Optimization of control systems with discontinuities and terminal constraints

Dyer, P.; McReynolds, Stephen R.

doi:10.1109/tac.1969.1099173

Cited by 14 publications

(11 citation statements)

References 9 publications

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“…Moreover, it is possible to derive a continuous linear feedback law [24] similar to those neighboring optimum feedback laws which are obtained using the backward sweep method to solve the linear boundary value problem (see e.g. [3], [21], [22], [23], Dyer, McReynolds [8], and Wood [31]). Because of the numerical instability, the use of such feedback laws is not recommended.…”

Section: Si~- C ~ Si B Cbmentioning

confidence: 99%

Numerical computation of neighboring optimum feedback control schemes in real-time

Pesch¹

1979

Appl Math Optim

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Abstract.A modification of the theory of neighboring extremals is presented which leads to a new formulation of a linear boundary value problem for the perturbation of the state and adjoint variables around a reference trajectory. On the basis of the multiple shooting algorithm, a numerical method for stable and efficient computation of perturbation feedback schemes is developed. This method is then applied to guidance problems in astronautics. Using as much stored a priori information about the precalculated flight path as possible, the only computational work to be done on the board computer for the computation of a regenerated optimal control program is a single integration of the state differential equations and the solution of a few small systems of linear equations. The amount of computation is small enough to be carried through on modern board computers for real-time. Nevertheless, the controllability region is large enough to compensate realistic flight disturbances, so that optimality is preserved.

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Section: Si~- C ~ Si B Cbmentioning

confidence: 99%

Numerical computation of neighboring optimum feedback control schemes in real-time

Pesch¹

1979

Appl Math Optim

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“…Neighboring optimal control (NOC) algorithms provide the simplicity we desire in the final guidance algorithm while also providing an approximate optimal solution to the underlying optimal control problem of interest. In early works [10]- [16] it is found that the solution of the NOC or second-variation control law is very similar to the solution algorithms which are used to solve the LQR problems. Solution algorithms use modified versions of the backward sweep [l]- [2] method to generate the required time-varying gain functions.…”

Section: The Linear Quadratic Regulatormentioning

confidence: 99%

“…4 Inertial properties Table 5.5 Constant parameters Table 5.6 Aerodynamic coefficients Table 5.7 Solutions with control-rate constraints Table 5.8 Solutions with acceleration constraints Table 5.9 Closed-loop performance with altitude dispersions Table 5.10 Closed-loop robustness with altitude dispersions 129 Table 5.11 Performance: solutions with flight path angle dispersions .... 136 Table 5.12 Robustness: solutions with flight path angle dispersions 136 Table 5.13 Performance: solutions with pitch attitude dispersions Table 5.14 Robustness: solutions with pitch attitude dispersions Table 5.15 Closed-loop performance: minimum-norm update Table 5. 16 Closed-loop performance: first-order update 144 Table 5.17 Performance of minimum-norm update; 2(to) + 100 144 Table 5. 18 Performance of first-order update; z{to) -|-100 Table 5.19…”

Section: Graduate Collegementioning

confidence: 99%

“…x{t) = f{x{t),u{t),t,p), (2.14) and subject to the system of boundary conditions, tp, defined as, and state inequality constraints of the form, 'ii(®(^)) > 0 i = 1,2,... ,n/i, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) and inequality constraints on the parameter vector of the form, q{p) > 0.…”

Section: Overview Of the Dms Algorithmmentioning

confidence: 99%

“…Their use has been limited primarily by the algorithm's complexity and by the numerical time and cost of its development. The original NOC methodology was published by Bryson [10], Kelley [12]- [13], Breakwell [11], and others [24]- [16]. Theoretical treatment and basic solution algorithms have been well documented in the well known publications by Bryson [1] and Lewis [2].…”

Section: Motivation and Introductionmentioning

confidence: 99%

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Development of a finite-difference neighboring optimal control law and application to the optimal landing of a reusable launch vehicle

Wetzel

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Real‐time computation of feedback controls for constrained optimal control problems. part 1: Neighbouring extremals

Pesch

1989

Optim Control Appl Methods

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SUMMARYA numerical method is developed for the real-time computation of neighbouring optimal feedback controls for constrained optimal control problems. The first part of this paper presents the theory of neighbouring extremals. Besides a survey of the theory of neighbouring extremals, special emphasis is laid on the inclusion of complex constraints, e.g. state and control variable inequality constraints and discontinuities of the system equations at interior points. The numerical treatment of these constraints is particularly emphasized. The linearization of all necessary conditions of optimal control theory leads to a linear, mulitpoint, boundary value problem with linear jump conditions that is especially well suited for numerical treatment.

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Optimization of control systems with discontinuities and terminal constraints

Cited by 14 publications

References 9 publications

Numerical computation of neighboring optimum feedback control schemes in real-time

Numerical computation of neighboring optimum feedback control schemes in real-time

Development of a finite-difference neighboring optimal control law and application to the optimal landing of a reusable launch vehicle

Real‐time computation of feedback controls for constrained optimal control problems. part 1: Neighbouring extremals

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