Optimal Control of Self-Powered Systems Using Primal-Dual Techniques
Friday, August 30, 2019|
10:00am - 12:00pm
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About the Event
Abstract: Vibration-based self-powered systems are electromechanical technologies that are mechanically coupled to vibratory phenomena, and have the capability to convert this mechanical energy into electrical energy to power their operations. The functionality of these systems is constrained due to the limited availability of the vibratory energy resource, and also due to the finite bounds of its on-board energy storage subsystem. We consider the general problem of control design for vibration-based self-powered systems in the context of discrete-time optimal control theory, and realize the optimal control solution in real-time using Model Predictive Control (MPC). The optimal control problem is, in general, a nonconvex quadratically constrained quadratic program. We formulate the (convex) dual relaxation, and illustrate that if a certain easy-to-check condition holds for the obtained dual optimum, then there is no duality gap, and consequently the dual and primal optima are coincident. In this situation, it follows that this duality technique can be used as a convex means of solving the primal (nonconvex) optimal control problem exactly. However, if there is a nonzero duality gap, the resulting trajectory does not satisfy the constraints of the original optimal control problem. In this case, we introduce an algorithm to guarantee that the first time-step of the trajectory is feasible and can be implemented in real-time via MPC.
Sponsor(s): Professor Jeff Scruggs
Open to: Public