Giuseppe Franzè

An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems

An off-line Model Predictive Control (MPC) method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances. In order to reduce the computational burdens and conservativeness of traditional polytopic MPC schemes, the present approach carries out off-line most of the computations and it makes use of closed-loop predictions to improve the control performance. This is done by recursively pre-computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on-line a simple and numerically low-demanding optimization problem subject to a set-membership constraint. Comparisons with three other recent off-line MPC approaches are also provided in the final example.

A feedback min-max MPC algorithm for LPV systems subject to bounded rates of change of parameters

A novel closed-loop model-based predictive control (MPC) strategy for input-saturated polytopic linear parameter varying (LPV) discrete-time systems is proposed. It is postulated that the plant belongs to a polytopic family of linear systems, each member of which being parameterized by the value that a parameter vector assumes in the unit simplex. Such a parameter can be measured online and used for feedback while a bound on its rate of change is known and exploited for predictions. The paper extends the MPC scheme presented by Lu et al. (2000) for the restricting case of 1-step long control horizons to the general case of control horizons of arbitrary length N. This is done by suitably modifying the robust MPC scheme presented by Casavola et al. (2000) for uncertain polytopic systems. The feasibility and closed-loop stability of this strategy are proved and a numerical example is also presented in order to show how the freedom of extending the control horizon and knowledge of the parameter is significant in order to improve the performance of the control strategy.

Robust constrained predictive control of uncertain norm-bounded linear systems

A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N. The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported.

Technical communique: Robust fault detection of uncertain linear systems via quasi-LMIs

Optimal H/sub /spl infin// deconvolution filters robust fault detection of uncertain polytopic linear systems subject to unknown input disturbance are described. The filter must be capable to satisfy two sets of H/sub /spl infin// constraints: the first is a disturbance attenuation and decoupling requirement whereas the second expresses the capability of the filter to enhance the fault signals. By means of the projection lemma and congruence transformations, a quasiconvex formulation of the problem is obtained via LMIs. The effectiveness of the design technique is illustrated via a numerical example.

Supervision of networked dynamical systems under coordination constraints

In this paper, we present a discrete-time predictive control strategy for the supervision of networked dynamic systems subject to coordination constraints. Such a network paradigm is characterized by a set of spatially distributed systems, possibly dynamically coupled and connected via communication links, which need to be controlled and coordinated in order to accomplish their overall objective. The network latency is modeled abstractly as a time-varying time-delay, which is allowed to become unbounded for taking into account data-loss. The method can be specialized to deal more efficiently either with random, possibly unbounded, time-delays, such as the case over the Internet, or constant/bounded time-delays, typically encountered in space and underwater applications. An example of coordination of two autonomous vehicles under input-saturation and formation accuracy constraints is presented.

Model predictive control for constrained networked systems subject to data losses

The paper addresses the stabilization problem for constrained control systems where both plant measurements and command signals in the loop are sent through communication channels subject to time-varying delays and data losses. A novel receding horizon strategy is proposed by resorting to an uncertain polytopic linear plant framework. Sequences of pre-computed inner approximations of the one-step controllable sets are on-line exploited as target sets for selecting the commands to be applied to the plant in a receding horizon fashion. The communication channel effects are taken into account by resorting to both Independent-of-Delay and Delay-Dependent stability concepts that are used to initialize the one-step controllable sequences. The resulting framework guarantees Uniformly Ultimate Boundedness and constraints fulfilment of the regulated trajectory regardless of plant uncertainties and data loss occurrences.

A fast ellipsoidal MPC scheme for discrete-time polytopic linear parameter varying systems

This paper proposes a fast ellipsoidal Model Predictive Control (MPC) strategy to address feedback regulation problems for constrained polytopic Linear Parameter Varying (LPV) systems subject to bounded disturbances. In order to deal with the specific non-convex structure of the state prediction tubes arising in LPV contexts, a new convexification procedure is proposed and, based on the off-line computation of a sequence of inner ellipsoidal approximations of exact one-step controllable sets, a computationally low-demanding MPC algorithm is presented. Comparisons with state-of-the-art MPC control algorithms for LPV systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction, control performance, numerical burdens and memory requirements.

An improved predictive control strategy for polytopic LPV linear systems

This paper presents a new dilated LMI approach to constrained MPC for LPV discrete-time systems. The main idea exploited in the proposed algorithm consists of using both the dilation argument and the direct measure of the LMI parameter at each time step. The effectiveness of the technique is compared to preexisting techniques by means of a numerical example

Fault-tolerance as a key requirement for the control of modern systems

Abstract Networks of Embedded Systems are becoming ubiquitous today. The performance of these networks is measured in terms of the Quality of Service (QoS) delivered. This has been taken on board by the Computer Scientists, who have developed concepts like “Ubiquitous” and “Pervasive” Computing. In the world of Control, there has always been an “implicit” QoS, in that the quality or level of performance has been measured using a cost function, often the error between the reference signals and the system outputs. However, such “point-to-point” notions of QoS are fast becoming redundant in the networked, information-rich world. This paper outlines a new way of formulating the Control problem which is suitable for the networked world, enabling Fault Tolerance to become a natural consequence to ensure that the system performance is maintained under all eventualities. Thus Control has to become more ubiquitous, pervasive, and intelligent. To facilitate this outcome, this paper proposes a new research direction which could be termed “Embedded Cognitive Control”, bringing together the various fields of Cognitive Science, Embedded Systems, and Control.

A robust fault detection filter for polynomial nonlinear systems via sum-of-squares decompositions

Abstract A novel diagnostic framework is discussed for fault detection of nonlinear systems whose structure is described by multivariate polynomials. The trade-off between disturbance rejection and fault sensitivity prescriptions is characterized via algebraic geometry conditions and the unknown input observer design problem is formulated via sum-of-squares (SOS) technicalities by exploiting the results of the Positivstellensatz Theorem. An adaptive threshold logic is proposed to reduce the generation of false alarms, and the diagnostic filter capabilities are illustrated via a numerical example taken from the literature.