Adaptive Multi-dimensional Taylor Network Control For Several Classes Of Stochastic Nonlinear Systems

With the rapid development of the modern engineering control technology,higher requirements have been put forward for the performance of the controlled system.More and more practical systems begin to consider the influence of stochastic factors,and the research on control theories of stochastic nonlinear systems has attracted extensive attentions.Compared with general nonlinear systems,the controller design and stability analysis of stochastic systems have become more complex and changeable due to the existence of these stochastic factors,and there is no a universal approach to solve these problems.Therefore,the problem of adaptive control for stochastic systems is a subject worthy of further study.In this paper,the adaptive control problems of several classes of stochastic systems are studied by using different methods,such as adaptive control,Backstepping technology,Lyapunov stability theory,finite-time control theory and multi-dimensional Taylor network(MTN).The main research contents are as follows:(1)The problem of adaptive MTN control for a class of stochastic systems with time-delay is investigated.In order to overcome the performance degradation resulting from the delay terms,a new integral type Lyapunov-Krasovskii functions is introduced.A novel adaptive MTN control scheme is provided via combining Backstepping technique and MTN-based approximation method.Then,by using the Lyapunov stochastic stability theory,it can be proved that the tracking error eventually converges to a small neighborhood of the origin and the closed-loop system is semi-globally uniformly ultimately bounded in probability.(2)The problem of adaptive MTN control for a class of stochastic systems with full state time-varying constraints and the finite-time output constraint is investigated.In order to implement the finite-time output constraint,the finite-time performance function is introduced in the control scheme.A novel adaptive MTN control scheme is provided via constructing the time-varying barrier Lyapunov function.The stability analysis of the system shows that the proposed scheme can ensure that the tracking error finally converges to a small neighborhood of the origin in the finite-time and the closed-loop system is semi-globally uniformly ultimately bounded in probability.(3)The problem of MTN finite-time control for a class of stochastic systems is investigated.By combining the MTN approximation method with Backstepping technology,a new MTN finite-time control scheme is proposed.In this scheme,the MTN approximation method successfully solves the unknown nonlinear problems of the system,and the finite-time Lyapunov stability theory can prove that the proposed scheme can ensure that the tracking error converges to a small neighborhood of the origin in the finite-time and the closed-loop system is semi-global finite-time stable in probability.(4)The problem of MTN finite-time fault-tolerant control for a class of stochastic nonlinear systems is investigated.The multiple faults including the actuator and abrupt system faults are first discussed in the same theoretical framework and a novel MTN finite-time fault-tolerant scheme is proposed.In the process of scheme design,MTN method is used to approximate the unknown nonlinear functions and the real control law and virtual control signals are constructed by combining Backstepping technology and finite-time control method.The stability analysis of the system shows that the proposed scheme can ensure that the tracking error converges to a small neighborhood of the origin in the finite-time and the closed-loop system is semi-global finite-time stable in probability.The simulation examples of the above control schemes verify that the MTN control schemes designed in this paper have the desired tracking effect,low calculation cost and good real-time performance.These research results further enrich and perfect the control theories of stochastic systems,and also open up new methods and ideas for the research of various stochastic systems control problems.