AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Robust model predictive controller with output feedback and target tracking

A model predictive controller (MPC) is proposed, which is robustly stable for some classes of model uncertainty and to unknown disturbances. It is considered as the case of open-loop stable systems, where only the inputs and controlled outputs are measured. It is assumed that the controller will work in a scenario where target tracking is also required. Here, it is extended to the nominal infinite horizon MPC with output feedback. The method considers an extended cost function that can be made globally convergent for any finite input horizon considered for the uncertain system. The method is based on the explicit inclusion of cost contracting constraints in the control problem. The controller considers the output feedback case through a non-minimal state-space model that is built using past output measurements and past input increments. The application of the robust output feedback MPC is illustrated through the simulation of a low-order multivariable system.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the Output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input-output, state variable feedback pole assignment, International journal of Control 46 (1987) 1867-1881; C. Wang, P.C. Young, Direct digital control by input-output, state variable feedback: theoretical background, International journal of Control 47 (1988) 97-109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states. (C) 2008 Elsevier Ltd. All rights reserved.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Dynamic positioning systems: An experimental analysis of sliding mode control

Vessel dynamic positioning (DP) systems are based on conventional PID-type controllers and an extended Kalman filter. However, they present a difficult tuning procedure, and the closed-loop performance varies with environmental or loading conditions since the dynamics of the vessel are eminently nonlinear. Gain scheduling is normally used to address the nonlinearity of the system. To overcome these problems, a sliding mode control was evaluated. This controller is robust to variations in environmental and loading conditions, it maintains performance and stability for a large range of conditions, and presents an easy tuning methodology. The performance of the controller was evaluated numerically and experimentally in order to address its effectiveness. The results are compared with those obtained from conventional PID controller. (c) 2010 Elsevier Ltd. All rights reserved.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

Quantum control and quantum entanglement

We discuss quantum error correction for errors that occur at random times as described by, a conditional Poisson process. We shoo, how a class of such errors, detected spontaneous emission, can be corrected by continuous closed loop, feedback.

Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

Integrated control of nitrate recirculation and external carbon addition in a predenitrification system

The integrated control of nitrate recirculation and external carbon addition in a predenitrification biological wastewater treatment system is studied. The proposed control structure consists of four feedback control loops, which manipulate the nitrate recirculation and the carbon dosage flows in a highly coordinated manner such that the consumption of external carbon is minimised while the nitrate discharge limits (based on both grab and composite samples) are met. The control system requires the measurement of the nitrate concentrations at the end of both the anoxic and the aerobic zones. Distinct from ordinary control systems, which typically minimise the variation in the controlled variables, the proposed control system essentially maximises the diurnal variation of the effluent nitrate concentration and through this maximises the use of influent COD for denitrification, thus minimising the requirement for external carbon source. Simulation studies using a commonly accepted simulation benchmark show that the controlled system consistently achieves the designated effluent quality with minimum costs.

RFID together with multi-agent systems to control global value chains

Nowadays, the cooperative intelligent transport systems are part of a largest system. Transportations are modal operations integrated in logistics and, logistics is the main process of the supply chain management. The supply chain strategic management as a simultaneous local and global value chain is a collaborative/cooperative organization of stakeholders, many times in co-opetition, to perform a service to the customers respecting the time, place, price and quality levels. The transportation, like other logistics operations must add value, which is achieved in this case through compression lead times and order fulfillments. The complex supplier's network and the distribution channels must be efficient and the integral visibility (monitoring and tracing) of supply chain is a significant source of competitive advantage. Nowadays, the competition is not discussed between companies but among supply chains. This paper aims to evidence the current and emerging manufacturing and logistics system challenges as a new field of opportunities for the automation and control systems research community. Furthermore, the paper forecasts the use of radio frequency identification (RFID) technologies integrated into an information and communication technologies (ICT) framework based on distributed artificial intelligence (DAI) supported by a multi-agent system (MAS), as the most value advantage of supply chain management (SCM) in a cooperative intelligent logistics systems. Logistical platforms (production or distribution) as nodes of added value of supplying and distribution networks are proposed as critical points of the visibility of the inventory, where these technological needs are more evident.

Robot Manipulator Systems: Analysis and Control

Manipulator systems are rather complex and highly nonlinear which makes difficult their analysis and control. Classic system theory is veil known, however it is inadequate in the presence of strong nonlinear dynamics. Nonlinear controllers produce good results [1] and work has been done e. g. relating the manipulator nonlinear dynamics with frequency response [2–5]. Nevertheless, given the complexity of the problem, systematic methods which permit to draw conclusions about stability, imperfect modelling effects, compensation requirements, etc. are still lacking. In section 2 we start by analysing the variation of the poles and zeros of the descriptive transfer functions of a robot manipulator in order to motivate the development of more robust (and computationally efficient) control algorithms. Based on this analysis a new multirate controller which is an improvement of the well known “computed torque controller” [6] is announced in section 3. Some research in this area was done by Neuman [7,8] showing tbat better robustness is possible if the basic controller structure is modified. The present study stems from those ideas, and attempts to give a systematic treatment, which results in easy to use standard engineering tools. Finally, in section 4 conclusions are presented.

An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method