A synthesis approach to predictive control for networked control systems

This paper studies a synthesis approach to predictive control for networked control systems with data loss and quantization. An augmented Markov jump linear model with polytopic uncertainties is modeled to describe the quantization errors and possible data loss. Based on this model, a predictive control synthesis approach is developed, which involves online optimization of a infinite horizon objective and conditions to deal with system constraints. The proposed MPC algorithm guarantees closed-loop mean-square stability and constraints satisfaction. © 2014 TCCT, CAA.postprin

Reliable controllable sets for constrained Markov-Jump Linear Systems

Robust λ-contractive sets have been proposed in previous literature for uncertain polytopic linear systems. It is well known that, if initial state is inside such sets, it is guaranteed to converge to the origin. This work presents the generalization of such concepts to systems whose behaviour changes among different linear models with probability given by a Markov chain. We propose sequence-dependent sets and associated controllers that can ensure a reliability bound when initial conditions are outside the maximal λ-contractive set. Such reliability bound will be understood as the probability of actually reaching the origin from a given initial condition without violating constraints. As initial conditions are further away from the origin, the likelihood of reaching the origin decreasesThis work has been supported by projects DPI2011-27845-C02-01, DPI2011-27845-C02-02 and FPU grant FPU12/02107, both from the Spanish Government.Hernández Mejías, MA.; Sala Piqueras, A.; Arino, C.; Querol, A. (2016). Reliable controllable sets for constrained Markov-Jump Linear Systems. International Journal of Robust and Nonlinear Control. 26(10):2075-2089. https://doi.org/10.1002/rnc.3394S20752089261

Mode-independent H2-control of a DC motor modeled as a Markov jump linear system

This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H2 -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that of a previous design, and its usefulness is illustrated by an application that considers the velocity control of a DC motor device subject to abrupt failures that is modeled as an MJLS

Adaptive Controller Placement for Wireless Sensor-Actuator Networks with Erasure Channels

Wireless sensor-actuator networks offer flexibility for control design. One novel element which may arise in networks with multiple nodes is that the role of some nodes does not need to be fixed. In particular, there is no need to pre-allocate which nodes assume controller functions and which ones merely relay data. We present a flexible architecture for networked control using multiple nodes connected in series over analog erasure channels without acknowledgments. The control architecture proposed adapts to changes in network conditions, by allowing the role played by individual nodes to depend upon transmission outcomes. We adopt stochastic models for transmission outcomes and characterize the distribution of controller location and the covariance of system states. Simulation results illustrate that the proposed architecture has the potential to give better performance than limiting control calculations to be carried out at a fixed node.Comment: 10 pages, 8 figures, to be published in Automatic

Receding-horizon switched linear system design: a semidefinite programming approach with distributed computation

This dissertation presents a framework for analysis and controller synthesis problems for switched linear systems. These are multi-modal systems whose parameters vary within a finite set according to the state of a discrete time automaton; the switching signal may be unconstrained or may be drawn from a language of admissible switching signals. This model of system dynamics and discrete logic has many applications in a number of engineering contexts. A receding-horizon type approach is taken by designing controllers with access to a finite-length preview of future modes and finite memory of past modes; the length of both preview and memory are taken as design choices. The results developed here take the form of nested sequences of SDP feasibility problems. These conditions are exact in that the feasibility of any element of the sequence is sufficient to construct a suitable controller, while the existence of a suitable controller necessitates the feasibility of some element of the sequence. Considered first is the problem of controller synthesis for the stabilization of switched systems. These developments serve both as a control problem of interest and a demonstration of the methods used to solve subsequent switched control problems. Exact conditions for the existence of a controller are developed, along with converse results which rule out levels of closed-loop stability based on the infeasibility of individual SDP problems. This permits the achievable closed-loop performance level to be approximated to arbitrary accuracy. Examined next are two different performance problems: one of disturbance attenuation and one of windowed variance. For each problem, controller synthesis conditions are presented exactly in the form of SDP feasibility problems which may be optimized to determine levels of performance. In both cases, the performance level may be taken as uniform or allowed to vary based on the switching path encountered. The controller synthesis conditions presented here can grow both large and computationally intensive, but they share a common structural sparsity which may be exploited. The last part of this dissertation examines this structure and presents a distributed approach to solving such problems. This maintains the tractability of these results even at large scales, expanding the scope of systems to which these methods can be applied

The Einstein Relation on Metric Measure Spaces

This note is based on F. Burghart's master thesis at Stuttgart university from July 2018, supervised by Prof. Freiberg. We review the Einstein relation, which connects the Hausdorff, local walk and spectral dimensions on a space, in the abstract setting of a metric measure space equipped with a suitable operator. This requires some twists compared to the usual definitions from fractal geometry. The main result establishes the invariance of the three involved notions of fractal dimension under bi-Lipschitz continuous isomorphisms between mm-spaces and explains, more generally, how the transport of the analytic and stochastic structure behind the Einstein relation works. While any homeomorphism suffices for this transport of structure, non-Lipschitz maps distort the Hausdorff and the local walk dimension in different ways. To illustrate this, we take a look at H\"older regular transformations and how they influence the local walk dimension and prove some partial results concerning the Einstein relation on graphs of fractional Brownian motions. We conclude by giving a short list of further questions that may help building a general theory of the Einstein relation.Comment: 28 pages, 3 figure