Discrete-Time Nonlinear Optimal Control via Generating Functions

Chen, Dijian; Fujimoto, Kenji; Suzuki, Tatsuya

doi:10.1587/transfun.e99.a.2037

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…The main disadvantage of this approach is the time-varying Riccati equation, which causes some difficulties in the practical implementation. The generating function (GF) method gives the optimal solutions according to the GFs, which are obtained numerically as the Taylor series expansion [19]. But this scheme is applicable to the systems close to linear form and it is dependent to the power series convergence, which is difficult to estimate its convergence region [20].…”

Section: Introductionmentioning

confidence: 99%

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

Abadi¹,

Vaziri²,

Jajarmi³

2019

JESA

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This article proposes a new and efficient iterative procedure to solve a class of discrete-time nonlinear optimal control problems. Based on the Pontryagin's maximum principle, the necessary optimality conditions are formulated in the form of a nonlinear discrete boundary value problem (BVP). This problem is then reduced into a sequence of linear discrete BVPs by applying a series expansion approach called the modal series method. Solving the aforementioned sequence by using the techniques of solving linear difference equations, the optimal control law is derived in the form of a uniformly convergent series. In order to demonstrate the efficiency of the proposed method in practice, an iterative algorithm with a fast rate of convergence is provided. In a recursive manner, only a few iterations are needed to find a suboptimal control law with enough accuracy. The effectiveness of this new technique is verified by solving some numerical examples.

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Section: Introductionmentioning

confidence: 99%

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

Abadi¹,

Vaziri²,

Jajarmi³

2019

JESA

View full text Add to dashboard Cite

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“…Some of them, such as linear quadratic control problems with a fixed terminal state, can be solved analytically [4]. However, solving them this way in general cases is extremely difficult, and various numerical methods have been proposed in the literature [1,5,6].…”

Section: Introductionmentioning

confidence: 99%

Algebraic approach to nonlinear finite-horizon optimal control problems of discrete-time systems with terminal constraints

Iori

Kawano

Ohtsuka

2017

2017 56th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE)

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This paper proposes a method to solve nonlinear finite-horizon optimal control problems of discrete-time polynomial systems with polynomial terminal constraints. Algebraic equations with all variables at each time step, which are independent of variables at other time steps, are derived from the necessary conditions for optimality by eliminating variables recursively. The candidates of the optimal solution are obtained by solving these equations, and algorithms to find all of these candidates are also proposed. Because of its structure, the proposed method is suitable for nonlinear model predictive control that needs only the initial optimal control law. A simple example to illustrate the methodology and a practical example with the nonlinear model predictive control framework are provided.

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Discrete-Time Nonlinear Optimal Control via Generating Functions

Cited by 2 publications

References 9 publications

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

Algebraic approach to nonlinear finite-horizon optimal control problems of discrete-time systems with terminal constraints

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