# Interdisciplinary Urban Tunnel Control within Smart Cities
## 2 Systemic Approach to Urban Road Tunnel
### Urban Tunnel Integrated Control  
Let us observe M parallel information variables (\(O_{1}\), \(O_{2}\),..., \(O_{\text{M}}\)) of a real system (city tunnel plus its surroundings). With respect to the system complexity, it is possible to identify \(j\)-th specialization that represents typically one of following areas: transportation, energy, environment, business, etc. Within \(j\)-th specialization (in our case one of the systems) the experts can find the set of L different scenarios \(\big{(}S_{j,1},S_{j,2}\),..., \(S_{j,L}\big{)}\). Scenarios \(\big{(}S_{j,1},S_{j,2}\),..., \(S_{j,L}\big{)}\) must be prepared beforehand. With the help of selected scenario \(S_{j,j}\), the control signals for each scenario are used to optimize the real system behavior.  
We suppose that there exists an inner \(N\)- knowledge vector (\(K_{1}\), \(K_{2}\),..., \(K_{N}\)) common for all specializations that best characterizes strong features of the real system of systems. All scenarios \(S_{j,i}\)(\(K_{1}\), \(K_{2}\),..., \(K_{N}\)) are supposed to be dependent on this knowledge vector. At the same time the quality assessment function \(Q_{i,j}\big{\{}S_{i,j}(K_{1}\), \(K_{2}\),..., \(K_{N})\big{\}}\) s assigned to each scenario \(S_{j,i}\)(\(K_{1}\), \(K_{2}\),..., \(K_{N}\)) is also dependent on this vector.  
The methodology of scenarios co-ordination can include the following 5 steps:  
1. Identification of knowledge base vector (\(K_{1}\), \(K_{2}\),..., \(K_{N}\)) from available data (\(O_{1}\), \(O_{2}\),... \(O_{M}\)). In transportation we can use strategic traffic detectors, in environmental areas selected climatic sensors, etc. The knowledge vector must be a low-dimensional one and all available data must be aggregated into it.
2. Selection of scenario \(S_{j,i}\)(\(K_{1}\), \(K_{2}\),..., \(K_{N}\)) in accordance with knowledge base (\(K_{1}\), \(K_{2}\),..., \(K_{N}\)). In transportation, for example, the best suited scenario is selected based on e.g., set of strategic detectors.
3. System control according to the selected scenario using real data. In transportation, for example, the selected scenario provides the traffic control of city tunnel based on measured traffic data. Appropriate control signals are distributed to variable signs. The scenarios are typically evaluated through micro/macro traffic simulations.
4. Quality assessment function depending on the selected \(i\)-th scenario in \(j\)-th specialization \(S_{j,i}\) (\(K_{1}\), \(K_{2}\),..., \(K_{N}\)). In transportation, for example, the normalized average travel time or the congestion length, etc. can be used as the control assessment function.
5. Cross-disciplinary \(i\)-th scenario selection for each \(j\)-th specialization to achieve the most appropriate (weighted) sum of quality assessment functions \(\sum\limits_{j,i}Q_{i,j}\big{\{}S_{ij,i}(K_{1},\ K_{2},\ldots,\ K_{N})\big{\}}\). The transportation scenario is selected, for example, to be as environmentally friendly as possible to take care of both transport and environment specializations.  
The above methodology describes the most general example parametrized by vector (\(K_{1}\), \(K_{2}\),..., \(K_{N}\)). In the real praxis we are not concerned about (\(j\), \(i\))-th scenario definition, the design of scenario's selection, data collection, transmission and processing (control system). The long term knowledge of each specialization has solved this problem and we can only register how many scenarios \(S_{j,i}\) exist in different areas such as transportation, energy supply, environmental protection and others [12].  
Further, we suppose that it is possible to determine the (normalized) assessment function \(Q_{j,i}\big{\{}S_{j,i}\big{\}}\) where (\(j\), \(i\))-th pair means the selected \(i\)-scenario for \(j\)-th specialization \(j\in\{1,2,\ldots\}\). If the problem has been linear we would have selected such (\(j\), \(i\))-th combination that simply maximizes the sum \(\sum\limits_{j}Q_{i,j}\big{\{}S_{j,i}\big{\}}\).