Samuel Daudin
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation are proved using convex duality techniques.
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In this paper, we study the regularity of the value function associated with a stochastic control problem where two controls act simultaneously on a modulated multidimensional diffusion process. The first is a switching control modelling a random clock. Every time the random clock rings, the generator matrix is replaced by another, resulting in a different dynamic for the finite state Markov chain of the modulated diffusion process. The second is a singular stochastic control that is executed on the process within each regime.
The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average…
This paper is concerned with solutions to a one dimensional linear diffusion equation and their relation to some problems in stochastic control theory. A stochastic variational formula is obtained for the logarithm of the solution to the diffusion equation, with terminal data which is the characteristic function of a set. In this case the terminal data for the control problem is singular, and hence standard theory does not apply. The variational formula is used to prove convergence in the zero noise limit of the cost function for the stochastic control problem and its first derivatives, to the…
Terminal Soft Landing Guidance Law Using Analytic Gravity Turn Trajectory
本文提出一种基于重力转弯轨迹解析解的终端软着陆制导律，通过有限时间非线性控制跟踪参考速度并引入碰撞规避，仿真验证了其燃料效率、鲁棒性与实用性。
Incomplete financial markets are considered, defined by a multi-dimensional non-homogeneous diffusion process, being the direct sum of an Itô process (the price process), and another non-homogeneous diffusion process (the exogenous process, representing exogenous stochastic sources). The drift and the diffusion matrix of the price process are functions of the time, the price process itself and the exogenous process. In the context of such markets and for power utility functions, it is proved that the stochastic control problem consisting of optimizing the expected utility of the terminal wealt…
In this paper, we generalise Pontryagin's stochastic maximum principle to controlled McKean-Vlasov equations with anticipating law. The associated new type of delayed backward equations with implicit terminal condition is studied.
Optimal control problems with free terminal time present many challenges including nonsmooth and discontinuous control laws, irregular value functions, many local optima, and the curse of dimensionality. To overcome these issues, we propose an adaptation of the model-based actor-critic paradigm from the field of Reinforcement Learning via an exponential transformation to learn an approximate feedback control and value function pair. We demonstrate the algorithm's effectiveness on prototypical examples featuring each of the main pathological issues present in problems of this type.
Stochastic maximum principle for optimal control problem with varying terminal time and non-convex control domain
本文研究终端时间随状态均值变化且控制域非凸的随机最优控制问题，通过建立渐近一阶和二阶伴随方程及变分方程，证明了相应的 Pontryagin 随机最大值原理，并用两个例子验证主要结果。
A typical bottleneck of model predictive control algorithms is the computational burden in order to compute the receding horizon feedback law which is predominantly determined by the length of the prediction horizon. Based on a relaxed Lyapunov inequality we present techniques which allow us to show stability and suboptimality estimates for a reduced prediction horizon. In particular, the known structural properties of suboptimality estimates based on a controllability condition are used to cut the gap between theoretic stability results and numerical observations.
