Optimization of a linear dynamic system with periodic changing parameters

The article deals with the problem of optimal control of a linear dynamic system with periodic parameters. The qualitative theory of such problems is developed very fully if the period of coefficients of the system is not very small. With a small period, there are serious difficulties with integration. Therefore, it is reasonable to supplement the constructive methods of solution with asymptotic ones. The article presents such an approach that the method of averaging is used to construct an auxiliary (basic) problem, estimates of the proximity of solutions to the initial and basic problems are obtained.

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Parameter Design in Optimal Control Problems for Linear Dynamic Systems Using a Canonical Form

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4025455 ◽

2013 ◽

Vol 136 (1) ◽

Author(s):

Ui-Jin Jung ◽

Gyung-Jin Park ◽

Sunil K. Agrawal

Keyword(s):

Optimal Control ◽

Dynamic System ◽

Dynamic Systems ◽

Control Method ◽

Linear Dynamic System ◽

Parameter Design ◽

Control Problems ◽

State Transformation ◽

Specific System ◽

Linear Dynamic

Control problems in dynamic systems require an optimal selection of input trajectories and system parameters. In this paper, a novel procedure for optimization of a linear dynamic system is proposed that simultaneously solves the parameter design problem and the optimal control problem using a specific system state transformation. Also, the proposed procedure includes structural design constraints within the control system. A direct optimal control method is also examined to compare it with the proposed method. The limitations and advantages of both methods are discussed in terms of the number of states and inputs. Consequently, linear dynamic system examples are optimized under various constraints and the merits of the proposed method are examined.

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Parameter Design in Optimal Control Problems for Linear Dynamic Systems Using a Canonical Form

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

10.1115/dscc2011-6056 ◽

2011 ◽

Cited By ~ 1

Author(s):

U. J. Jung ◽

G. J. Park ◽

S. K. Agrawal

Keyword(s):

Optimal Control ◽

Dynamic System ◽

Dynamic Systems ◽

Optimization Methods ◽

Linear Dynamic System ◽

Parameter Design ◽

Control Problems ◽

Specific System ◽

Linear Dynamic ◽

Conventional Optimization

Control problems in dynamic systems require optimal selection of input trajectories and the system parameters. In this paper, a novel procedure for optimization of linear dynamic system is proposed that solves simultaneously the parameter design problem and the optimal control problem using a specific system state transformation. Conventional optimization methods are also examined to compare with the proposed method. The limitations and advantages of both methods are discussed in terms of the number of states and inputs. Consequently, linear dynamic system examples are optimized under various constraints and the merits of the proposed method are examined.

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