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Guo X.,Sun Yat Sen University | Hernandez-del-Valle A.,SEPI | Hernandez-Lerma O.,CINVESTAV
European Journal of Control | Year: 2012

This paper concerns first passage problems for nonstationary nonlinear discrete-time stochastic control systems. The state and control spaces are general Borel spaces, the transition probabilities are nonstationary, the costs/rewards are time-varying and may be unbounded. The optimal control problem is to minimize the expected discounted costs incurred until the first passage time to some target set, in which the discount factors are allowed to be both time- and state-dependent. Under reasonably mild conditions we establish the so-called first passage optimality equations, and prove that the optimal cost/reward functions satisfy the optimality equations. Furthermore, from the optimality equations we show the existence of optimal Markov policies. © 2012 EUCA.

Bejarano F.J.,SEPI
Systems and Control Letters | Year: 2015

Observability and detectability conditions are obtained for a sort of linear time invariant systems affected by unknown inputs. It is assumed that the system can be described using matrices whose elements are within a principal ideal domain (PID). It is shown that, under suitable hypothesis, the obtained conditions are necessary and sufficient. The analysis is carried out by making use of the Smith normal form of matrices over a PID. The obtained conditions are a generalization of known conditions for particular sorts of systems which are included in those considered here. © 2015 Elsevier B.V. All rights reserved.

Bejarano F.J.,SEPI | Perruquetti W.,French Institute for Research in Computer Science and Automation | Floquet T.,French Institute for Research in Computer Science and Automation | Zheng G.,French Institute for Research in Computer Science and Automation
IEEE Transactions on Automatic Control | Year: 2015

A method to carry out the state estimation is proposed for a class of nonlinear systems with unknown inputs whose dynamics is governed by differential-algebraic equations (DAE). We achieve, under suitable conditions, to replace the original DAE for a system with differential equations only by using a zeroing manifold algorithm inducing a state space dimension reduction. Observability conditions can be checked using the original system parameters. The state estimation is done using a sliding mode high order differentiator. © 1963-2012 IEEE.

Bejarano F.J.,SEPI | Zheng G.,French Institute for Research in Computer Science and Automation
Automatica | Year: 2014

This paper investigates the observability analysis for linear time systems whose outputs are affected by unknown inputs. Three different definitions of observability are proposed. By introducing the Smith form and comparing the invariant factors, a sufficient condition is deduced for each proposed observability definition. Three examples are given for the purpose of highlighting the effectiveness of the proposed approach.

Bejarano F.J.,SEPI | Zheng G.,French Institute for Research in Computer Science and Automation
Systems and Control Letters | Year: 2016

In this manuscript we give sufficient conditions guaranteeing the observability of singular linear systems with commensurable delays affected by unknown inputs appearing in both the state equation and the output equation. These conditions allow for the reconstruction of the entire state vector using past and actual values of the system output. The obtained conditions coincide with known necessary and sufficient conditions of singular linear systems without delays. © 2015 Elsevier B.V. All rights reserved.

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