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

Abstract

This 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.