W. Cebuhar and V. Costanza. Approximation procedures for the optimal control of bilinear and nonlinear systems. Journal of Optimizatoin Theory and Applications, 43:615--627, 1984. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Finite Time Near-Optimal Control for the Singularly Perturbed.. - Kim (Correct)
....of these optimal control laws. But the decomposed subsystems are also bilinear systems, which means that there are no optimal control in the explicit feedback form. Prior works on the optimal control for the singularly perturbed bilinear systems have been carried out by many researchers [2][3][4] 5] 7] 8] 9] 11] The main result in [5] states that applying the linear optimal control theory to the bilinear systems with the iteration steps is carried out by using the Riccati equations. In [6] a finite time optimal control of singularly perturbed bilinear systems is derived with a ....
....result in [5] states that applying the linear optimal control theory to the bilinear systems with the iteration steps is carried out by using the Riccati equations. In [6] a finite time optimal control of singularly perturbed bilinear systems is derived with a sequence of Riccati equations. In [3], an infinite time optimal control of singularly perturbed bilinear systems is derived with a sequence of Riccati equations. In [2] a composite near optimal for the same problem is derived by using the fixed point algorithm. In [12] a recursive algorithm with a sequence of time varying ....
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W. Cebuhar and V. Costanza. Approximation procedures for the optimal control of bilinear and nonlinear systems. Journal of Optimizatoin Theory and Applications, 43:615--627, 1984.
Feedback Control Methodologies for Nonlinear Systems - Beeler, Tran, Banks (2000) (Correct)
....than the one we will consider, for example, with a nonlinear function of the control as well as the state. There are also methods which are designed for other specific problems, such as the bilinear system x = Ax Bu ( P x j N j )u. Methods to solve this type of problem are discussed in [22, 23, 24, 25, 26]. Another 2 variation on the nonlinear control problem is an uncertain system, where unknown parameters are involved in the equation, as discussed in [27, 28] A method dealing only with systems where the number of state and control variables are the same is presented in [29] In this paper a ....
Cebuhar, W. A. and Costanza, V., "Approximation Procedures for the Optimal Control of Bilinear and Nonlinear Systems," Journal of Optimization Theory and Applications, Vol 43, pp615-627 (1984).
Galerkin Approximations of the Generalized.. - Beard, Saridis, Wen (1996) (3 citations) (Correct)
....that is employed (in a different context) in this paper. In [36] the authors reduce the optimal bilinear control problem to successive iterations of a sequence of Riccati equations. In [3] the same problem is further reduced to successive approximations of a sequence of Lyapunov equations. In [18] the bilinear control problem is reduced to a sequence of linear control problems that converge uniformly to the optimal bilinear control. Another approach taken in [58] is to cast the nonlinear optimal control problem in the form of a nonlinear programming problem. The method is formulated in ....
....if not impossible to estimate the region of convergence. Consequently, it is equally difficult to estimate the stability region of a control calculated from a truncated power series. For bilinear systems, however, it appears that that the region of attraction can be estimated, as reported in [18]. In [35] the authors present a method that is similar to perturbation methods. The basic idea is to represent the integral curve of the solution (via Green s functions) as a basic linear operator and then invert the operator. The method has several advantages over perturbation methods. Namely, ....
W. A. Cebuhar and V. Costanza. Approximation procedures for the optimal control of bilinear and nonlinear systems. Journal of Optimization Theory and Applications, 43(4):615-- 627, August 1984.
Approximate Solutions to the Time-Invariant.. - Beard, Saridis, Wen (1998) (2 citations) (Correct)
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CEBUHAR, W. A., AND COSTANZA, V. Approximation Procedures for the Optimal Control of Bilinear and Nonlinear Systems. Journal of Optimization Theory and Applications, Vol. 43, No. 4, pp. 615--627, August 1984.
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