• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.580-583
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• 2003

The general time optimal control law provides the optimal solution for a minimum time control problem. But in most real systems with disturbances and model uncertainties, the time optimal control law leads to chattering effect. This chattering effect can cause the system to be unstable. Therefore, we propose a robust optimal control algorithm for the nonlinear second order systems with model uncertainty. The proposed algorithm is combined with bang-bang control and sliding mode control. Thus the proposed algorithm has two state space regions to implement to control algorithm. In each region, the appropriate linear or nonlinear feedback control law is used satisfying the dynamic system equations. Simulation results show the superiority of the proposed controller in comparison with pure time optimal control(bang-bang control).

• Structural Engineering and Mechanics
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• v.38 no.1
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• pp.39-63
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• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• East Asian mathematical journal
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• v.16 no.2
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• pp.267-275
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• 2000

In this paper, we study the duality theory of nonlinear parabolic systems. The main objective is to prove the duality theorem under general conditions within an infinite-dimensional framework. As an application, an example is given.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.583-595
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• 2008

In this paper, we introduce a fuzzy nonlinear feedback approach to the control of a class of chaotic dynamical systems. The fuzzy Parallel Distributed Compensation with Reduced Rule Base approach (PDC_RRB) is proposed. The design procedure is conceptually simple and considered to a nonlinear optimal and robust control problem due to the nonlinear nature of the Takagi-Sugeno (TS) fuzzy system. Simulation results are provided to show the effictiveness of the proposed methodology.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.10
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• pp.2651-2659
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• 2009

In this paper, inverse optimal control for nonlinear systems with structural uncertainty is considered. The first, the bounded of structural uncertainty is introduced and based on the control Lyapunov function, a theorem for the globally asymptotic stability is presented. From this a less conservative condition for the inverse optimal control is derived. The result is used to design an inverse optimal controller for a class of nonlinear systems, that improves and extends the existing results. The class of nonlinear system considered is also enlarger. The simulation results show the effectiveness of the method.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.4
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• pp.142-147
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• 2000

An overhead crane system which transports an object by girder motion, trolley motion, and hoist motion becomes a nonlinear system because the length of a rope changes. To develope the position control algorithm for the nonlinear crane systems, we apply a nonlinear optimal control method which uses forward and backward difference methods and obtain optimal inputs. This method is suitable for the overhead crane system which is characterized by the differential equation of higher degree and swing motion. From the results of computer simulation, it is founded that the position of the overhead crane system is controlled, and the swing of the object is suppressed.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.12
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• pp.1086-1089
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• 2012

We propose a near optimal controller design method for ramp metering based on SDRE (State Dependent Riccati Equation) approach. We parameterize the optimal nonlinear controller in terms of the solution matrices of an SDRE. We also give a simple algorithm to obtain the controller gain. Finally we give numerical results to show the effectiveness of the proposed near optimal traffic controller design method.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.10
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• pp.1037-1043
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• 2011

Two-wheeled balancing mobile robots are currently controlled in terms of linear control methods without considering the nonlinear dynamical characteristics. However, in the high maneuvering situations such as fast turn and abrupt start and stop, such neglected terms become dominant and greatly influence the overall driving performance. This paper addresses the SDRE nonlinear optimal control method to take advantage of the exact nonlinear dynamics of the balancing robot. Simulation results indicate that the SDRE control outperforms LQR in the respect of transient performance and required wheel torques. A design example is suggested for the state matrix that provides design flexibility in the SDRE control. It is shown that a well-planned state matrix by reflecting the physics of a balancing robot greatly contributes to the driving performance and stability.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.279-282
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• 1995

In this paper, a moving horizon control algorithm, which can be applied for a wide class of nonlinear systems with control and state constraints, is considered. In a neighborhood of the origin, a linear feedback controller is applied. Outside this neighborhood, a moving horizon control law is applied. The time taken to solve an optimal control problem is considered in the algorithm so that the proposed control law can be applied as an on-line controller.