Minimum energy control

Abstract: Feedback controls based on the receding horizon method have proven to be a useful and easy tool in stabilizing linear ordinary differential systems. In this paper the receding horizon method is applied to linear systems with delay in the control. An open-loop optimal control which minimizes control energy subject to certain side constraints is first derived and then transformed to a closed-loop control via the receding horizon concept. The resulting feedback system is shown to be asymptotically stable under a complete controllability condition. It is also shown how the receding horizon control suggests a more general class of stabilizing feedback control laws. The control laws of this paper are perhaps the easiest way to stabilize a linear system with delay in the control.

Abstract: 1. Introduction.- 2. Liapunov's direct method.- 3. Linear systems x' = Ax..- 4. An algorithm for computing An..- 5. A characterization of stable matrices. Computational criteria..- 6. Liapunov's characterization of stable matrices. A Liapunov function for x' = Ax..- 7. Stability by the linear approximation..- 8. The general solution of x' = Ax. The Jordan Canonical Form..- 9. Higher order equations. The general solution of ?(z)y = 0..- 10. Companion matrices. The equivalence of x' = Ax and ?(z)y = 0..- 11. Another algorithm for computing An..- 12. Nonhomogeneous linear systems x' = Ax + f(n). Variation of parameters and undetermined coefficients..- 13. Forced oscillations..- 14. Systems of higher order equations P(z)y = 0. The equivalence of polynomial matrices..- 15. The control of linear systems. Controllability..- 16. Stabilization by linear feedback. Pole assignment..- 17. Minimum energy control. Minimal time-energy feedback control..- 18. Observability. Observers. State estimation. Stabilization by dynamic feedback..- References.

Abstract: Broadcasting is a method that allows the distributed nodes in a wireless sensor network to share its data efficiently among each other. Due to the limited energy supplies of a sensor node, energy efficiency has become a crucial issue in the design of broadcasting protocols. In this paper, we analyze the energy savings provided by a cooperative form of broadcast, called the opportunistic large arrays (OLA), and compare it to the performance of conventional multi-hop networks where no cooperation is utilized for transmission. The cooperation in OLA allows the receivers to utilize for detection the accumulation of signal energy provided by the transmitters that are relaying the same symbol. In this work, we derive the optimal energy allocation policy that minimizes the total energy cost of the OLA network subject to the SNR (or BER) requirements at all receivers. Even though the cooperative broadcast protocol provides significant energy savings, we prove that the optimum energy assignment for cooperative networks is an NP-complete problem and, thus, requires high computational complexity in general. We then introduce several suboptimal yet scalable solutions and show the significant energy-savings that one can obtain even with the approximate solutions

Abstract: Energy awareness is a crucial component in the design of wireless sensor networks at all layers. This paper looks into efficient energy utilization of a target-tracking sensor network by predicting a target's trajectory through experience. While this is not new, the chief novelty comes in conserving energy through both dynamic spatial and temporal management of sensors while assuming minimal locality information. We adapted our target trajectory model from the Gauss-Markov mobility model, formulated the tracking problem as a hierarchical Markov decision process (HMDP), and solved it through neurodynamic programming. Our HMDP for target-tracking (HMTT) algorithm conserves energy by reducing the rate of sensing (temporal management) but maintains an acceptable tracking accuracy through trajectory prediction (spatial management) of multiple targets. We derived some theoretical bounds on accuracy and energy utilization of HMTT. Simulation results demonstrated the effectiveness of HMTT in energy conservation and tracking accuracy against two other predictive tracking algorithms, with accuracy of up to 47% higher and energy savings of up to 200%