McKean–Vlasov optimal control: The dynamic programming principle

Stable Optimal Control and Semicontractive Dynamic Programming

We consider discrete-time infinite horizon deterministic optimal control problems with nonnegative cost per stage, and a destination that is cost-free and absorbing. The classical linear-quadratic regulator problem is a special case. Our assumptions are very general, and allow the possibility that the optimal policy may not be stabilizing the system, e.g., may not reach the destination either a...

Dynamic programming and optimal control, 3rd Edition

Dynamic Programming and Bellman’s Principle

In control theory one is given a system-usually described by differential equations-that can be influenced by an external action. In optimal control problems, such an action is to be exercised for minimizing a given cost functional. The cost functionals of interest may be of very different nature. In general, they may depend on the state of the system, on the control, and possibly on the system...

Stochastic Dynamic Programming with Markov Chains for Optimal Sustainable Control of the Forest Sector with Continuous Cover Forestry

We present a stochastic dynamic programming approach with Markov chains for optimal control of the forest sector. The forest is managed via continuous cover forestry and the complete system is sustainable. Forest industry production, logistic solutions and harvest levels are optimized based on the sequentially revealed states of the markets. Adaptive full system optimization is necessary for co...

Pontryagin's Minimum Principle for Fuzzy Optimal Control Problems

The objective of this article is to derive the necessary optimality conditions, known as Pontryagin's minimum principle, for fuzzy optimal control problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its $alpha$-level sets.