Design of observers and certainty equivalence controllers for differential inclusions: a passivity approach

This paper deals with the design of state observers for a class of systems with set-valued right-hand-sides. Two main classes of set-valued mappings are considered: maximal monotone and time-invariant; or normal cones to possibly time-varying sets (not necessarily convex). Such controlled systems can be embedded in various kinds of differential inclusions with absolutely continuous and bounded variation solutions (inclusions with maximal monotone multivalued mappings, and the perturbed Moreau's sweeping process), using a suitable state space transformation. The well-posedness properties of the observers dynamics are carefully analyzed. The stability of the observation error is proved. Then the problem of stabilization with a feedback control using the estimated state is studied in a particular case. Most of the results rely on rendering some suitable operator dissipative (or SPR in the linear case)

Design of observers and certainty equivalence controllers for differential inclusions: a passivity approach

This paper deals with the design of state observers for a class of systems with set-valued right-hand-sides. Two main classes of set-valued mappings are considered: maximal monotone and time-invariant; or normal cones to possibly time-varying sets (not necessarily convex). Such controlled systems can be embedded in various kinds of differential inclusions with absolutely continuous and bounded variation solutions (inclusions with maximal monotone multivalued mappings, and the perturbed Moreau's sweeping process), using a suitable state space transformation. The well-posedness properties of the observers dynamics are carefully analyzed. The stability of the observation error is proved. Then the problem of stabilization with a feedback control using the estimated state is studied in a particular case. Most of the results rely on rendering some suitable operator dissipative (or SPR in the linear case)

Observer design for dissipative multivalued dynamical systems

research work on observer design for nonsmooth dynamical systems, and separation principle.This paper deals with the design of state observers for a class of systems with set-valued right-hand-sides. Two main classes of set-valued mappings are considered: maximal monotone and time-invariant; or normal cones to possibly time-varying sets (not necessarily convex). Such controlled systems can be embedded in various kinds of differential inclusions with absolutely continuous and bounded variation solutions (inclusions with maximal monotone multivalued mappings, and the perturbed Moreau's sweeping process), using a suitable state space transformation. The well-posedness properties of the observers dynamics are carefully analyzed. The stability of the observation error is proved. Then the problem of stabilization with a feedback control using the estimated state is studied in a particular case. Most of the results rely on rendering some suitable operator dissipative (or SPR in the linear case)

An ℓ2-consistent event-triggered control policy for linear systems

In this article, we consider the design of an event-triggered ℓ2-control policy, for a setting where a scheduler is arbitrating state transmissions from the sensors to the controller of a discrete-time linear system. We start by introducing a periodic time-triggered ℓ2-controller for different transmission time-periods with a given ℓ2-gain bound using the minimax game-theoretical approach. After that, we propose an ℓ2-consistent event-triggered controller in the sense that it guarantees at least the same ℓ2-gain bound as the designed periodic time-triggered ℓ2-controller, however with a larger, or at most equal, average inter-transmission time. In practice, for typical disturbances, the proposed event-triggered scheme can lead to significant gains, both in terms of communication savings and disturbance attenuation, compared to periodic time-triggered policies, which is illustrated through a numerical example

Computing minimal and maximal allowable transmission intervals for networked control systems using the hybrid systems approach

International audienceA popular design framework for networked control systems (NCSs) is the emulation-based approach combined with hybrid systems analysis techniques. In the rich literature regarding this framework, bounds on the maximally allowable transmission interval (MATI) are provided to guarantee stability properties of the NCS, while the minimal allowable transmission interval (MIATI) is always taken to be (essentially) zero. In this letter, we show for the first time how knowledge of the MIATI can also be exploited in the hybrid systems/emulation-based framework leading to (guaranteed) higher values for the MATI, while still obtaining stability of the NCS

An Average Allowable Transmission Interval Condition for the Stability of Networked Control Systems