Online Markov Decision Processes with Terminal Law Constraints
本文提出无重置的周期性框架，旨在通过周期性策略在动态未知的在线场景中实现非渐近保证的最优学习。
Optimal Guidance with Terminal Intercept-Angle Constraints and Acceleration Bounds
针对机动目标，提出有界加速度的线性二次最优制导律，通过分段饱和指令和闭式可达角条件，显著减小饱和时的脱靶量和终端角误差。
Nonlinear Stochastic Optimal Control and Optimal Stopping using the Fokker-Planck Transformation
本文提出一种非线性随机最优控制与最优停止的理论框架，通过建立扩散过程的密度确定性表示，推导出确定性特征动力学，复现随机系统的边际规律，并利用Stein型恒等式展示分布动态规划方程与分布随机Hamilton-Jacobi-Bellman公式的相同二阶微分算子。
Optimal drift optimizer for non-convex optimization
研究有限时域随机控制准则下的非凸优化问题，通过平衡布朗探索与二次控制成本，导出最优漂移的三种精确表示（势、平均梯度、重心），并分析其在终端时间逼近和低温渐近下的优化行为。
Low-Thrust Orbital Differential Games with Speed Constraint Enforcement Using Cost Weighting
针对近圆轨道上两航天器近距离交会的终端相对速度约束问题，提出线性二次零和微分博弈模型，推导出解析闭环最优制导律，并通过成本函数权重选择实现任意终端速度。
Analytic Bridge Diffusions for Controlled Path Generation
本文提出可解析求解的LQ-GM-PID模型，将桥扩散转化为路径塑形的解析可控实验室，在多类路径生成任务中验证其有效性，可作为测试相关方法的参考模型。
In this paper we prove a weak necessary and sufficient maximum principle for Markovian regime switching stochastic optimal control problems. Instead of insisting on the maximum condition of the Hamiltonian, we show that 0 belongs to the sum of Clarke's generalized gradient of the Hamiltonian and Clarke's normal cone of the control constraint set at the optimal control. Under a joint concavity condition on the Hamiltonian and a convexity condition on the terminal objective function, the necessary condition becomes sufficient. We give four examples to demonstrate the weak stochastic maximum prin…
Generic Solutions to Controlled Balance Laws
本文证明受控标量平衡律的通有 Cauchy 解仅有有限激波且终端时刻无相互作用或新激波，并通过最优控制例子揭示优化问题通有解可在终端时刻发生激波合并。
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion. We make the following contributions: We provide a unified viewpoint on both sampling and variational inference in such generative models through the lens of stochastic control. We quantify the expressiveness of diffusion-based generative models. Specifically, we show that one can efficiently sample from a wide class of terminal target distributions b…
On generalized terminal state constraints for model predictive control
提出一种广义终端状态约束方法，用于设计模型预测控制律，在相同计算复杂度下扩大可行域，并引入新的滚动时域策略保证有限时间收敛。
Bang-Bang Evasion: Its Stochastic Optimality and a Terminal-Set-Based Implementation
研究平面终局交战最优规避问题，构建含不完美信息和有界控制的随机框架，证明最优规避策略存在且含 bang-bang 策略，提出基于闭环终端集的规避（TSE）策略，仿真显示其优于传统随机规避策略。
Adaptive Disturbance Observer-based Full-Order Integral-Terminal Sliding Mode Control with Unknown A Priori Bound on Uncertainty
针对外部扰动界未知的非线性积分器链系统，提出ADO-FOITSMC连续有限时间控制方法，利用非单调自适应观测器增益抑制抖振并保证状态全局有界，且在刚性航天器姿态稳定中得到验证。
We consider a couple of integrodifferential PDEs arising from a stochastic Markovian control problem subjected to initial-terminal conditions. These equations correspond to the MFG system for a controlled jump-diffusion process. We prove that for a specific choice of the control function the expectation of the jump-diffusion process can be found explicitly. The study is an extension of similar results known for the pure diffusion process. As an example, we show how this can be applied to the problem of investors evaluating the trend of an asset when choosing an optimal portfolio.
Terminally constrained flow-based generative models from an optimal control perspective
TOCFlow从最优控制视角提出一种几何感知的采样方法，通过终端共动框架实现二阶曲率效应捕捉，提升约束满足性能。
Soft-constrained Schrodinger Bridge: a Stochastic Control Approach
本文提出软约束薛定谔桥（SSB），通过惩罚终端与目标分布的KL散度推广薛定谔桥问题，推导出最优终端分布为几何混合，并扩展至时间序列，提出基于分数匹配的算法应用于鲁棒生成扩散模型。
Distribution Steering via Sliced Optimal Transport Control
本文针对动力系统分布引导问题，提出基于切片最优传输的有限时间控制框架，通过投影最优传输映射构造反馈律，实现分布引导并验证其收敛性，扩展至线性系统并给出数值示例。
A Blob Method for Mean Field Control With Terminal Constraints
针对带源约束和终端约束的一般平均场控制问题，提出一种无网格粒子方法，通过软非局部近似强制执行终端约束，证明Gamma收敛性并扩展离散到连续收敛结果，数值验证其在示例问题中的收敛特性与应用表现。
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