-line. We assume that the plant model is known, is discrete-time and linear time-invariant, is subject to unknown but bounded state disturbances and that the states of the system are measured. Two numerical examples are presented;one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible. Copyright (C) 2004 John Wiley Sons, Ltd.
This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multiobjective ...
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This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multiobjective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets. (C) 2008 Elsevier B.V. All rights reserved.
Let P(lambda, mu) = min {f1(x) + lambda-f2(x) + mu-f3(x)\x is-an-element-of D}. We present a method that constructs P(lambda, mu) for all lambda, mu in a given interval in O(f.T(n) + f2) time, where f denotes the numb...
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Let P(lambda, mu) = min {f1(x) + lambda-f2(x) + mu-f3(x)\x is-an-element-of D}. We present a method that constructs P(lambda, mu) for all lambda, mu in a given interval in O(f.T(n) + f2) time, where f denotes the number of faces of P(lambda, mu) in the interval and T(n) denotes the time needed to solve the associated nonparametric problem.
An efficient optimization method is proposed for linear-quadratic optimal control problems with state and control constraints. We describe an active set solver that uses Riccati recursions to solve a sequence of equal...
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An efficient optimization method is proposed for linear-quadratic optimal control problems with state and control constraints. We describe an active set solver that uses Riccati recursions to solve a sequence of equality-constrained subproblems. The main contribution is a homotopy method based on relaxing inequality constraints. This overcomes known shortcomings of Riccati active set solvers relating to their initialization and their application to problems with time-varying model data. It can be used exclusively or in combination with established Riccati active set solvers. The efficiency is demonstrated in numerical examples against state-of-the-art quadratic programming solvers.
In the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solution are proposed.
In the paper a definition of the optimal solution of the transportation problem with fuzzy cost coefficients as well as an algorithm determining this solution are proposed.
This article presents an algorithm for the exact solution of explicit hybrid model-predictive control problems of time-invariant, discrete-time mixed logical dynamical systems. Using multiparametric programming, this ...
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This article presents an algorithm for the exact solution of explicit hybrid model-predictive control problems of time-invariant, discrete-time mixed logical dynamical systems. Using multiparametric programming, this control problem is formulated as a multiparametric mixed-integer quadratic programming problem where the initial states of the system are treated as parameters. In conjunction with decomposition type or branch-and-bound type approaches, the proposed solution strategy first creates affine relaxations of nonconvex critical regions that result from the comparison of two quadratic objective functions. These relaxations are then used to generate an affine outer approximation for the critical regions. Upon termination, the bounded space of the initial states is partitioned into possibly nonconvex critical regions and corresponding optimal control laws. (C) 2015 Elsevier Ltd. All rights reserved.
The purpose of this paper is to give a geometrical answer to the question: do the strong second order sufficienty conditions hold at any local minimum point for almost all nonlinear programs? Our idea is to reduce the...
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The purpose of this paper is to give a geometrical answer to the question: do the strong second order sufficienty conditions hold at any local minimum point for almost all nonlinear programs? Our idea is to reduce the nonlinear programming problem to a finite family of 'well-behaved' nonlinear programs by perturbing the objective function in a linear fashion and perturbing the right-hand side of the constraints by adding a constants. Each of the 'well-behaved' nonlinear programs will consist of minimizing a Morse function on a manifold with boundary, where the Morse function has no critical points on the boundary. [ABSTRACT FROM AUTHOR]
The concept of opposition-based learning (OBL) was first introduced as a scheme for machine intelligence. In a very short period of time, some other variants of opposite numbers were proposed and opposition was applie...
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The concept of opposition-based learning (OBL) was first introduced as a scheme for machine intelligence. In a very short period of time, some other variants of opposite numbers were proposed and opposition was applied to various research areas. In metaheuristic optimization algorithms, the main idea behind applying opposite numbers is the simultaneous consideration of a candidate solution and its corresponding opposite candidate in order to achieve a better approximation for the current solution. This paper proposes an opposition-based metaheuristic optimization algorithm (OBA) and a new and efficient opposition named comprehensive opposition (CO) as its main operator. In this paper it is mathematically proven that CO not only increases the chance of achieving better approximations for the solution but also guarantees the global convergence of OBA. The efficiency of the proposed method has been compared with some well-known heuristic search methods. The obtained results confirm the high performance of the proposed method in solving various function optimizations. (C) 2014 Elsevier Ltd. All rights reserved.
Move blocking is an input parameterization scheme that fixes the decision variables over arbitrary time intervals, commonly referred to as blocks, and it is widely implemented in model predictive control (MPC) to redu...
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Move blocking is an input parameterization scheme that fixes the decision variables over arbitrary time intervals, commonly referred to as blocks, and it is widely implemented in model predictive control (MPC) to reduce the computational load during on-line optimization. Since the blocking position acts as the search direction in the solution space, selection of the blocking structure has a significant effect on the optimality of moved blocked MPC. However, existing move blocked MPC schemes apply arbitrary time-invariant blocking structures without considering the optimality of the blocking structure due to the difficulty in deriving a proper time-varying blocking structure on-line. Thus, we propose a semi-explicit approach for move blocked MPC that solves a multiparametric program for the blocking position set off-line and a simplified on-line optimization problem. This approach allows for a proper time-varying blocking structure for the current state on-line. The proposed approach can efficiently improve the optimality performance of move blocked MPC with only a little additional computational cost for critical region search while guaranteeing the recursive feasibility and closed-loop stability. (c) 2020 Elsevier Ltd. All rights reserved.
Zero-wait (ZW) is a special type of batch operation in which products are processed without being stored in order to produce a number of low volume high value-added chemical products. Because of its economic impact, t...
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Zero-wait (ZW) is a special type of batch operation in which products are processed without being stored in order to produce a number of low volume high value-added chemical products. Because of its economic impact, there have been a number of studies on the scheduling of ZW processes. However, they are mainly focusing on formulating it into mathematical optimization problems assuming deterministic information. In reality, parameters in the ZW scheduling problem are subject to variation, which may make a fixed schedule suboptimal or even infeasible. Therefore. the scheduling problem has to be solved over and over again using the varying parameters. In order to overcome the inefficiency of such repeated computations, this paper introduces parametric programming technique for solving the ZW scheduling problem under uncertainty. The main advantage using the proposed technique is that a complete map of optimal schedules is obtained as a simple function of varying parameters. A new optimal schedule is thus obtained as a simple function evaluation instead of additional resource-expensive optimization computations. Computational experience with the proposed model and algorithm is presented in the form of two numerical examples. (c) 2006 Elsevier Ltd. All rights reserved.
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