Controller Design For Stochastic Systems Research Articles

Attack‐parameter‐dependent state feedback controller design for stochastic systems with denial‐of‐service attacks

AbstractIn this article, we investigate the attack‐parameter‐dependent controller synthesis problem for a class of stochastic control system under aperiodic denial‐of‐service (DoS) attacks. Different from the classic DoS attack models, which are characterized by DoS frequency and DoS duration, a new type of time‐constrained DoS attack model that only restricts the upper and lower bounds of the sleeping and active periods of the DoS attacker is introduced. Considering the effect of such DoS attacks, a switching‐like stochastic system model is built. Then based on the attack‐parameter‐dependent time‐varying stochastic Lyapunov function method, a new mean square exponential stability criterion of the resulting stochastic system under the DoS attacks is formulated in the form of linear matrix inequalities. Also, the attack‐resilient controller is designed. Finally, taking an aircraft system as an example, the validity of the obtained theoretical results is verified.

Backstepping control design for stochastic systems driven by Lévy processes

This paper presents a constructive method to design control inputs that almost surely globally -exponentially stabilise strict-feedback systems driven by Lévy processes, which consist of Wiener and compensated Poisson processes, at the origin. The control design is based on a recently developed Lyapunov-type theorem for the study of well-posedness and almost sure -exponential stability of SDEs driven by Lévy processes, the backstepping method, and new Lyapunov functions.

Controller Design for Stochastic Systems Based on Optimally Controlled Stationary States

In this paper, a method for controller design for stochastic systems based on optimally controlled stationary states is proposed. The Key idea in this method is invoking the optimally controlled system states to control the system states so as to the system states tend the controlled states close to desired system states. By computational experiments, it is shown that the proposed method is effective to control the nonlinear stochastic systems described by swing equation.

Towards fully probabilistic control design

Control design for stochastic systems is traditionally based on optimization of the expected value of a suitably chosen loss function. Despite the theoretical attractiveness of such a design methodology, its applicability is very limited owing to its computational overhead. Thus it is worthwhile to seek an alternative formulation resulting in a more tractable design. In this paper, an alternative is presented that leads to a simpler form of design equations. The proposed controller minimizes the Kullback-Leibler distance between the actual probabilistic descriptions of the closed-loop behaviour and the desired one. Its explicit randomized form depends on the solution of a functional equation with a simpler structure than that of the general dynamic programming equations. A basic paradigm is proposed, and the resulting algorithm is discussed. For illustration purposes, it is applied to linear Gaussian systems, and the desired result is obtained: The optimal controller is determined by a discrete-time Riccati equation.

Towards Fully Probabilistic Control Design

Control design for stochastic systems is traditionally based on the optimization of the expected value of a suitably chosen loss function. This well elaborated and understood task is practically restricted by the computational complexity of the related dynamic programming equations or its equivalents. For this reason, it is worthwhile to search for an alternative formulation which would lead to a more tractable design. Here, such an alternative is presented which leads to a simpler form of design equations. A way is open to a systematic approximation of the optimizing control design. The controller is designed in such a way that Kullback-Leibler distance between probabilistic description of the closed loop and the required description is minimized. It leads to explicit form of a randomized optimal controller which depends on a solution of a functional equation with a simpler structure than general dynamic programming equations. The basic paradigm is proposed and the resulting algorithm is discussed. For illustration purposes, it is applied to linear Gaussian systems. The desirable result is obtained: the optimal controller is determined by a discrete time Riccati equation. Less trivial applications will be treated elsewhere.

Multivariable control design for stochastic systems with saturated driving: LQG optimal approach

A stability criterion for stochastic multivariable feedback systems with saturated actuators is derived. An algorithm is proposed to choose an appropriate linear-quadratic-gaussian (LQG) performance index scalar to satisfy the stability criterion, and then a robust LQG optimal controller is obtained to override the limit cycle or instability incurred by saturated actuators employed in control systems. Finally, a simulation is given to support the results.

Low-sensitivity feedback controllers for linear systems with incomplete state information

Abstract The problem of output feedback controller design with low trajectory sensitivity to small system parameter variations is considered for both deterministic and stochastic systems. The performance index is of the standard linear regulator type modified to include a quadratic sensitivity term. A concise derivation of the necessary conditions for optimality is presented for deterministic systems using the method of Lagrange multipliers and existence of an optimal solution is proven. The low sensitivity controller is realized by a gain matrix obtained from the solution of a set of non-linear matrix equations. Also, use is made of recent observer-estimator results to present a unified approach to low-sensitivity controller design for stochastic systems.