Finite-Time Control And Application Of Singular Nonlinear Time-Delay Systems

Singular system is a kind of dynamic system with a wider range and more important than normal state space system.In recent decades,the theory of linear singular systems has been basically mature.But for nonlinear singular systems,the research results so far are relatively few,and the main difficulty is the design of its controller.Based on the Hamiltonian function method,this paper studies the finite-time stabilization and finite-time robust stabilization of nonlinear singular time-delay systems,and the finite-time simultaneous stabilization and finite-time robust simultaneous stabilization of multiple nonlinear singular time-delay systems.It is worth pointing out that because there is no finite-time stability criterion for nonlinear singular time-delay systems,this paper proposes a new dual-composite asymptotic method to study the finite-time stability of the system(that is,infinite time global stability plus local finite-time asymptotic stability),and gives some example simulations.The specific research contents include the following three parts:(1)Based on Hamiltonian method,we study the finite-time stabilization and finite-time robust stabilization of nonlinear singular time-delay systems.First,according to the structural characteristics of nonlinear singular Hamiltonian system,and considering the effect of time-delay on the singular system,we obtain the equivalent nonlinear differential algebraic Hamiltonian form of the original system.Then,by designing appropriate state feedback,the differential-algebraic system is transformed into a strictly dissipative Hamiltonian system.We study the finite-time stabilization of the system.On this basis,by adding the disturbance term,we design a robust controller for nonlinear singular time-delay Hamiltonian systems and give a sufficient condition for the finite-time robust stability of nonlinear singular time-delay Hamiltonian systems.(2)Based on Hamiltonian method,we study the finite-time simultaneous stabilization and finite-time robust simultaneous stabilization of multiple nonlinear singular time-delay systems.First,we obtain the equivalent Hamiltonian forms of two nonlinear singular time-delay Hamiltonian systems by nonsingular transformation,and then,by designing a state feedback,they are converted to their strictly dissipative Hamiltonian forms respectively.Combining with dimension expansion technology,the two strictly dissipative Hamiltonian systems are extended to a strictly dissipative Hamiltonian system,and we study the finite-time stabilization and finite-time robust stabilization of the extended system.(3)Simulation test of nonlinear singular circuit system based on power electronic simulation platform.First of all,we design a nonlinear singular circuit system model in the power electronics simulation software(PSIM),and consider the influence of time-delay on the system.Realize the joint simulation of PSIM and MATLAB through the Sim Couple module.Then the finite-time controller designed in MATLAB is loaded into the PSIM circuit system,and we use the Sim Code module in PSIM to convert the control circuit into C language program code,which is compiled in the TI CCS development environment.Finally,the code is solidified into the digital signal processing chip DSP to control the circuit system and observe the state response of the circuit system through the DSP oscilloscope.