Detecting vulnerabilities of information resources of unmanned vehicles method based on dynamic evaluation of Markov sequences properties

Related to the development and research of methods for ensuring computer security of unmanned vehicles in the information infrastructure of a smart city approaches are considered. The approaches are based on nonparametric statistics methods for evaluating changes in the information states of controlled UMV resources, which include communication channel, processor, and memory. It is proposed to evaluate the changes for each of these resources in such characteristics as the degree of resource loading and its rate of change. State recognition is performed under conditions of a lack of a priori information about the properties of the intrusion source and the stochastic nature of the recognized events. The presented approach is based on dynamic estimation of information States of UMV resources using Markov sequences.

ICMSIT 2020 Journal of Physics: Conference Series 1515 (2020) 022033 IOP Publishing doi: 10.1088/1742-6596/1515/2/022033 2 (TPMS), battery charging system, remote key management system (RKS), and information and multimedia system, are presented. The paper [7] is devoted to the development of models of protection mechanisms in information and computer networks. The development of methods based on the assessment of the information state of UMV resources should be considered one of the primary tasks for ensuring UMV security. The proposed solutions are based on the use of small amounts of samples when measuring resource metrics; methods that have low labor intensity and high speed; and criteria for evaluating information situations of changes in the state of resources.

Problem statement
The purpose of this work is to develop a method for dynamic assessment of the state of UMV resources based on the automaton and Markov model to increase the level of reliability of classification of information situations that occur when monitoring the characteristics of UMV resources. The main task in constructing Markov models is to collect data for calculating transient probabilities and constructing transition probability matrices, which requires information about changes in the state of UMV resources that occur over certain time intervals. It is proposed to use the Kulbak divergence [8] as an informational measure of the difference between two matrices, one of which describes the transition probabilities under the normal state of resources, and the second-under external influence. The main advantages of the proposed method for evaluating the information state of resources based on Kulbak divergence are sensitivity to changes in the state of resources and adaptability to external influences. Ensuring these requirements allows us to achieve: • high reliability of determining the information state of the resource; • reducing the magnitude of type 1 and type 2 errors; • minimum possible damage from loss of information.
At the same time, ensuring high reliability of control in combination with minimal damage will lead to an increase in control time and the computational cost of control. There is a contradiction when the improvement of some control characteristics causes the deterioration of others. The general recommendation for evaluating the detection of the resource's information state is the following. Depending on the purpose of the system, an expert (DM) may ask the value of p -confidence level and the corresponding limit value of the Kullback distance, depending on the criticality of the resource for which, on the one hand, will ensure a high accuracy of characteristic values of resources, on the other hand, will achieve the acceptable number of type 1 and type 2 errors, and thus will be reduced the risks in making wrong decisions.
With a fairly general problem statement we are talking about the need to assess changes in the state of UMV resources based on the results of observations over a certain time interval. We denote RV = { RV1,…,RVj,…,RVm }set of controlled UMV resources; We will determine the controlled characteristics of resources that will be used to evaluate their state: We assume that the state of the RVj resource at a given time t depends on the values of the controlled characteristics of the Dj, Vj. Let these states be denoted by S t j ={ S t j0 , S t j1, S t j2}-the set of possible states  For example, areas are separated by straight lines, although in real conditions, the size of the areas and the shape of the lines are determined by the expert for specific conditions of difference in the state of resources. Let's denote the set of these states {0,1,2}. Without breaking the generality of the description, let's assume that the area with the number " 0 "-indicates a normal state, area" 1 "-a precritical state, a slight deviation from the normal state, and area" 2 " correspond to the critical state of the resource, when the deviation from the normal state is significant.

Methods and results
We will record changes in the state of resources To evaluate the dynamic states of resources, we suggest using an automaton model. As we know, the finite state automaton is a powerful tool for construction of system-wide descriptions [9]. For this  , (µj,Mj )). We will consider the automaton operation in relation to specific tacts of time t1, t2 , t3, since each time tact ti will have its own output signal Y(ti). At the initial time t0 the automaton is in the state Sн. At each moment of time ti the automaton is in one of the internal states, is able to receive an input signal, generate a new internal state, and output the corresponding output signal.
Let's denote by the symbol хi the input signal S about the resource state received at the moment of time ti , i ϵ { 1,2,3 }, хi ϵ { 0,1,2 }. We introduce the symbol Sx1х2х3 for the sequence of changes in the internal state of the automaton in three tacts. For example, the value Sx1х2х3 = S001 means that the internal state of the automaton corresponding to the normal state of the resource has not changed in two cycles, since х1 =0, х2 =0, and in the third tact х3=1the pre-critical state of the resource. Thus, after the third tact each of the internal states of the machine contains a sequence of changes in the state of resources.
The construction of the automaton grammar. Automaton grammar follows the transition rules and includes: G={ The initial grammar character is mapped to the initial state of the automaton -Sн. The alphabet of nonterminal characters VН is mapped to the alphabet of internal states and the initial vertex. The terminal character alphabet VT is mapped to the internal state code alphabet and an empty vertex. The operation S→e corresponds to the final vertex of the automaton. The grammar rules correspond to the transition function of the automaton S t+1 =  (S t , (Dj,Vj)). The presented grammar is right-sided. Let's model the operation of the automaton for a given input sequence x1,х2,х3. Information about state changes and output signals is presented in a table containing four rows: «Tacts», «Х», «S», «Y», where Хthe actual input sequence, S -the sequence of the automaton states, Y -the output sequence. The columns correspond to the tacts of automaton operation. Let's build a reaction of the automaton to the input effect «0-1-1», which is a change of resource states. Initial state of the automaton: Sн. The table of the automaton operation will look like this: Thus, during the operation of the automaton at each time interval Tr [T1; ТN] ( r=1,2,…,N) at times t1, t2, t3 output signals and internal states Sx1х2х3 are formed which capture the dynamics of changes in the state of resources, namely transitions between states S0 , S1 , S2 .
To assess the qualitative states of UMV resources, we will use three states: S0, S1, S2, which are defined above. For simplicity, we consider the case when the state of a UMV resource is characterized by a single parameter. The general algorithm for vulnerabilities detection using the dynamic assessment of the state of UMV resources based on the Markov model contains the following sequence of actions: • sets the vector of initial probabilities of resources being in states {S0, S1, S2}p(0) = {p(0)(0), p(0)(1), p(0)(2)}; • the state vector Si is played and the sequence Si,…. Sj,…Sl, is constructed, where i, j, l ϵ {0,1,2}; • the number of received pairs of the form Si,j, is calculated, where, Sij -the transition from the current Si state to the next Sj state; • state transition probabilities Pij are found; • the transition probability matrix Pij is constructed; • the above actions are repeated at the interval [TN+1;Т2N], dynamic changes in the state of UMV resources are checked when comparing two transition probability matrices based on the Kullback divergence estimation. The proposed algorithm is based on the use of nonparametric methods for estimating differences in the states of UMV resources. It is assumed that the state of UMV resources is observed first at one time interval -TN, and then at another time interval-T2N, where disturbances are introduced into the flow of simulated data [10] , which lead to an increase in the number of pre-critical and critical states and a decrease in the number of normal states. Figure 3 shows the display of a set of points with coordinates (µj,Mj) that are obtained at the time interval ТN и Т2N. As you can see in the figures, the location of points in the absence of attacks is in the «0» и «1» (figure 3(а)) while under external influence, the points are located in areas «1» и «2» ( figure 3(b)).  Changing the load state of UMV resources when exposed to attacks.