Controllability is a fundamental property of control systems,serving as the prerequisite for controller design.While controllability test is well established in modelic(i.e.,model-driven)control systems,extending it t...Controllability is a fundamental property of control systems,serving as the prerequisite for controller design.While controllability test is well established in modelic(i.e.,model-driven)control systems,extending it to datatic(i.e.,data-driven)control systems is still a challenging task due to the absence of system models.In this study,we propose a general controllability test method for nonlinear systems with datatic description,where the system behaviors are merely described by data.In this situation,the state transition information of a dynamic system is available only at a limited number of data points,leaving the behaviors beyond these points unknown.Different from traditional exact controllability,we introduce a new concept calledϵ-controllability,which extends the definition from point-to-point form to point-to-region form.Accordingly,our focus shifts to checking whether the system state can be steered to a closed state ball centered on the target state,rather than exactly at that target state.Given a known state transition sample,the Lipschitz continuity assumption restricts the one-step transition of all the points in a state ball to a small neighborhood of the subsequent state.This property is referred to as one-step controllability backpropagation,i.e.,if the states within this neighborhood areϵ-controllable,those within the state ball are alsoϵ-controllable.On its basis,we propose a tree search algorithm called maximum expansion of controllable subset(MECS)to identify controllable states in the dataset.Starting with a specific target state,our algorithm can iteratively propagate controllability from a known state ball to a new one.This iterative process gradually enlarges theϵ-controllable subset by incorporating new controllable balls until allϵ-controllable states are searched.Besides,a simplified version of MECS is proposed by solving a special shortest path problem,called Floyd expansion with radius fixed(FERF).FERF maintains a fixed radius of all controllable balls based on a mutual controllability assumption of neighboring states.The effectiveness of our method is validated in three datatic control systems whose dynamic behaviors are described by sampled data.展开更多
基金National Key R&D Program of China(No.2022YFB2502901)National Natural Science Foundation of China(No.52221005).
文摘Controllability is a fundamental property of control systems,serving as the prerequisite for controller design.While controllability test is well established in modelic(i.e.,model-driven)control systems,extending it to datatic(i.e.,data-driven)control systems is still a challenging task due to the absence of system models.In this study,we propose a general controllability test method for nonlinear systems with datatic description,where the system behaviors are merely described by data.In this situation,the state transition information of a dynamic system is available only at a limited number of data points,leaving the behaviors beyond these points unknown.Different from traditional exact controllability,we introduce a new concept calledϵ-controllability,which extends the definition from point-to-point form to point-to-region form.Accordingly,our focus shifts to checking whether the system state can be steered to a closed state ball centered on the target state,rather than exactly at that target state.Given a known state transition sample,the Lipschitz continuity assumption restricts the one-step transition of all the points in a state ball to a small neighborhood of the subsequent state.This property is referred to as one-step controllability backpropagation,i.e.,if the states within this neighborhood areϵ-controllable,those within the state ball are alsoϵ-controllable.On its basis,we propose a tree search algorithm called maximum expansion of controllable subset(MECS)to identify controllable states in the dataset.Starting with a specific target state,our algorithm can iteratively propagate controllability from a known state ball to a new one.This iterative process gradually enlarges theϵ-controllable subset by incorporating new controllable balls until allϵ-controllable states are searched.Besides,a simplified version of MECS is proposed by solving a special shortest path problem,called Floyd expansion with radius fixed(FERF).FERF maintains a fixed radius of all controllable balls based on a mutual controllability assumption of neighboring states.The effectiveness of our method is validated in three datatic control systems whose dynamic behaviors are described by sampled data.
