Structural models of Mealy finite state machines detecting faults in control systems

The subject matter of this article is a control system for unmanned aerial vehicles (UAVs) whose mathematical model is a finite state machine (FSM). The goal is to develop FSM structural models that enable (1) detection of multiple faults of FSM elements caused by an electromagnetic pulse or laser beam, and (2) prevent negative impacts on the controlled object. The tasks to be solved are as follows: to develop FSM structural models to detect invalid input vector X for the whole FSM and in each state, to detect invalid output vector Y for the whole FSM, at each transition and in each state, invalid code of the present (current) state, invalid code of the next state, and invalid transition between states; to determine the possible causes of the faults, which can be the failure in the logic Φ of forming the code of the next state, the invalid input vector X, the failure in the feedback circuit, the failure in the logic Ψ of forming the output vector, the failure in the state register R, the failure in the wire between the FSM input and the input of the logic Ψ; development of a combined structural model for the detection of all listed faults with a minimum number of additional combinational circuits, as well as a structural model that combines all additional combinational circuits. The methods used are: the theory of finite state machines, structural models of FSMs, state encoding methods of FSMs, representation methods of FSMs, and Verilog hardware description language. The following results were obtained: (1) the Mealy FSM structural models were developed to detect all the above mentioned faults, (2) the combined FSM structural models were developed, and (3) the possible causes of faults detected by each FSM structural model were identified. Experimental studies have shown that for the presented FSM structural models, the area overhead averages 3-23%, for one-hot encoding of FSM states, and 2-8%, for binary encoding of FSM states. Conclusions. The scientific novelty of the obtained results consists in the following for the first time FSM faults that are not caused by radiation and cosmic rays but by an electromagnetic pulse affecting the control device are considered; the number of faults is not limited for the state codes as well as for the input and output vectors; the faults can be detected not only in the state register R but also in the input vector X, in the logic Φ of generating the next state code, in the logic Ψ of generating the output signals, and in the feedback circuit; the invalid transitions of FSMs and the transitions to invalid states are also detected; the proposed structural models not only detect FSM failures but also prevent their negative impact on the controlled object; combined structural models allow simultaneous detection of faults in all elements of the FSM. Future research will focus on developing structural models for correcting FSM failures.