Design And Application Of Optimal Control Algorithm For Semi-Markov Jump Systems

Most practical systems are often affected by random mutation factors such as changes in the working environment,damage to system components,and changes in the correlation among subsystems,which may lead to mutations in their own structure and parameters.As an important class of stochastic switching systems,semi-Markov jump systems(SMJSs)have been widely concerned by scholars at home and abroad because of their ability of modeling systems with such characteristics very well.Based on the existing research results,this paper studies the design of optimal control algorithm for a class of SMJSs with complex structures from the aspects of performance index,actuator failures,and network environment of system operation.The resulting optimized control algorithm is applied to some practical system models.The details are as follows:(1)For a class of one-area power systems with semi-Markov jump parameters,the load frequency control problem under the H_?performance index is studied.In the design process of the controller,the time delays in the communication network are fully considered.The main purpose is to design a PI-type load frequency controller such that the closed-loop system is stochastically stable and satisfies the prescribed H_?performance index.With the help of Lyapunov stability theory and the improved inequality technique as well as the novel matrix decoupling method,sufficient conditions for the existence of the controller are established.Finally,the obtained control strategy is applied to the analysis and load frequency control of a one-area power system model,and the feasibility of the proposed control scheme is verified.(2)For a class of SMJSs with actuator failures,the problem of fault-tolerant control is studied.Considering the case that actuators may encounter some failures during system operation,the fault-tolerant mechanism is introduced in the process of controller design to enhance the fault-tolerance of the studied system.Based on Lyapunov stability theory and the concept of semi-Markov kernel,a set of criteria guaranteeing the?-error mean-square stability of the closed-loop system are established.According to these criteria,the design methodology of the fault-tolerant controller is put forward.Finally,the obtained controller design method is applied to the analysis and optimal control of a DC motor system model,and the practicability and rationality of the developed control scheme are verified.(3)For a class of SMJSs with unreliable links,the problem of quantized output feedback control is studied.The phenomena of packet dropouts and signal quantization in the communication link are taken into account simultaneously,and the stochastic variable subject to Bernoulli distribution and logarithmic quantization function are respectively introduced to make a reasonable mathematical description of the above two phenomena.The main purpose is to synthesize an output feedback controller,which ensures that the closed-loop system is?-error mean-square stable.By means of Lyapunov stability theory and stochastic analysis theory,a set of sojourn time-dependent stability criteria are established to design the desired output feedback controller.Based on the criteria,the controller gains could be obtained by finding a solution to a convex optimization problem.Finally,the obtained control strategy is applied to the analysis and optimal control of a PWM-driven DC-DC boost converter system model,and the availability and feasibility of the proposed design method are confirmed.