Output Feedback Stabilization for Dynamic MIMO Semi-linear Stochastic Systems with Output Randomness Attenuation

In this paper, the problem of randomness attenuation is investigated for a class of MIMO semi-linear stochastic systems. To achieve this control objective, a m-block backstepping controller is designed to stabilize the closed-loop systems in probability sense. In addition, the output randomness attenuation can be achieved by optimising the design parameters using minimum entropy criterion. The effectiveness of this presented control algorithm can be verified by a given numerical example. In summary, the main contributions of this paper are characterized as follows: (1) an output feedback design method is adapted to stabilise the dynamic multi-variable semi-linear stochastic systems by block backstepping; (2) randomness of the system output is attenuated by searching the optimal design parameter based on the entropy criterion; (3) a framework of performance enhancement for stochastic systems is developed

Output Feedback Stabilization for MIMO Semi-linear Stochastic Systems with Transient Optimisation

YesThis paper investigates the stabilisation problem and consider transient optimisation for a class of the multi-input-multi-output (MIMO) semi-linear stochastic systems. A control algorithm is presented via an m-block backstepping controller design where the closed-loop system has been stabilized in a probabilistic sense and the transient performance is optimisable by optimised by searching the design parameters under the given criterion. In particular, the transient randomness and the probabilistic decoupling will be investigated as case studies. Note that the presented control algorithm can be potentially extended as a framework based on the various performance criteria. To evaluate the effectiveness of this proposed control framework, a numerical example is given with simulation results. In summary, the key contributions of this paper are stated as follows: 1) one block backstepping-based output feedback control design is developed to stabilize the dynamic MIMO semi-linear stochastic systems using a linear estimator; 2) the randomness and probabilistic couplings of the system outputs have been minimized based on the optimisation of the design parameters of the controller; 3) a control framework with transient performance enhancement of multi-variable semi-linear stochastic systems has been discussed.Higher Education Innovation Fund (No. HEIF 2018-2020), De Montfort University, Leicester, UK

Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems

This paper investigates the randomness assignment problem for a class of continuous-time stochastic nonlinear systems, where variance and entropy are employed to describe the investigated systems. In particular, the system model is formulated by a stochastic differential equation. Due to the nonlinearities of the systems, the probability density functions of the system state and system output cannot be characterised as Gaussian even if the system is subjected to Brownian motion. To deal with the non-Gaussian randomness, we present a novel backstepping-based design approach to convert the stochastic nonlinear system to a linear stochastic process, thus the variance and entropy of the system variables can be formulated analytically by the solving Fokker–Planck–Kolmogorov equation. In this way, the design parameter of the backstepping procedure can be then obtained to achieve the variance and entropy assignment. In addition, the stability of the proposed design scheme can be guaranteed and the multi-variate case is also discussed. In order to validate the design approach, the simulation results are provided to show the effectiveness of the proposed algorithm

Design of Sliding Mode PID Controller with Improved reaching laws for Nonlinear Systems

In this thesis, advanced design technique in sliding mode control (SMC) is presented with focus on PID (Proportional-Integral-Derivative) type Sliding surfaces based Sliding mode control with improved power rate exponential reaching law for Non-linear systems using Modified Particle Swarm Optimization (MPSO). To handle large non-linearities directly, sliding mode controller based on PID-type sliding surface has been designed in this work, where Integral term ensures fast finite convergence time. The controller parameter for various modified structures can be estimated using Modified PSO, which is used as an offline optimization technique. Various reaching law were implemented leading to the proposed improved exponential power rate reaching law, which also improves the finite convergence time. To implement the proposed algorithm, nonlinear mathematical model has to be decrypted without linearizing, and used for the simulation purposes. Their performance is studied using simulations to prove the proposed behavior. The problem of chattering has been overcome by using boundary method and also second order sliding mode method. PI-type sliding surface based second order sliding mode controller with PD surface based SMC compensation is also proposed and implemented. The proposed algorithms have been analyzed using Lyapunov stability criteria. The robustness of the method is provided using simulation results including disturbance and 10% variation in system parameters. Finally process control based hardware is implemented (conical tank system)