• Journal of applied mathematics & informatics
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• v.42 no.1
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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.

• The Journal of Korean Association of Computer Education
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• v.8 no.1
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• pp.73-80
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• 2005

To achieve a natural and plausible interaction with deformable objects and to setup the desirable initial conditions of simulation, user should be able to define and control the geometric constraints intuitively. In addition, user should be able to utilize the simulation as a problem solving platform by experimenting various simulation situations without major modification of the simulator. The proposed physically based geometric constraint simulation system solves the problem using a non-linear finite element method approach to represent deformable objects and constraint forces are generated by defining geometric constraints on the nodes of the object to maintain the restriction. It allows user to define and modify geometric constraints and an algorithm converts these geometric constraints into constraint forces which seamlessly integrate controllability to the simulation system. Simulator can handle linear, angular, inequality based geometric constraints on the objects. Our experimental results show that constraints are maintained in the tight error bound and preserve desired shape of deformable object during the entire simulation.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.11
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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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• 2003.10a
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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.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.3
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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.

• Proceedings of the KIEE Conference
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• 2000.11d
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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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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• v.5 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.37 no.4
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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.