Discrete-time controller for stochastic nonlinear polynomial systems with Poisson noises

A Lyapunov-based distributed consensus filter for a class of nonlinear stochastic systems

This article investigates the event-triggered optimized tracking control problem for stochastic nonlinear systems based on reinforcement learning (RL). By using the backstepping strategy, an adaptive RL algorithm is performed under the identifier-critic-actor architecture to achieve event-triggered optimized control (ETOC). Moreover, a novel dynamically adjustable event-triggered mechanism is delicately designed, which adjusts the triggering threshold online to economize communication resources and reduce the computation burden. To overcome the difficulty that the virtual control signals are discontinuous due to the state-triggering, the virtual controllers are designed with the continuous sampling states signals, and the actual optimal controller is redesigned by using the triggered states in the last step. Furthermore, the proposed ETOC in this paper has significant advantages in terms of saving network resources because the event-triggered mechanism is employed in the sensor-to-controller channel and the event-sampled states are utilized to directly activate the control actions. Finally, it can be guaranteed that all signals of the stochastic system are bounded under the presented ETOC method. A simulation example is carried out to illustrate the effectiveness of the proposed ETOC algorithm.

A new practically oriented generation of nonlinear filtering toolbox

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

This paper mainly focuses on output feedback practical tracking controller design for stochastic nonlinear systems with polynomial function growth conditions. Mostly, there are some studies on output feedback tracking control problem for general nonlinear systems with parametric certainty in existing achievements. Moreover, we extend it to stochastic nonlinear systems with parametric uncertainty and system nonlinear terms are assumed to satisfy polynomial function growth conditions which are more relaxed than linear growth conditions or power growth conditions. Due to the presence of unknown parametric uncertainty, an output feedback practical tracking controller with dynamically updated gains is constructed explicitly so that all the states of the closed-loop systems are globally bounded and the tracking error belongs to arbitrarily small interval after some positive finite time. An example illustrates the efficiency of the theoretical results.

In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic nonlinear control systems with possibly degenerate distributed disturbances. The notions are inspired by the analogue notions that exist for probabilistic chains and for behavioral systems, respectively. Connections between the two notions and also with stochastic reachability are discussed. For the subclass of discrete-time stochastic linear control systems with multivariate possibly degenerate normal distributed disturbances, geometric necessary and sufficient conditions for checking stochastic bisimulation equivalence and stochastic external behavior equivalence are derived. The proposed results nicely extend the theory of bisimulation equivalence and equivalence of external behavior known for non-deterministic control systems to a stochastic setting.

In this paper, the Kalman-type recursive filtering problem is investigated for a class of discrete-time stochastic non-linear systems subject to time-delays and randomly occurring deception attacks. The deception attack under consideration is assumed to be bounded and occur in a random way, which is characterized by using the Bernoulli distribution white sequences. The purpose of the problem addressed in this paper is to design the Kalman-type recursive filter such that for all admissible randomly occurring cyber attacks, time-delays, Gaussian noises, deterministic nonlinearities and stochastic nonlinearities, an upper bound of the filtering error covariance matrix can be obtained in terms of two Riccati-like difference equations. Subsequently, by minimizing such an upper bound, the optimized filter gain can be derived. Finally, a simulation example is proposed to illustrate the effectiveness of the proposed Kalman-type recursive filter design scheme.

This paper investigates the stabilization problem for a class of discrete‐time stochastic non‐affine nonlinear systems based on T‐S fuzzy models. Based on the function approximation capability of a class of stochastic T‐S fuzzy models, it is shown that the stabilization problem of a stochastic non‐affine nonlinear system can be solved as a robust stabilization problem of the stochastic T‐S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non‐affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

We consider an infinite-horizon minimax optimal control problem for nonlinear stochastic uncertain systems governed by a discrete-state continuous-time chain. The chain and system dynamics are subject to uncertain disturbances. Using the large deviations theory we construct a robust stabilizing suboptimal guaranteed-performance controller. Conditions are presented under which this controller is optimal. We then present a numeric algorithm for calculating a robust (sub)optimal controller using a Markov chain approximation technique.

A Unified Approach to Optimal State Estimation for Stochastic Singular Systems

This paper deals with the robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of nonlinear discrete time stochastic systems. The system involves system noise, measurement output noise, nonlinear disturbance signal, and external perturbation. The aim of this paper is to design a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter such that the filtering error system is robustly exponentially stable with a given decay rate, and a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> disturbance attenuation level is guaranteed. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method.

This paper presents an innovative application of the particle filtering techniques to the vertical gyro problem, which is a highly nonlinear and non Gaussian recursive state estimation problem. The classical approach to recursive state estimation problem of nonlinear and/or non Gaussian systems is based on the extended Kalman filter (EKF), which is a heuristic method based on the linearization of the state dynamics and observations near a nominal path. Depending on the amount of nonlinearities and non Gaussian noise, the EKF often provides a solution far from acceptable. The vertical gyro is an instrument adopted to measure the tilt angles (pitch and roll) of an aircraft with respect to local vertical. It is composed by three orthogonal gyros that are used as process sensors and by three orthogonal accelerometers that are used as aiding sensors. The output of accelerometers is filtered using a proper low-pass filter to allow for the estimation of the local direction of the gravity vector that is assumed the same of the local vertical. In the application to the vertical gyro, Gordon's version of the particle filter was used. The relevant dynamical model is based on non-linear attitude rate equation using Euler angles rather than quaternions. The algorithm, developed in Matlab environment, was first calibrated and tested in simulations, obtaining very appealing performances. Subsequently, it was implemented using real data, acquired by means of an inertial unit produced by Crossbow <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> (model DMU-HDX <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> ), and its results were compared to those provided by the proprietary EKF embedded in the unit. First of all, stationary tests were performed. Sensor data were input to the particle filter that outputs the tilt angles (roll and pitch) with respect to the local geodetic reference. The results were compared to those provided by the internal EKF. Subsequently, the same operation was done using data that were acquired with moving platform. The accuracy of the filter was tested also for degraded operating conditions (lower data rates) and large initial errors. The main advantage of the methodology is that, while the internal filter works with 7 states (quaternions, biases and temperature), the particle filter ensures the convergence with 3 states, and provides acceptable performances with 1000 particles only, appearing promising for a real time application.

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.

This paper is concerned with the output feedback \(\mathcal {H}_\infty \) control problem for a class of stochastic nonlinear systems with time-varying state delays; the system dynamics is governed by the stochastic time-delay It\(\hat{o}\)-type differential equation with state and disturbance contaminated by white noises. The design of the output feedback \(\mathcal {H}_\infty \) control is based on the stochastic dissipative theory. By establishing the stochastic dissipation of the closed-loop system, the delay-dependent and delay-independent approaches are proposed for designing the output feedback \(\mathcal {H}_\infty \) controller. It is shown that the output feedback \(\mathcal {H}_\infty \) control problem for the stochastic nonlinear time-delay systems can be solved by two delay-involved Hamilton–Jacobi inequalities. A numerical example is provided to illustrate the effectiveness of the proposed methods.

Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults