## 5 Active Coating and its Control Algorithm
### The Scattering Suppression System and Algorithm
#### 6.2.1 Targeting of One Incident Wave  
The first incident wave (with number \(i=1\)) forms its bearing group, which consists of the four microphones (Figure 11a). These microphones differ from each other by their participation in the following events:  
**1. ** First contact between the front of an incident wave with any microphone on \(S_{p}\) means, that at this moment \(t=\widetilde{t}(1,0)\) (first for \(\forall t\leq\widetilde{t}(1,0)\)) on the microphone \(\bigstar\) with number \(m=\widetilde{m}(1,0)\) at the point \(\mathbf{r}=\mathbf{R}_{\widetilde{m}(1,0)}\) the modulus \(\left|\overline{Q}\Xi_{1}[t-(\mathbf{r},\mathbf{w}_{1})\mathcal{c}_{w}^{-1}]\right|\) of the acoustical pressure \(P_{\widetilde{m}(1,0)}(t)\) of a first incident wave had crossed (from the bottom to the top) the threshold level \(P_{\bullet}\) of fixation, which satisfies the condition:  
\[\sigma_{P}<<P_{\bullet}<<\left|\Xi_{i}\right|_{\max}. \tag{19}\]  
**2. ** 2-nd contact between front of an incident wave with any (another) microphone on \(S_{p}\) means, that at this moment \(t=\widetilde{t}(1,1)\) (first for \(\forall t\leq\widetilde{t}(1,1)\)) on the microphone \(\bigstar\) with number \(m=\widetilde{m}(1,1)\) at the point \(\mathbf{r}=\mathbf{R}_{\widetilde{m}(1,1)}\) the modulus \(\left|\overline{Q}\Xi_{1}[t-(\mathbf{r},\mathbf{w}_{1})\mathcal{c}_{w}^{-1}]\right|\) of the acoustical pressure \(P_{\widetilde{m}(1,1)}(t)\) of a first incident wave had crossed (from the bottom to the top) the threshold level \(P_{\bullet}\) of fixation. **3. ** 3-rd contact between front of an incident wave with any (another) microphone on \(S_{p}\) means, that at this moment \(t=\widetilde{t}(1,2)\) (firstly for \(\forall t\leq\widetilde{t}(1,2)\)) on the microphone \(\bigstar\) with number \(m=\widetilde{m}(1,2)\) at the point \(\mathbf{r}=\mathbf{R}_{\widetilde{m}(1,2)}\) the modulus \(\left|\overline{Q}\Xi_{1}[t-(\mathbf{r},\mathbf{w}_{1})\mathcal{c}_{w}^{-1}]\right|\) of acoustical pressure \(P_{\widetilde{m}(1,2)}(t)\) of a first incident wave had crossed (from the bottom to the top) with the threshold level \(P_{\bullet}\) of fixation. _Algorithms_**2009**_, 2_  
**Figure 11.** Targeting of one (a) and three (b) incident waves. Incident wave (a) forms the bearing group of microphones (one title \(\bigstar\) microphone and three benchmark \(\bigstar\) ones) on the surface \(S_{p}\) to match with the surface \(S_{l^{\prime}}\) of a protected body, covered by an active coating with pistons \(\overline{S}_{k}\). Three incident waves (b), arriving from different directions \(\mathbf{w}_{1}\), \(\mathbf{w}_{2}\), \(\mathbf{w}_{3}\) create three nonintersecting bearing groups. **4. ** 4-th contact between front of incident wave with any (another) microphone on \(S_{p}\) means, that at this moment \(t=\widetilde{t}(13)\) (firstly for \(\forall t\leq\widetilde{t}(13)\)) on the microphone \(\bigstar\) with number \(m=\widetilde{m}(13)\) in the point \(\mathbf{r}=\mathbf{R}_{\widetilde{m}(1,3)}\) the modulus \(\left|\overline{Q}\Xi_{\mathbf{i}}[t-(\mathbf{r},\mathbf{w}_{1})c_{w}^{-1}]\right.\) of acoustical pressure \(P_{\widetilde{m}(1,3)}(t)\) of a first incident wave had crossed (from the bottom to the top) with the threshold level \(P_{\bullet}\) of fixation. The microphone \(\bigstar\) in the point \(\mathbf{R}_{\widetilde{m}(1,0)}\) we'll call the _title_ microphone with pressure signal \(P_{\widetilde{m}(1,0)}(t)\) and other microphones \(\bigstar\) in the points \(\mathbf{R}_{\widetilde{m}(1,1)}\), \(\mathbf{R}_{\widetilde{m}(1,1)}\), \(\mathbf{R}_{\widetilde{m}(1,3)}\) we'll call _benchmark_ microphones with pressure signals \(P_{\widetilde{m}(1,1)}(t)\), \(P_{\widetilde{m}(1,2)}(t)\), \(P_{\widetilde{m}(1,3)}\) respectively.