arXiv subjects

Shize Lin

Publications and source records attributed to Shize Lin.

3 recordsLinked to original sources

arXiv2024

A Novel State-Centric Necessary Condition for Time-Optimal Control of Controllable Linear Systems Based on Augmented Switching Laws (Extended Version)

Most existing necessary conditions for optimal control based on adjoining methods require both state and costate information, yet the unobservability of costates for a given feasible trajectory impedes the determination of optimality in practice. This paper establishes a novel theoretical framework for time-optimal control of controllable linear systems with a single input, proposing the augmented switching law (ASL) that represents the input control and the feasibility in a compact form. Given a feasible trajectory, the perturbed trajectory under the constraints of ASL is guaranteed to be feasible, resulting in a novel state-centric necessary condition without dependence on costate information. A first-order necessary condition is proposed that the Jacobian matrix of the ASL is not of full row rank, which also results in a potential approach to optimizing a given feasible trajectory with the preservation of arc structures. The proposed necessary condition is applied to high-order chain-of-integrator systems with full box constraints, contributing to some theoretical results challenging to reason by costate-based conditions.

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arXiv2024

Chattering Phenomena in Time-Optimal Control for High-Order Chain-of-Integrator Systems with Full State Constraints (Extended Version)

Time-optimal control for high-order chain-of-integrator systems with full state constraints remains an open and challenging problem within the discipline of optimal control. The behavior of optimal control in high-order problems lacks precise characterization, and even the existence of the chattering phenomenon, i.e., the control switches for infinitely many times over a finite period, remains unknown and overlooked. This paper establishes a theoretical framework for chattering phenomena in the considered problem, providing novel findings on the uniqueness of state constraints inducing chattering, the upper bound of switching times in an unconstrained arc during chattering, and the convergence of states and costates to the chattering limit point. For the first time, this paper proves the existence of the chattering phenomenon in the considered problem. The chattering optimal control for 4th-order problems with velocity constraints is precisely solved, providing an approach to plan time-optimal snap-limited trajectories. Other cases of order $n\leq4$ are proved not to allow chattering. The conclusions rectify a longstanding misconception in the industry concerning the time-optimality of S-shaped trajectories with minimal switching times.

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arXiv2023

Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States (Extended Version)

Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further comprehension of the problem, this paper establishes a novel notation system and theoretical framework, providing the switching manifold for high-order problems in the form of switching laws. Through deriving properties of switching laws regarding signs and dimension, this paper proposes a definite condition for time-optimal control. Guided by the developed theory, a trajectory planning method named the manifold-intercept method (MIM) is developed. The proposed MIM can plan time-optimal jerk-limited trajectories with full state constraints, and can also plan near-optimal non-chattering higher-order trajectories with negligible extra motion time compared to optimal profiles. Numerical results indicate that the proposed MIM outperforms all baselines in computational time, computational accuracy, and trajectory quality by a large gap.

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