R. W. Beard, G. N. Saridis, and J. T. Wen, \Approximate solutions to the time-invariant hamiltonjacobi -bellman equation," Journal of Optimization Theory and Applications, vol. 96, No 3, pp. 589-626, 1998. Home/Search Document Details and Download
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Solutions to Nonlinear Optimal and Robust Control Problems Via a.. - Alamir (Correct)
....sophisticated performance objectives. Theoretical results in nonlinear # # control were developed in the late 1950 s and 1960 s [1, 2, 3] while nonlinear ## theory has been developed more recently [4, 5, 6] The existing approaches to solve the resulting Hamilton Jacobi Isaacs (HJI) equations [7, 8, 9, 10] share a technical requirementthatisinherently associated to the Galerkin method, namely the need to performahighnumber of multi dimensional (generally n dimensional) quadratures. In this paper, it is shown that these quadratures can be avoided if collocation approach is adopted provided that an ....
R. W. Beard, G. N. Saridis, and J. T. Wen, \Approximate solutions to the time-invariant hamiltonjacobi -bellman equation," Journal of Optimization Theory and Applications, vol. 96, No 3, pp. 589-626, 1998.
Feedback Control Methodologies for Nonlinear Systems - Beeler, Tran, Banks (2000) (Correct)
....to find a sequence of approximations approaching the solution of the HJB equation. This is done by solving a sequence of generalized Hamilton Jacobi Bellman (GHJB) equations, and is discussed in [7, 8] in a general context. A more concrete technique for finding the desired solution is described in [9, 10], where a Galerkin procedure is used to find a numerical solution to the GHJB equation. Other methods include the state dependent Riccati equation (SDRE) which is an extension of the Riccati equation to nonlinear systems [11, 12, 13] The coefficients in the SDRE are functions of the state ....
....which would produce only a suboptimal control even if solved exactly, while the HJB method is approximating the HJB equation itself. 3.3. Successive Galerkin Approximation Instead of the regular HJB equation (2) the successive Galerkin approximation (SGA) method (from Beard, Saridis and Wen in [9, 10]) uses the generalized Hamilton Jacobi Bellman (GHJB) equation. Because there is an error in the paper by Beard et al. 10] on page 602, we rederive the proposed method here. Consider the cost functional V (x 0 ; u) J(x 0 ; u) Z 1 0 (x T Qx u T Ru)dt where x(t) satisfies the ....
[Article contains additional citation context not shown here]
Beard, R. W., Saridis, G. N., and Wen, J. T., "Approximate Solutions to the Time-Invariant Hamilton-Jacobi-Bellman Equation," Journal of Optimization Theory and Applications, Vol 96, pp589-626 (1998).
Successive Galerkin Approximation Algorithms for Nonlinear.. - Beard, al. (1998) (4 citations) Self-citation (Beard) (Correct)
.... equations first appeared in [23] An overview of the algorithm and some initial applications appear in [24] The convergence of the Galerkin approximation of the Generalized Hamilton Jacobi Bellman equation is shown in [25] and the convergence of the SGA algorithm for the HJB equation is shown in [26]. The algorithm has also been applied to several problems. In [27] the SGA algorithm was used to synthesize nonlinear optimal controls for a hydraulically actuated positioning systems. In [28] a nonlinear optimal control is designed for a missile autopilot. Finally, in [29] a nonlinear optimal ....
....of state dependent basis functions that make up the control. ffl The approximation algorithm can be computed off line. Once the coefficients are computed, the control (16) can be calculated on line in a number of different ways: digitally, analog hardware, etc. ffl It has been shown in [26] that for N sufficiently large, the control u (i) N is stabilizing on Omega (for all i) and is robust in the same sense as the optimal control u . ffl It was also shown in [26] that as N 1, V (i) N V and u (i) N u . 2.3.2 Nonlinear H1 Control As in the previous section, we ....
[Article contains additional citation context not shown here]
R. Beard, G. Saridis, and J. Wen, "Approximate solutions to the timeinvariant Hamilton-Jacobi-Bellman equation," Journal of Optimization Theory and Applications, vol. 96, March 1998.
Successive Galerkin Approximation Of The Isaacs Equation. - Beard, McLain, Wen (1999) Self-citation (Randal Wen) (Correct)
.... (HJB) equation that has several desirable characteristics, namely (1) feedback control, 2) guaranteed stability, 3) a welldefined region of state space over which the approximation is valid, and (4) off line computations (Beard, 1995; Beard et al. 1996; Beard et al. 1997; Beard et al. 1998). In (Beard and McLain, 1998) this algorithm was extended to the Hamilton Jacobi Isaacs equation, however the convergence properties of the extended algorithm have not yet been studied in detail. The objective of this paper is to describe the SGA algorithm for the HJI equation and to demonstrate ....
Beard, Randal, George Saridis and John Wen (1998). Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation. Journal of Optimization Theory and Applications.
The Nonlinear Projection Filter - Beard, Gunther, Lawton, Stirling (1998) Self-citation (Beard) (Correct)
No context found.
R. Beard, G. Saridis, and J. Wen, "Approximate solutions to the timeinvariant Hamilton-Jacobi-Bellman equation," Journal of Optimization Theory and Applications, vol. 96, March 1998.
Mitigating the Curse of Dimensionality in the Approximation of .. - Lawton, Beard Self-citation (Beard) (Correct)
....Galerkin Approximation (SGA) algorithm that is based on a simultaneous approximation in policy space and a Galerkin spectral approximation. The algorithm was initially described in [5] with a tutorial published in [6] Conditions guaranteeing the convergence of the algorithm are reported in [7,8]. A similar method has been reported in [9] In [10] these results are applied to the solution of the HamiltonJacobi Issacs Equation. The major drawback of the algorithm is that it suffers from the so called curse of dimensionality [11] The algorithm approximates the optimal control by a ....
....represents a nonlinear partial differential equation, which is difficult, and often impossible, to solve analytically. As is the case for the linear version of this equation, the algebraic Riccati equation, the HJB equation has many solutions, but only one corresponds to a stabilizing solution. In [5 8] the authors present the Successive Galerkin Approximation (SGA) algorithm to the Hamilton Jacobi Bellman equation. This approach approximates the solution to Equation (5) if a stabilizing control to system (1) is known a priori. Under the technical conditions listed in [12] we may approximate ....
[Article contains additional citation context not shown here]
R. Beard, G. Saridis, and J. Wen, "Approximate solutions to the timeinvariant Hamilton-Jacobi-Bellman equation," Journal of Optimization Theory and Applications, vol. 96, March 1998.
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