Using local reachability sets in guiding mobile actuator and its orbiting sensors to approximate state feedback kernels in output control of PDEs

This paper considers a class of distributed parameter systems that can be controlled by an actuator onboard a mobile platform. In order to avoid computational costs and control architecture complexity associated with a joint optimization of actuator guidance and control law, a suboptimal policy is proposed that significantly reduces the computational costs. By utilizing a continuous-discrete optimal control design, a mobile actuator moves to a new position at the beginning of a new time interval and resides for a prescribed time. Using the cost to go with variable lower limit, the optimization simplifies to solving algebraic Riccati equations instead of differential Riccati equations. Adding a hardware feature whereby the mobile sensors are constrained to stay within the proximity of the mobile actuator, a feedback kernel decomposition scheme is proposed to approximate a full state feedback controller by the weighted sum of sensor measurements.