Strong structural controllability and the multi-link inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

Strong structural controllability and the multilink inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Energy-efficient multihop cooperative MISO transmission with optimal hop distance in wireless ad hoc networks

In this paper, we investigate the hop distance optimization problem in ad hoc networks where cooperative multiinput- single-output (MISO) is adopted to improve the energy efficiency of the network. We first establish the energy model of multihop cooperative MISO transmission. Based on the model, the energy consumption per bit of the network with high node density is minimized numerically by finding an optimal hop distance, and, to get the global minimum energy consumption, both hop distance and the number of cooperating nodes around each relay node for multihop transmission are jointly optimized. We also compare the performance between multihop cooperative MISO transmission and single-input-single-output (SISO) transmission, under the same network condition (high node density). We show that cooperative MISO transmission could be energyinefficient compared with SISO transmission when the path-loss exponent becomes high. We then extend our investigation to the networks with varied node densities and show the effectiveness of the joint optimization method in this scenario using simulation results. It is shown that the optimal results depend on network conditions such as node density and path-loss exponent, and the simulation results are closely matched to those obtained using the numerical models for high node density cases.