Iven Mareels

An observer looks at synchronization

In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory,.

Putting energy back in control

Energy is one of the fundamental concepts in science and engineering practice, where it is common to view dynamical systems as energy-transformation devices. This perspective is particularly useful in studying complex nonlinear systems by decomposing them into simpler subsystems that, upon interconnection, add up their energies to determine the full systems behavior. The action of a controller may also be understood in energy terms as another dynamical system. The control problem can then be recast as finding a dynamical system and an interconnection pattern such that the overall energy function takes the desired form. This energy-shaping approach is the essence of passivity-based control (PBC), a controller design technique that is very well known in mechanical systems. Our objectives in the article are threefold. First, to call attention to the fact that PBC does not rely on some particular structural properties of mechanical systems, but hinges on the more fundamental (and universal) property of energy balancing. Second, to identify the physical obstacles that hamper the use of standard PBC in applications other than mechanical systems. In particular, we show that standard PBC is stymied by the presence of unbounded energy dissipation, hence it is applicable only to systems that are stabilizable with passive controllers. Third, to revisit a PBC theory that has been developed to overcome the dissipation obstacle as well as to make the incorporation of process prior knowledge more systematic. These two important features allow us to design energy-based controllers for a wide range of physical systems.

A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.

On non-local stability properties of extremum seeking control

In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.

Topological feedback entropy and Nonlinear stabilization

It is well known in the field of dynamical systems that entropy can be defined rigorously for completely deterministic open-loop systems. However, such definitions have found limited application in engineering, unlike Shannons statistical entropy. In this paper, it is shown that the problem of communication-limited stabilization is related to the concept of topological entropy, introduced by Adler et al. as a measure of the information rate of a continuous map on a compact topological space. Using similar open cover techniques, the notion of topological feedback entropy (TFE) is defined in this paper and proposed as a measure of the inherent rate at which a map on a noncompact topological space with inputs generates stability information. It is then proven that a topological dynamical plant can be stabilized into a compact set if and only if the data rate in the feedback loop exceeds the TFE of the plant on the set. By taking appropriate limits in a metric space, the concept of local TFE (LTFE) is defined at fixed points of the plant, and it is shown that the plant is locally uniformly asymptotically stabilizable to a fixed point if and only if the data rate exceeds the plant LTFE at the fixed point. For continuously differentiable plants in Euclidean space, real Jordan forms and volume partitioning arguments are then used to derive an expression for LTFE in terms of the unstable eigenvalues of the fixed point Jacobian.

Stability theory for differential/algebraic systems with application to power systems

Motivated by transient stability analysis of power systems, a framework for study of Lyapunov stability of equilibria in differential/algebraic (DA) systems is presented. Following a basic result on existence and uniqueness of solutions, it is easy to state general stability results. Several useful stability criteria for special DA structures are derived. One result for a Hamiltonian-type structure is applied to the study of undamped power systems. >

Control of Large-Scale Irrigation Networks

Irrigation networks of open-water channels are used throughout the world to support agricultural activity. By and large, these networks are managed in open loop. To achieve closed-loop water distribution management, it is necessary to augment these civil engineering systems with an appropriate information infrastructure-sensors, actuators, information processing, and communication resources. Recent pilot projects in Australia demonstrate the significant potential of closed-loop management, which can yield a significant improvement in the quality of service, while achieving improved water distribution efficiency. This paper focuses on the modelling and closed-loop control of open-water channels from the perspective of large-scale irrigation network management. Several feedback information structures are discussed and the key design tradeoffs identified

A unifying framework for global regulation via nonlinear output feedback: from ISS to iISS

This paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input-to-state stable inverse dynamics, subject to possibly unknown control direction. The contribution of the paper is two-fold. Firstly, we consider the problem of global regulation, instead of global asymptotic stabilization (GAS), for systems with generalized dynamic uncertainties. It is shown by an elementary example that GAS is not solvable using conventional smooth output feedback. Secondly, we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system. Using our framework, most of the known classes of output feedback form systems are broadened in several directions: unmeasured states and unknown parameters can appear nonlinearly, restrictive matching and growth assumptions are removed, the dynamic uncertainty satisfies the weaker condition of Sontags integral input-to-state stability, and the sign of high-frequency gain may be unknown. A constructive strategy is proposed to design a dynamic output feedback control law, that drives the state to the origin while keeping all other closed-loop signals bounded.

An efficient brute-force solution to the network reconfiguration problem

The authors suggest a method for determining a minimal-loss radial configuration for a power distribution network, using an exhaustive search algorithm. While exhaustive, the method is highly efficient, deriving its efficiency from the use of graph-theoretic techniques involving semi-sparse transformations of a current sensitivity matrix. The algorithm can he applied to networks of moderate size and has advantages over existing algorithms for network reconfiguration in that it guarantees a globally optimal solution (under appropriate modeling assumptions), and is easily extended to take account of phase imbalance and network operation constraints. A 33-bus example is used to demonstrate the operation of the algorithm.

High Performance Control

Performance enhancement stabilizing controllers design environment off-line controller design iterated and nested (S, Q) design direct adaptive-Q control indirect (S, Q) adaptive control adaptive-Q application to non-linear systems real-time implementation laboratory case studies.