A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with Lyapunov-based analysis techniques for hybrid systems. In virtually all papers that use this framework, bounds in terms of the maximal allowable transmission interval (MATI) are provided to guarantee stability, and performance properties of the NCS. However, having only such a MATI condition is rather restrictive, and unrealistic in practice due to various network effects such as packet losses, leading to conservative bounds. In this article, we therefore consider an alternative condition on the communication instants to better capture the time-varying properties of the transmission intervals. In particular, we propose, in addition to the existence of a MATI, to also impose a bound on the average allowable transmission interval, expressed in terms of a reverse average dwell-time condition on the transmission intervals. We demonstrate by means of a novel Lyapunov-based analysis that stability of the NCS can still be guaranteed under this different condition on the transmission intervals, which can, in addition, lead to a significant improvement of the MATI. The strengths of these new results will be illustrated on a numerical example

A unified numerical scheme for linear-quadratic optimal control problems with joint control and state constraints

This paper presents a numerical scheme for solving the continuous-time convex linear-quadratic (LQ) optimal control problem with mixed polyhedral state and control constraints. Unifying a discretization of this optimal control problem as often employed in model predictive control and that obtained through time-stepping methods based on the differential variational inequality reformulation, the scheme solves a sequence of finite-dimensional convex quadratic programs (QPs) whose optimal solutions are employed to construct a sequence of discrete-time trajectories dependent on the time step. Under certain technical primal–dual assumptions primarily to deal with the algebraic constraints involving the state variable, we prove that such a numerical trajectory converges to an optimal trajectory of the continuous-time control problem as the time step goes to zero, with both the limiting optimal state and costate trajectories being absolutely continuous. This provides a constructive proof of the existence of a solution to the optimal control problem with such regularity properties. Additional properties of the optimal solutions to the LQ problem are also established that are analogous to those of the finite-dimensional convex QP. Our results are applicable to problems with convex but not necessarily strictly convex objective functions and with possibly unbounded mixed state–control constraints.

On the graphical stability of hybrid solutions with non-matching jump times

We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time mismatch is allowed between the jump times of neighbouring solutions and the ‘peaking phenomenon’ is avoided. We provide conditions such that this stability notion is implied by stability with respect to a specifically designed distance-like function. Hence, stability of solutions in the graphical sense can be analysed with existing Lyapunov techniques

P 23 Maternal vascular malperfusion in spontaneous preterm birth and outcome of subsequent pregnancy

INTRODUCTION Spontaneous preterm birth (SPTB) common complicates pregnancy. It has several causes and its pathophysiology has not yet been elucidated. In a significant proportion of SPTB, placental histology shows signs of maternal vascular malperfusion; these signs are commonly associated with hypertensive disorders of pregnancy (HD) or fetal growth restriction (FGR). Therefore, we hypothesized that women with a SPTB and signs of maternal vascular malperfusion in the placenta are at risk for HD and FGR in a subsequent pregnancy. OBJECTIVE The objective of this study was to describe the association between placental histology of SPTB and the incidence of HD and FGR in the subsequent pregnancy. MATERIALS AND METHODS We included women with a history of SPTB, and a subsequent ongoing pregnancy (n=110). Histological placental characteristics in the pregnancy complicated by SPTB were described according to new international guidelines, and related to the outcome of the subsequent pregnancy. RESULTS Delivery in the index pregnancy had a median gestational age of 27.7 weeks. In 61.8% (n=68) of the placentas signs of vascular malperfusion were observed. Maternal and respectively fetal inflammatory response was observed in 51.8 %(n=57) and 46.4% (n=51) and was observed as a secondary finding in 42.6% (n=29) and 36.8% (n=25) of the placentas with maternal vascular malperfusion. In the index pregnancy HD was present in 8.2% (n=9), and FGR in 10.9% (n=12). In the subsequent pregnancy HD was present in 12.7% (n=14) and FGR in 5.5 % (n=6). The incidence of HD or FGR in the subsequent pregnancy was not associated with histological signs of maternal vascular malperfusion in the index pregnancy. CONCLUSION Women with a history of SPTB have an elevated risk on hypertensive diseases in the subsequent pregnancy, when compared to epidemiologic data on the incidence of HD in women with a prior term birth. The incidence of HD was not associated with of the presence of placental maternal vascular malperfusion in the index pregnancy. This data suggest that signs of maternal vascular malperfusion by placental histology in SPTB cannot be used as a marker for adverse outcome in a subsequent pregnancy