18.086 Project Report: A linear programming approach for dynamic system control with inequality constraints

The presence of inequality constraint on the state variables and control effort is a distinctive feature of many practical control problems. In control of mechanical servo systems, the limitation of the control effort may comes from the physical limitation as the actuator’s maximum ability, and the limitation of state variables may comes from the control objectives. For example, when controlling the motion of a machine tool, the position accuracy of the tool should be limited in certain range to avoid damage the part being cutting. Another example will be when a robot manipulating, the robot arm should be remained in certain range to avoid collision. Further more, these constraints can change with time in an unpredictable manner due to the change of the environment, equipment availability, or a shift in control objectives. Thus control in the presence of constraints is important and interesting from a practical point of view. Linear programming (LP) has proved to be a powerful method to solve optimal control problems for linear systems with linear equality and inequality constraints. Significant attention has been paid to the classical time-optimal and energy-consumption-optimal problems. [1] have proposed resolving the time-optimal control problem on-line at each sample instant to generate a feedback control strategy. [2] gives a comprehensive introduction on the linear programming applying on optimal control. In this project, a feedback control strategy is presented for multi-variable control problem with inequality constraints on the states and input control variables. At each sample instant, a linear programming problem is solved in real-time to determine the optimal value of the control input with minimize a linear performance index while satisfying the inequality constraints. The potential advantages of this linear programming based control strategy are: