Robust mixed H-2/H∞ control for a class of nonlinear stochastic systems

The problem of mixed H2/H∞ control is considered for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities are described by statistical means of the stochastic variables and the uncertainties are represented by deterministic norm-bounded parameter perturbations. The mixed H2/H∞ control problem is formulated in terms of the notion of exponentially mean-square quadratic stability and the characterisations of both the H2 control performance and the H∞ robustness performance. A new technique is developed to deal with the matrix trace terms arising from the stochastic nonlinearities and the well-known S-procedure is adopted to handle the deterministic uncertainities. A unified framework is established to solve the addressed mixed H2/H∞ control problem using a linear matrix inequality approach. Within such a framework, two additional optimisation problems are discussed, one is to optimise the H∞ robustness performance, and the other is to optimise the H2 control performance. An illustrative example is provided to demonstrate the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G and the Alexander von Humboldt Foundation of Germany, the National Natural Science Foundation of China under Grant 60474049 and the Fujian provincial Natural Science Foundation of China under Grant A0410012

Study on State Predictive Controllers for Networked Control System

When different control components of a closed loop control system are connected through a common network channel then the resulting control system is a Networked Control System. This spatially distributed system has several advantages like reduced system wiring, easy fault detection and maintenance capability.Unfortunately the introduction of communication channel results in several disadvantages like network induced delays and packet dropouts leading to loss of synchronism in the control system. The network induced imperfections causes system instability and complexity for the control engineers to design a suitable controller in order to compensate their effect on closed loop control system. In addition to the complexity in design the network induced imperfections should be measured, analysed by incorporating them in the closed loop control system. The project investigates the problem of network induced time delays in a networked control system by studying the behaviour of network induced time delay in a control system controlled by Linear Quadratic controller or a Pole placement controller using the states obtained from discrete Kalman filter state estimation, which estimates the current state in the presence of state and output noises. Further a control augmentation method is used by incorporating network induced delay in the plant model control vector. The time delayed control vector creates difficulty in designing the controller which is solved by time shifting approach. Further a state predictor is designed by using plant model transition matrix to predict the future states from present and past values of control vector and state estimate. Hence an optimal predictive controller is designed wherein the Linear Quadratic or pole placement controller uses the predictive state obtained from the state predictor to compensate the effect of network induced time delay and improve the control system performance

A maximum principle for a stochastic control problem with multiple random terminal times

In the present paper we derive, via a backward induction technique, and ad hoc maximum principle for an optimal control problem with multiple random terminal times. Therefore we apply the aforementioned result to the case of a linear quadratic controller, providing solutions for the optimal control in terms of Riccati backward SDE with random terminal time. Eventually all the above results are applied to a system of interconnected banks