AI 中文总结
本文提出一种无雅可比的迭代模型预测控制算法，通过依赖状态与控制的系数将非线性系统转化为线性二次规划，复杂度为O(ℓ)，在多个基准系统上验证了其性能优于密集序列二次规划等方法。
AI 中文摘要
本文提出一种迭代模型预测控制算法，可在不计算任何被控对象导数的前提下稳定受约束非线性系统。通过利用依赖状态与控制的系数（SCDCs）将精确非线性动力学分解为伪线性形式，我们用一系列受约束线性二次规划替代标准非凸优化。沿先前预测轨迹重新冻结系数矩阵可驱动迭代过程。在原点附近，我们证明该序列收敛至唯一不动点；明确界定了达到任意停止容差所需的迭代次数，并量化了不动点到真实Karush-Kuhn-Tucker点的距离，表明当状态趋近原点时，该最优性间隙呈二次方消失。通过放大离散代数黎卡提方程生成终端要素，可保证递归可行性与渐近稳定性，即便求解器提前终止也成立。我们在线调整终端惩罚，证明其保持一致有界，并通过块可观规范型实现输出反馈，该规范型可直接从过往输入输出中提取精确系统状态。保留子问题的块带状结构可使计算成本随时域长度ℓ线性缩放，该O(ℓ)复杂度与迭代线性二次调节器（iLQR）相当，但显著低于密集序列二次规划（SQP）的O(ℓ³)缩放。对饱和四旋翼、非完整积分器及非最小相位系统的数值研究验证了理论界限，并对比了该算法与iLQR、SQP及线性参数变模型预测控制的性能。
英文摘要
This paper presents an iterative model predictive control algorithm that stabilizes constrained nonlinear systems without evaluating a single plant derivative. By factoring the exact nonlinear dynamics into a pseudo-linear form using state- and control-dependent coefficients (SCDCs), we replace the standard nonconvex optimization with a sequence of constrained linear-quadratic programs. Refreezing the coefficient matrices along the previously predicted trajectory drives the iteration. Near the origin, we prove this sequence contracts to a unique fixed point. We explicitly bound the number of iterations required to reach any stopping tolerance, and we quantify the distance from the fixed point to a true Karush-Kuhn-Tucker point, showing this optimality gap vanishes quadratically as the state approaches the origin. Inflating the discrete algebraic Riccati equation generates terminal ingredients that guarantee recursive feasibility and asymptotic stability, even when the solver terminates early. We adapt the terminal penalty online, proving it remains uniformly bounded, and we secure output feedback through the block-observable canonical form, which extracts the exact system state directly from past inputs and outputs. Retaining the block-banded structure of the subproblem forces the computational cost to scale linearly with the horizon length $\ell$. This $O(\ell)$ complexity matches the iterative linear quadratic regulator (iLQR) but sharply undercuts the $O(\ell^3)$ scaling of dense sequential quadratic programming (SQP). Numerical studies on a saturated quadrotor, a nonholonomic integrator, and a nonminimum-phase plant illustrate the theoretical bounds and map how the algorithm compares with iLQR, SQP, and linear-parameter-varying MPC.
