An iterative method for the finite-time bilinear-quadratic control problem

Hofer, Eberhard P.; Tibken, Bernd

doi:10.1007/bf02346161

Cited by 106 publications

(40 citation statements)

References 9 publications

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“…of the Inverted Pendulum The present approach of optimal control for bilinear systems is based on HJBE solution [7,8]. However, it is known that solving HJBE analitically is not easy.…”

Section: Inverse Optimal Control For the Bilinear Systemmentioning

confidence: 99%

Bilinear system approximation-based inverted pendulum stabilization in three dimensions

Fujita

Ibuki

Sampei

2014

2014 Proceedings of the SICE Annual Conference (SICE)

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This paper considers inverse optimal control design for an inverted pendulum with three-dimensional movements. We show that the inverted pendulum model can be transformed into the bilinear system via a quadratic approximation and coordinate/input transformations. Then, the inverse optimal controller proposed in one of our previous works is applied to the resulting bilinear system. We next show that the present scheme has a better performance than traditional linear optimal control for linearly approximated systems by effectively utilizing the vertical movement of the pendulum system. This result is confirmed by conducting numerical simulations.

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“…of the Inverted Pendulum The present approach of optimal control for bilinear systems is based on HJBE solution [7,8]. However, it is known that solving HJBE analitically is not easy.…”

Section: Inverse Optimal Control For the Bilinear Systemmentioning

confidence: 99%

Bilinear system approximation-based inverted pendulum stabilization in three dimensions

Fujita

Ibuki

Sampei

2014

2014 Proceedings of the SICE Annual Conference (SICE)

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“…Generally, for the numerical solution of the optimal control problem of a finite dimensional bilinear system, a convergent scheme based on quasi-linearization has been proposed in [15], and references therein, to solve the optimality conditions successively. The algorithm in [15], constructs linear systems by updating system and input matrices at each iteration step. The linear state-costate duality structure of the optimality conditions is preserved at each iteration step.…”

Section: Introductionmentioning

confidence: 99%

Iterative design of suboptimal feedback control for bilinear parabolic PDE systems

Schuster

2009

2009 American Control Conference

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Optimal control of infinite dimensional systems is one of the central problems in the control of distributed parameter systems. With the development of high performance computers, numerical methods for optimal control design have regained attention and achieved significant progress, mostly in the form of open-loop solutions. We consider in this work an optimal control problem for a bilinear parabolic partial differential equation (PDE) system. Based on the optimality conditions derived from Pontryagin's maximum principle for a reduced-order model, and stated as a two-boundaryvalue problem, we propose an iterative scheme for suboptimal closed-loop control design. In each iteration step, we take advantage of linear synthesis methods to construct a sequence of controllers. The convergence of the controller sequence is proved in appropriate functional spaces. When compared with previous iterative schemes, the proposed scheme avoids repeated numerical computation of the Riccati equation and therefore reduces significantly the number of ODEs that must be solved at each iteration step. A numerical simulation study shows the effectiveness of this new approach.

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“…Some of the obtained optimal control laws rely on a quadratic cost function, modified by incorporation of nonnegative state-dependent penalizing functions [7]- [9], [10]. An iterative method for the solution of the finite-time optimization problem is presented in [11]. In [12], the recursive scheme in [11] is applied, together with the reduced order method for weakly coupled control problems studied in [13], in order to obtain a nearly optimal closed-loop control.…”

Section: Introductionmentioning

confidence: 99%

“…An iterative method for the solution of the finite-time optimization problem is presented in [11]. In [12], the recursive scheme in [11] is applied, together with the reduced order method for weakly coupled control problems studied in [13], in order to obtain a nearly optimal closed-loop control. The idea of decomposing the system into subsystems is further exploited in [14].…”

Section: Introductionmentioning

confidence: 99%

Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

Ekman

2005

IEEE Trans. Contr. Syst. Technol.

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A suboptimal solution to the bilinear quadratic regulator problem with infinite final time is studied. The proposed control law is based on the steady-state solution of the state-dependent Riccati equation. A power-series approach of the Riccati equation is presented which results in offline calculations of one Riccati equation and a sequence of Lyapunov equations. Special emphasize is devoted to illustrate the performance of the derived control law applied to the activated sludge process. Index Terms-Activated sludge process (ASP), bilinear systems, power series, Riccati equations, suboptimal control.

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An iterative method for the finite-time bilinear-quadratic control problem

Cited by 106 publications

References 9 publications

Bilinear system approximation-based inverted pendulum stabilization in three dimensions

Bilinear system approximation-based inverted pendulum stabilization in three dimensions

Iterative design of suboptimal feedback control for bilinear parabolic PDE systems

Suboptimal control for the bilinear quadratic regulator problem: application to the activated sludge process

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