In this paper we solve a finite-horizon partially observed risk-sensitive stochastic optimal control problem for discrete-time nonlinear systems and obtain small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic con...

The notes derive the salient features of optimal control theory for an infinite horizon objective function. For concreteness, the necessary and sufficient conditions are derived with reference to the neoclassical model of growth. However, the ideas easily extend to other economic problems. The need for the exercise arises from the lack of a single source which students can access for a developm...

Manufacturers, who re-supply a large number of customers, continually struggle with the question of how to formulate a replenishment strategy. The purpose of this paper is to determine the optimal set of routes for a group of vehicles in the transportation network under defined constraints – which is known as the Vehicle Routing Problem (VRP) – delivering new items, and resolving the invent...

Bilevel optimization problems require every feasible upperlevel solution to satisfy optimality of a lower-level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy development, transportation problems, and others. In the context of a bilevel single objective problem, there exists a nu...

The optimal survivor search problem is to maximize the probability of finding a moving target alive. The target may be a person missing at sea or lost in a wilderness area. In a multistate target problem, the target is moving and changing states stochastically. Each state may imply different motion and detectability assumptions. We find necessary and sufficient conditions for optimal detection ...

A control system design problem involves making trade-offs among multiple competing objectives. This paper studies two multiple objective control problems via nonsmooth analysis. First, a new minimax solution approach to the multiple objective linear-quadratic optimal control problem is presented. The solution to this problem is characterized by a set of coupled Riccati equations. Second, the s...

in this paper, the problem of optimal path following for a high speed planing boat is addressed. first, a nonlinear mathematical model of the boat’s dynamics is derived and then the serret-frenet frame is presented to facilitate the path following control design. to satisfy the constraints on the states and the input controls of the boat's nonlinear dynamics and minimize both the cross tracking...