Browsing by Author "Martins, Nuno C."
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Item Design of optimal servomechanisms for Markovian jump linear systems (First Draft)(2007) Martins, Nuno C.In this paper we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview. In particular, given a reference sequence, we obtain the optimal control law for the fully observed case, while the output feedback case is also briefly discussed. We provide the optimal control law for the infinite and finite optimization-horizon cases. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term which is identical to the standard LQR solution. We provide explicit formulas for computing the feedforward term, while establishing a comparison with the internal model principle.Item Finite Gain l_p Stabilization Requires Analog Control(2005) Martins, Nuno C.; ISRA causal feedback map, taking sequences of measurements and producing sequences of controls, is denoted as finite-set if its range, for any arbitrary finite time interval, is a finite set. Bit-rate constrained or digital control are particular cases of finite-set feedback, where the range of the feedback map has an upper-bound on the rate of exponential growth. In this paper, we show that the finite gain (FG) l_p stabilization of a discrete-time, linear and time-invariant unstable plant is impossible by finite-set feedback. In addition, we show that, under finite-set feedback, weaker (local) versions of FG l_p stability are also impossible. These facts are not obvious, since recent results have shown that input to state stabilization (ISS) is viable by bit-rate constrained control. In view of such existing work, this paper has two conclusions: (1) in spite of ISS stability being attainable under finite-set feedback, small changes in the amplitude of the external excitation may cause, in relative terms, a large increase in the amplitude of the state (2) FG l_p stabilization requires logarithmic precision around zero. Since our conclusions hold with no assumption on the feedback structure, they cannot be derived from existing results. We adopt an information theoretic viewpoint, which also brings new insights into the problem of stabilization.Item Jointly optimal power allocation and constrained node placement in wireless networks of agents(2008-07) Firouzabadi, Sina; Martins, Nuno C.In this paper, we investigate the optimal design of wireless networks. We consider wireless networks that have fixed and movable nodes, and we assume that all nodes feature adjustable transmission power. Hence, we aim at maximizing network centric objectives, by optimizing over admissible choices of the positions of the movable nodes as well as the transmission power at all the nodes. We adopt exponential path loss, which is a realistic assumption in urban and sub sea environments, and we propose ways of using this assumption to obtain a tractable optimization problem. Our formulation allows for the optimization of typical network centric objectives, such as power and throughput. It also allows signal-to-interference based constraints, such as rate-regions and outage probabilities, under the high signal to interference regime. We show that our optimization paradigm is convex and that it can be solved up to an arbitrary degree of accuracy via geometric programming techniques. By using a primal-dual decomposition, we also provide a case-study that illustrates how certain instances of our optimization paradigm can be solved via distributed iterative algorithms. We show that such a solution method also leads to a convenient layering in the primal step, whereby the power allocation and the node placement become two independent sub-problems.Item Optimal Output Feedback Control Using Two Remote Sensors over Erasure Channels(2007) Gupta, Vijay; Martins, Nuno C.; Baras, John S.; Martins, Nuno C.; ISR