Discrete-time stochastic systems employing possibly discontinuous state-feedback control laws are addressed in this paper. Allowing discontinuous state-feedback control laws is in fact fundamental for stochastic systems regulated, for instance, by optimization-based control laws. We introduce generalized random solutions for discontinuous stochastic systems in order to guarantee existence of so...

Optimal feedback controls of PDor PID-type can be approximated very efficiently by optimal open-loop feedback controls based on optimal open-loop controls. Extending the standard construction, stochastic optimal open-loop feedback controls are constructed by taking into account still the random parameter variations in the control system. Hence, corresponding to the standard deterministic case, ...

This paper applies nonlinear 3t, control techniques to linear systems with actuator nonlinearities. In [3], this was treated under the certainty equivalence assumption. The control design produces a finite dimensional measurement feedback controller which is computable online provided certain conditions are met. In this paper, we do not use certainty equivalence theory. Instead, we use the more...

Based on the traditional linear algebra theory, this paper propose the attack detection schemes for networked control systems (NCSs) under single stochastic cyber-attack and multiple stochastic cyber-attacks aiming at multiple communication channels of NCSs, respectively. The focus is on designing an anomaly detector for NCSs under cyber-attacks. First, we construct a model of stochastic NCSs w...

This paper is devoted to studying an extended class of time-continuous branching processes, motivated by the study of stochastic control theory and interacting particle systems. The uniqueness, extinction, recurrence and positive recurrence criteria for the processes are presented. The main new point in our proofs is the use of several different comparison methods. The resulting picture shows t...

This paper clariies the relationship between risk-sensitive and robust control. This topic has received attention in the recent literature. We show that the formulations are related through an appropriate limit that is more natural than the small noise limit considered previously. The relationship we discuss is more closely related to that which has been shown in the linear systems setting. 1 S...

In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the d...

Finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic re...

In this paper we consider a linear discrete-time control system affected by an additive sinusoidal disturbance with known frequencies but unknown amplitudes and phases. The problem is to damp this forced oscillation in an optimal fashion. We show that the natural solution from the point of view of optimal control is neither robust with respect to errors in the frequencies, and thus not optimal ...

A control system is proposed for the regulation problem of the roll-motion of a manned sea-surface vehicle. Taking into account the roll-ship equations coming from the Conolly theory, a novel stochastic model has been proposed for the uncertainties driving the total mechanical torque acting on the vehicle, deriving from the wind and/or the sea-wave action. The proposed model results in a biline...