Symplectic Numerical Approach for Nonlinear Optimal Control of Systems with Inequality Constraints

Yoshiki Abe, G. Nishida, N. Sakamoto, Y. Yamamoto
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引用次数: 1

Abstract

This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic structure is derived from Hamiltonian systems that are equivalent to Hamilton-Jacobi equations. In the representation, the constraints can be described as an input-state transformation of the system. Therefore, it can be seamlessly applied to the stable manifold method that is a precise numerical solver of the Hamilton-Jacobi equations. In conventional methods, e.g., the penalty method or the barrier method, it is difficult to systematically assign the weights of penalty functions that are used for realizing the constraints. In the proposed method, we can separate the adjustment of weights with respect to objective functions from that of penalty functions. Furthermore, the proposed method can extend the region of computable solutions in a state space. The validity of the method is shown by a numerical example of the optimal control of a vehicle model with steering limitations.
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不等式约束系统非线性最优控制的辛数值方法
本文从辛结构的角度出发,提出了一种统一不等式约束非线性最优控制问题控制设计与数值计算的系统表示。辛结构是由等价于哈密顿-雅可比方程的哈密顿系统导出的。在表示中,约束可以被描述为系统的输入状态转换。因此,它可以无缝地应用于稳定流形方法,这是一个精确的数值求解汉密尔顿-雅可比方程。在传统的方法中,例如惩罚法或障碍法,很难系统地分配用于实现约束的惩罚函数的权值。在该方法中,我们可以将目标函数的权值调整与惩罚函数的权值调整分离开来。此外,该方法还扩展了状态空间中可计算解的范围。通过一个具有转向限制的车辆模型的最优控制数值算例,验证了该方法的有效性。
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