optimalcontrol problem for linear systems of arbitrary fractional order in the sense of Riemann-Liouville is treated in the paper. The technique of attainability sets and their support functions is used to obtain suf...
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optimalcontrol problem for linear systems of arbitrary fractional order in the sense of Riemann-Liouville is treated in the paper. The technique of attainability sets and their support functions is used to obtain sufficient conditions for time-optimalcontrol similar to that of Pontryagin's maximum principle. Theoretical results are supported by example.
In this paper, we obtain the approximate solutions for optimalcontrol of linear systems, which have a quadratic performance index. The differential transform method (DTM) is applied for solving the extreme conditions...
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In this paper, we obtain the approximate solutions for optimalcontrol of linear systems, which have a quadratic performance index. The differential transform method (DTM) is applied for solving the extreme conditions obtained from the Pontryagin's maximum principle. The differential transform method is one of the approximate methods, which can be easily applied to many linear and nonlinearproblems and is capable of reducing the size of computational work. Applying DTM, we construct an optimal feedback control law. The results reveal that the proposed method are very effective and simple. Comparisons are made between the results of the proposed methods, homotopy perturbation method, Adomian decomposition method and exact solutions.
This paper discusses the reduction of the minimum cost caused by the presence of input redundancies on linear quadratic regulator problems. An upper bound is first established for the problem with identical input redu...
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This paper discusses the reduction of the minimum cost caused by the presence of input redundancies on linear quadratic regulator problems. An upper bound is first established for the problem with identical input redundancies. And this is further extended to the one with arbitrary input redundancies. Meanwhile, an algorithm is proposed to estimate the upper bound with given accuracy. Finally, a numerical example of Boeing 747 jet liner is employed to demonstrate the main results.
This paper investigates the effects of adding input redundancies repeatedly into linear quadratic regulator (LQR) problems. As the number of input redundancies increases, three equivalent conditions are stated to guar...
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This paper investigates the effects of adding input redundancies repeatedly into linear quadratic regulator (LQR) problems. As the number of input redundancies increases, three equivalent conditions are stated to guarantee a strict decrease of the minimum cost, which is constrained by a pair of lower and upper bounds. The contribution of a new added input redundancy to reduce the minimum cost will diminish after more redundancies are added. Moreover, the minimum cost will converge to zero as the number of input redundancies goes toward infinity, which is proven by transferring the LQR problem into a cheap control problem.
This paper briefly reviews the literature on necessary optimality conditions for optimalcontrolproblems with state-variable inequality constraints. Then, it attempts to unify the treatment of linearoptimalcontrol ...
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This paper briefly reviews the literature on necessary optimality conditions for optimalcontrolproblems with state-variable inequality constraints. Then, it attempts to unify the treatment of linear optimal control problems with state-variable inequality constraints in the framework of continuous linear programming. The duality theory in this framework makes it possible to relate the adjoint variables arising in different formulations of a problem; these relationships are illustrated by the use of a simple example. This framework also allows more general problems and admits a simplex-like algorithm to solve these problems.
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