We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows us to numerically solve stochastic control problems with controlled volatility, possibly degenerate. Our backward scheme, based on leastsquares regressions,...

Abstrucf-We formulate and solve a dynamic stochastic optimization problem of a nonstandard type, whose optimal solution features active learning. The proof of optimality and the derivation of the corresponding control policies is an indirect one, which relates the original single-person optimization problem to a sequence of nested zero-sum stochastic games. Existence of saddle points for these ...

─ This paper describes some aspects about dynamical performance of irreversible systems on the control systems theory and shows how for irreversible processes, the uncertainty and disturbances turn controllability analysis for this kind of systems as a very difficult task. Finally, a similar analysis is done for batch processes, which are known as irreversible processes, showing that their prob...

We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the conventional adaptive control proofs, where the Lyapunov analysis either encompasses the complete closed-loop state or is done in multiple steps through comparison or...

Networked control systems enable for flexible systems operation and reduce cost of installation and maintenance, potentially at the price of increasing the uncertainty due to information exchange over the network. We focus on the problem of information loss in terms of packet drops, which are modelled as stochastic events that depend on the current state of the network. To design reliable contr...

In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the...

The purpose of this paper is to formulate and study the optimal control of partially observed stochastic systems with exponential-of-integral-sample cost, known as risk-sensitive problems, using Lie algebraic tools. This leads to the introduction of the su cient statistic algebra, Ls, through which one can determine a priori the maximum order of the controller. When dim(Ls) < 1, the constructio...

This paper presents a solution to certain problems in switched controller design for stochastic dynamical systems. The main result is a separation theorem for partial information systems. This result is then used to convert the partial information stochastic control problem to a complete information stochastic control problem. We also show that certainty equivalence does not hold. The optimal s...

The contents of this thesis can be separated into two distinct divisions. The first is concerned with the development of a general theory of decomposition algorithms for optimization problems. The second develops an application of the methodology of the decomposition theory to a decentralized linear stochastic control problem. An indirect approach to the development of the theory of decompositi...