Observability Of Nondeteministic Logical Dynamic Systems With Time Delays

A logical dynamic system is a dual-discrete system,i.e.,discrete-time and discrete-space.It can be applied in many fields such as biological system,power system,fault detection,network synchronization and query.However,due to the discrete system structure of logical dynamic systems,the lack of effective mathematical tools for the study of its control problems has restricted its development for a long time.With the introduction of matrix semi-tensor product tool in recent years,logical dynamic system can be transformed into corresponding algebraic expressions by using a matrix semi-tensor product method,and then its control problems can be studied by using traditional methods,which makes the theory of logical dynamic systems develop vigorously,and formed a relatively complete theoretical frameworkIn the traditional linear and time invariant systems,controllability and observability are always dual existence,so controllability and observability are always described together.Although this duality does not exist in logical dynamic systems,they are also studied together for habitual considerations.But unlike controllability,which is studied in time orderly,observability is studied in reverse order in time,which is relatively difficult.Therefore,relative controllability,there are still few research results on observability of logical dynamic systems,and the observability of nondeteministic logical dynamic systems with time delays has not been solved.Influenced by the speed of information transmission,environmental factors and the randomness of the system,time delays and nondeteministic are ubiquitous phenomena in nature.Therefore,it is meaningful to study the nondeteministic logic dynamic system with time delays.In this paper,a structural forest is constructed to decompose the logical dynamic system with time delays into several subsystems without time delays,thus we can study on the logical dynamic system with time delays.This paper proves that the equivalence between the observability of the observability constructed path in structural forest and the observability of original system,this paper studies the observability of the observability constructed path in order to study the observability of the nondeteministic logic dynamic system with time delays under various definitions of observability.In this paper,three concepts of observability for the nondeteministic logic dynamic system with time delays are proposed,and the corresponding constructing algorithm of the observability constructed path based on finite automata and methods of observability determination for these three definitions are given.On this basis,the simulation examples without time-delays,with constant time-delays and with variant time-delays are given respectively for comparative analysis to verify the effectiveness of the method.