• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.149-158
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• 2024

A least squares problem without correspondences is expressed as the following optimization: Π∈P^min_{m, x∈ℝn} ║Ax-Πy║, where A ∈ ℝ^m×n and y ∈ ℝ^m are given. In general, solving such an optimization problem is highly challenging. In this paper we use the rearrangement inequalities to find the closed form of solutions for certain cases. Moreover, despite the stringent constraints, we successfully tackle the nonlinear least squares problem without correspondences by leveraging rearrangement inequalities.

• 컴퓨터교육학회논문지
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• 제8권1호
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• pp.73-80
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• 2005

변형 가능한 물체들 간의 자연스럽고 그럴듯한 상호작용을 얻거나, 시뮬래이션을 사용자가 원하는 시작 조건으로 설정하기 위해서는 이를 제어할 수 있는 기하학적인 제한을 직관적으로 정의하거나 제어 할 수 있어야 한다. 또한 사용자가 시뮬레이터의 중대한 변경 없이 시뮬레이션을 다양한 환경의 시뮬레이션문제를 풀기위한 기반으로 사용할 수 있어야 한다. 본 논문에서 제안된 물리학 기반의 기하학적 제한 시뮬레이션 시스템은 변형 가능한 물체를 표현하기 위혜서 비선형적인 유한요소 해석 방법을 사용하였으며, 제약 조건을 지키기 위해서 물체의 노드에 기하학적인 제한을 설정함으로써 제한 힘이 생성된다. 또한 사용자가 기하학적인 제한을 설정하고 변경 할 수 있도록 해주며, 이러한 제약들은 지속적으로 시뮬레이션 시스템을 통제 할 수 있도록 제한 힘으로 변환된다. 따라서 시뮬레이터는 물체에 적용되는 선형적, 각도, 부동식 등의 기하학적 제한을 통제 할 수 있다. 본 연구의 실험적인 결과들은 전체 시뮬레이션 동안 기하학적 제한이 작은 오차 범위 내에서 잘 지켜지고, 변형 가능한 물체의 원하는 형태를 잘 보존하고 있음을 보여준다.

• 제어로봇시스템학회논문지
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• 제9권11호
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.1905-1910
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• 2003

It is well known that parameter uncertainties and time-delays cannot be avoided in practice and result in poor performance and even instability. Nevertheless, to the authors' best knowledge, there exist few results on model predictive control (MPC) handling explicitly uncertain time-delayed systems. In this paper, we present an MPC algorithm for uncertain time-varying systems with input constraints and state-delay. An optimization problem is suggested to find a memoryless state-feedback MPC law and the closed-loop stability is established under feasibility and certain conditions.

• 대한수학회지
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• 제41권5호
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• 전기학회논문지
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• 제58권3호
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• pp.614-620
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• 2009

The force distribution in multi-legged robots is a constrained, optimization problem. The solution to the problem is the set points of the leg contact forces for a particular system task. In this paper, an efficient and general formulation of the force distribution problem is developed using linear programming. The considered walking robot is a quadruped robot with a locked-joint failure, i.e., a joint of the failed leg is locked at a known place. For overcoming the drawback of marginal stability in fault-tolerant gaits, we define safety margin on friction constraints as the objective function to be maximized. Dynamic features of locked-joint failure are represented by equality and inequality constraints of linear programming. Unlike the former study, our result can be applied to various forms of walking such as crab and turning gaits. Simulation results show the validity of the proposed scheme.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 추계학술대회 논문집 학회본부 D
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• pp.697-699
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• 2000

In this paper, an extension of model predictive controller for nonlinear process using Takagi-Sugeno(TS) fuzzy model is proposed Since the consequent parts of TS fuzzy model comprise linear equations of input and output variables. it is locally linear, and the Generalized Predictive Control(GPC) technique which has been developed to control Linear Time Invariant(LTI) plants, can be extended as a parallel distributed controller. Also fuzzy soft constraints are introduced to handle both equality and inequality constraints in a unified form. So the traditional constrained GPC can be transferred to a standard fuzzy optimization problem. The proposed method conciliates the advantages of the fuzzy modeling with the advantages of the constrained predictive control, and the degree of freedom is increased in specifying the desired process behavior.

• 제어로봇시스템학회논문지
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• 제14권12호
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• pp.1212-1217
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• 2008

This paper studies the feasibility of using the nonlinear model predictive control as a formation flight control algorithm for unmanned aerial vehicles. The optimal control inputs for formation flight are calculated through the cost function which incorporates the relative positions of the individual vehicles to maintain a desired formation and also the inequality constraints on inputs and states using the Karush-Kuhn-Tucker conditions. In the nonlinear model predictive control setting, the optimal control inputs are implemented in a receding horizon manner, which is suitable for dealing with dynamic constraints. Numerical simulations are executed for the validation of the proposed scheme.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제5권5호
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• pp.1069-1084
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• 2011

This paper considers an optimal base station clustering problem for designing a mobile (wireless) communication network. For a given network with a set of nodes (base stations), the problem is to optimally partition the set of nodes into subsets (each called a cluster) such that the associated inter-cluster traffic is minimized under certain topological constraints and cluster capacity constraints. In the problem analysis, the problem is formulated as an integer programming problem. The integer programming problem is then transformed into a binary integer programming problem, for which the associated linear programming relaxation is solved in a column generation approach assisted by a branch-and-bound procedure. For the column generation, both a heuristic algorithm and a valid inequality approach are exploited. Various numerical examples are solved to evaluate the effectiveness of the LP (Linear Programming) based branch-and-bound algorithm.

• 대한수학회지
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• 제37권4호
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• pp.625-643
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• 2000

In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.