We consider a controlled stochastic system with an a.s. locally exponentially controllable compact set. Our aim is to characterize the set of points which can be driven by a suitable control to this set with either positive probability or with probability one. This will be obtained by associating to the stochastic system a suitable control problem and the corresponding Bellman equation. We then...

We consider a controlled stochastic system with an a.s. locally exponentially controllable compact set. Our aim is to characterize the set of points which can be driven by a suitable control to this set with some prescribed probability. We show that a generalization of Zubov’s method leads to this characterization and can be used as basis for numerical computations. Copyright c ©2005 IFAC.

While the current robust nonlinear control toolbox includes a number of methods for systems aane in a deterministic bounded disturbances, the problem when the disturbance is unbounded stochastic noise has hardly been considered. We present a control design which achieves global asymptotic (Lyapunov) stability in probability for a class of strict-feedback nonlinear continuous-time systems driven...

This paper is concerned with a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. The proposed approach uses the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions described by a new notion of so-called stochastic storage functions. The interconnected abstraction framework is ...

The optimal control of nonlinear stochastic systems is considered in this paper. The central role played by the Fokker-Planck-Kolmogorov equation in the stochastic control problem is shown under the assumption of asymptotic stability. A computational approach for the problem is devised based on policy iteration/ successive approximations, and a finite dimensional approximation of the control pa...

This article is a survey of the early development of selected areas in nonlinear continuous-time stochastic control. Key developments in optimal control and the dynamic programming principle, existence of optimal controls under complete and partial observations, nonlinear filtering, stochastic stability, the stochastic maximum principle and ergodic control are discussed. Issues concerning wide ...

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise. We investigate two optimiz...

We consider damped stochastic systems in a controlled (time-varying) quadratic potential and study their transition between specified Gibbs-equilibria states in finite time. By the second law of thermodynamics, the minimum amount of work needed to transition from one equilibrium state to another is the difference between the Helmholtz free energy of the two states and can only be achieved by a ...

a memory control for t-s fuzzy discrete-time systems with sto- chastic input delay is proposed in this paper. dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis- tribution. a new state space model of the discrete-time t-s fuzzy system is derived by introducing some stocha...

Modelling of the motion of a helicopter with a suspended load is described. The mathematical model takes into account stochastic disturbances acting on the load suspension point. The proposed approach allows solution of the problem of optimal control with minimization of oscillation and control power expenditure. The evolution of the system solution with time is investigated for various disturb...