Optimization Algorithms for Predictive Control Approach to Networked Bilinear Systems
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摘要: 本文对一类离散时间双线性系统进行网络化预测控制研究.针对控制系统网络信道传输引起的前向通道和反馈通道时延问题，基于双线性系统结构特性提出2种逐步优化算法对非凸优化问题进行求解，进而得到未来时刻的预测控制序列.仿真实例说明所求预测控制序列可以主动补偿网络引起的时延问题，从而说明所提出预测控制算法的有效性.Abstract: This paper is concerned with the networked predictive control of discrete-time bilinear systems. To deal with the network-induced communication delay that exists in both forward channel (controller to actuator) and feedback channel (sensor to controller), a bilinear networked predictive control scheme is proposed. Then a non-convex optimization problem of solving the predictive control sequence is presented, for which two gradually-optimized algorithms are proposed based on the special structure of bilinear system dynamics model. The numerical simulation indicates that the resulting predictive control sequence can compensate for the network-induced issues actively, which proves the effectiveness of the proposed predictive control strategy.
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Key words:
- Bilinear systems /
- networked control systems (NCSs) /
- non-convex optimization /
- predictive control
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Table 1
Algorithm 1 Stepwise iterative algorithm Step 1. Given an initial predictive control sequence $\overline{U}_0$ and a threshold $\lambda$. Step 2. Calculate $J_{\rm old}(k)$ by using $\overline{U}_0$. Step 3. Determine the communication delay $k_t$ in the feedback channel. For the forward communication delay $i=0, 1, \ldots, \overline{M}$: Step 3.1 Calculate $K_i$ according to (12); Step 3.2 Calculate $V_i$ according to (13); Step 3.3 Calculate $u^{\star}_{t+i|t-k_t}$ according to (15). Step 4. Calculate $J_{\rm new}(k)$ by using the obtained $\overline{U}^{\star}_{t+\overline{M}}$. Step 5. If $[J_{\rm old}(k)-J_{\rm new}(k)]/J_{\rm old}(k)>\lambda$, let $J_{\rm old}(k)=J_{\rm new}(k), $ $\overline{U}_0=\overline{U}^{\star}_{t+\overline{M}}$, and go to Step 3; Otherwise, stop iterating and let $\overline{U}^{\star}_{t+\overline{M}}$ as the final optimal predictive control sequence. 
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Table 2
Algorithm 2 Approximate forward stagewise algorithm Step 1. Calculate $u^{\star}_{t|t-k_t}$ according to Remark 8 for the case of no delay in the forward channel. Step 2. For the forward communication delay $i_t=1, 2, \ldots, \overline{M}$: Step 2.1 Add $\hat{x}^T_{t+i_t+1|t-k_t}$ into state vector $\overline{X}$; Step 2.2 Add $u_{t+i_t|t-k_t}$ into input vector $\overline{U}$; Step 2.3 Extend matrixes $Q_{k_t, 0}$ and $R_{k_t, 0}$ to the corresponding dimensions; Step 2.4 Calculate $\overline{K}_{i_t}$ and $\overline{V}_{i_t}$ according to (17) and (18); Step 2.5 Obtain $\overline{U}^{\star}_{k_t, i_t}$ according to (20). Step 3. Take $\overline{U}^{\star}_{\overline{N}, \overline{M}}$ as the final predictive control sequence and send it to the actuator via the forward channel.
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