Inverse optimal control problem for bilinear systems: Application to the inverted pendulum with horizontal and vertical movement

Kanazawa, Masanori; Nakaura, Shigeki; Sampei, Mitsuji

doi:10.1109/cdc.2009.5399912

Cited by 22 publications

(21 citation statements)

References 10 publications

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“…Inverse optimal control techniques are being increasingly considered for a large range of control systems applications (see references [4], [9], [10], [13]). Inverse optimality was used for satellite attitude control by Krstic and Tsiotras in reference [11], followed by [15] and [17] where continuous state feedback controllers were designed to solve a HJB (or HJ-Isaacs) equation by minimizing a 'meaningful' weighted cost function.…”

Section: Introductionmentioning

confidence: 99%

Gain-Scheduled Inverse Optimal Satellite Attitude Control

Horri

Palmer

Roberts

2012

IEEE Trans. Aerosp. Electron. Syst.

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Despite the theoretical advances in optimal control, satellite attitude control is still predominantly performed by standard controllers, such as PD laws, which are easier to implement. A switched controller is proposed, based on inverse optimal control theory, which circumvents the complex task of numerically solving online the Hamilton Jacobi Bellman (HJB) partial differential equation of the global nonlinear optimal control problem. The inverse optimization problem consists of minimizing the norm of the control torque subject to a constraint on the convergence rate of a parameterized Lyapunov function, under the effect of the benchmark controller, which is chosen to be a PD law without loss of generality. The controller is then modified by gain scheduling to achieve a tradeoff enhancement compared to the benchmark controller, while maintaining torque saturation limits. The extent to which performance can be enhanced is shown to be dependent on the controller parameters. A controller tuning analysis shows how a design settling time limit can be achieved, within the problem's constraints on the maximum torque and the total integrated torque. The proposed optimization approach is globally stabilizing and presents low implementation complexity, which is highly desirable given the limited resources onboard satellites.

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Section: Introductionmentioning

confidence: 99%

Gain-Scheduled Inverse Optimal Satellite Attitude Control

Horri

Palmer

Roberts

2012

IEEE Trans. Aerosp. Electron. Syst.

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“…In view of this fact, a stabilization way for inverted pendulums with two-dimensional (2D) inputs has been proposed in [5] and the work [6] has conducted the experiments for the validity in real systems. The work [5] has shown that a 2D inverted pendulum system can be transformed into the bilinear system by coordinate/input transformations.…”

Section: Introductionmentioning

confidence: 99%

“…The work [5] has shown that a 2D inverted pendulum system can be transformed into the bilinear system by coordinate/input transformations. Then, the authors have tried to design optimal controllers for the bilinear system by the HamiltonJacobi Bellman equation (HJBE).…”

Section: Introductionmentioning

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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“…The inverse optimality approach used in [4] and [5] requires the knowledge of a control Lyapunov function and a stabilizing control law of a particular form. In [6] an optimal feedback controller for bilinear systems is obtained that minimizes a quadratic cost function. This inverse optimal control design is also applied to the problem of the stabilization of an inverted pendulum on a cart with horizontal and vertical movement.…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear optimal control problems based on the concept of the inverse optimality have been revisited by several researchers such as [4], [5], [6], [7], and [8]. In terms of applications, [4] presents an inverse optimal control approach for regulation of a rotating rigid spacecraft by solving an HJB equation.…”

Section: Introductionmentioning

confidence: 99%

An inverse optimality method to solve a class of third order optimal control problems

Omrani

Rabbath

Rodrigues

2010

49th IEEE Conference on Decision and Control (CDC)

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The main contribution of this paper is to analytically solve the Hamilton-Jacobi-Bellman equation for a class of third order nonlinear optimal control problems for which the dynamics are affine and the cost is quadratic in the input. The proposed solution method is based on the notion of inverse optimality with a variable part of the cost to be determined in the solution. One special advantage of the proposed method is that the solution is directly obtained for the control input without the computation of a cost function first. The cost can however also be obtained based on the control input. Furthermore, a Lyapunov function can be constructed for a subclass of optimal control problems, yielding a proof certificate for stability. Experimental results of a path following problem of a unicycle are also presented.

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Inverse optimal control problem for bilinear systems: Application to the inverted pendulum with horizontal and vertical movement

Cited by 22 publications

References 10 publications

Gain-Scheduled Inverse Optimal Satellite Attitude Control

Gain-Scheduled Inverse Optimal Satellite Attitude Control

Bilinear system approximation-based inverted pendulum stabilization in three dimensions

An inverse optimality method to solve a class of third order optimal control problems

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