## 1 Introduction
(2) Searching for a strategy with insufficient reference, agents encountering communication breaks will obtain sensing data and obtain reference expectedly. In this paper, information processing is introduced for the nonlinear maneuvers [2; 11]. Through the coordinate's transformation, virtual reference information including velocity and acceleration are estimated. Then, a nonlinear controller is proposed with the Lyapunov method and the CA algorithm. Given the input saturation, parameters tuning principles of the controller are established based on the Lyapunov method. As for communication breaks, a sensing graph is introduced, and the requirements of the sensing graph are given in terms of various situations. Then, the Laplacian matrix is computed, and the interference resistance ability of agents can be enhanced with the Laplacian matrices of the communication graph. Considering the bearing information only [1], a nonlinear dynamic programming regulator for positions estimation is proposed. Finally, three tests are carried out and the proposed law is proved stable and feasible. The contributions of this paper are listed below. 1. A definite bounded control law is proposed for anti-saturation control. The nonlinearity caused by maneuvers is considered compared with [24], then a controller with nonlinear parameters is proposed in this paper. Those parameters are designed as functions of states, and the values space of critical parameters is analyzed subsequently. Differing from the use of auxiliary variables in previous literature, parameters of reference are altered adaptively according to the value of inputs, which will be more applicable and easier to be realized. 2. A nonlinear dynamic programming regulator is proposed for reference with bearings only for some agents encountering breaks. Instead of expected locations change for all agents, we expect to change the expected locations of agents encountering saturation only for sensing measurements. Thus, most parts of the formation won't be altered if they are not expected to be changed. The remaining sections are organized as follows. Section 2 describes the problems, and a robust controller is proposed in Section 3. Then, Section 4 uses three tests to verify the proposed strategy. The conclusion is given in Section 5. **Notation:** we use \(\mathbb{R}^{r\times c}\) to indicate the matrix space of which the matrix has \(r\) rows and \(c\) columns. \(\mathbb{R}^{n}\) denotes the \(n\)-dimensional vector space. \([*]^{r}_{r}\) represents the stacked matrix concatenated with elements indicated in the bracket, and \([*]^{r}_{r}\in\mathbb{R}^{r\times c}\). \(D_{1}(*)\) indicates the first-time derivative, and \(D_{2}(*)\) indicates the second-time derivative. \(\text{rank}(*)\) represents the rank of the matrix in the bracket. The matrix operator \(\circ\) denotes the Hadamard product and \(\otimes\) indicates the Kronecker product operator. \(\left\|*\right\|_{2}\) indicates the L2 norm form of the vector, and \(\left\|\mathbf{x}\right\|_{\mathbf{M}}=\mathbf{x}^{\text{T}}\mathbf{M}\mathbf{x}\) represents the \(\mathbf{M}\) norm form of the vector, where \(\mathbf{M}\) denotes the symmetric positive definite matrix. \(\mathbf{\Lambda}_{L}(*)\) indicates the diagonal matrix with size \((L*d_{1})\times(L*d_{2})\), where \((d_{1},d_{2})\) is the dimension of the diagonal element in the bracket.