This work is aimed at the study of optimal control problems with higher-order state constraints. These are due to multi-level dynamical control systems of triangle-type which are often appear in various engineering applications. One example of the k-order problem of such type is considered. The Pontryagin maximum principle is applied and the corresponding optimality conditions are analyzed. The main conclusion is that the direct landing on the boundary of the state domain is possible only when k = 1, 2. For k > 2, this is not the case in the general situation as the extremal begins to undulate before landing.

This paper presents the prototype of the instrument that supports the control of assets and liabilities by a bank using the mathematical computations. The specifics of the approach lies in the application of the recent advances in the control theory to provide the strategic analysis for various planning horizons and scenarios of external and internal factors.

Complex economic models often describe the agent's decisions, i.e. choice of some controlled variables in accordance with criteria set by agents. Unlike purely statistical ones, agent-based models allow to describe processes with different modes, in which the agent's behavior changes quali-tatively when the environment (including the actions of other agents) change. The practical use of mathematical models of complex systems with a number of interacting agents is limited by complexity of their construction and possible errors when dealing with multitude of expressions. Computer tools, such as the “Ecomod” system discussed in the article, can substantially reduce the time spent on model creation and processing, and help to coordinate the work of several researchers on the model.

Profit is one of the key performance indicators of the company and each company needs to allocate resources in such a way that it achieves the greatest possible profit. The profit maximization problem is typically a dynamic optimization problem. This paper considers an approach to solving the problem of expanding production, using methods of Reinforcement Learning. The goal is to choose the firm's strategy for the long term: how to use the resources to maximize profits in the long-term period. To make the problem realistic, we consider the case of unstable demand. We study applicability of machine learning methods to optimal control problems, in particular Reinforcement Learning (RL), to optimal control problems arising in economics. To confirm or refute this possibility, we compare the analytical solution to the problem and the estimate obtained using the RL algorithms.

This paper presents the approach to modelling the system of agents making transactions at random time. The two main ideas are, to obtain the agents’ optimal control in the form of synthesis (feedback) and, secondly, to make the aggregate dynamics stock-flow consistent on the average, not strictly at any moment of time. We present a model of a large number of consumers and producers that take loans from the bank to buy consumption goods or investment. The moments of deals form described the Poisson flow. Consumers and producers optimally solve their stochastic optimal control problems. The solution to the OC problems are in the closed-loop form, obtained using asymptotic methods for large frequency of transactions. The optimal policy functions appear to be linear in the state variables, if time is far from the planning horizon. This enables aggregation across a large population of consumers or producers. As a result, the description of the dynamics of their aggregate state might be substituted by deterministic dynamics. The system of equations for the aggregate dynamics is reduced to one differential equation. The equation is studied numerically and the results are presented.