Control of input-affine nonlinear dynamical systems is investigated in this paper. In this regard, a system of linear inequalities (SLI) in the control inputs is developed, and it is proved that if this SLI has a solution at all times, applying it to the system leads to moving its state trajectories towards the desired point in space for all initial conditions. But, since it may happen that this SLI has infinitely many solutions or even no solution, the best (possibly, approximate) solution is obtained by solving a linear programming (LP) problem. Different LP problems with different properties and applications are proposed for this purpose. Formulation of the control problem as an LP makes it possible to take into account the effect of actuator saturation simply by adding bound constraints to the problem. We can also make the resulting control system robust to model uncertainties. Some numerical examples including the output voltage regulation of double-source DC-DC converter and robot path-planning, both by considering the effect of actuators saturation and taking into account the uncertainties in model, are also presented.

本文研究了输入仿射非线性动力系统的控制。在这方面，开发了控制输入中的线性不等式 (SLI) 系统，并证明如果该 SLI 始终有解决方案，则将其应用于系统会导致其状态轨迹向期望点移动所有初始条件的空间。但是，由于这个 SLI 可能有无限多个解或什至没有解，因此最好的（可能是近似的）解是通过求解线性规划 (LP) 问题来获得的。为此提出了具有不同性质和应用的不同 LP 问题。将控制问题表述为 LP 可以通过向问题添加边界约束来考虑执行器饱和的影响。我们还可以使最终的控制系统对模型不确定性具有鲁棒性。还给出了一些数值例子，包括双源 DC-DC 转换器的输出电压调节和机器人路径规划，既考虑了执行器饱和的影响，又考虑了模型的不确定性。