Sequential Synthesis of Distributed Controllers for Cascade Interconnected Systems

We consider the problem of designing distributed controllers to ensure passivity of a large-scale interconnection of linear subsystems connected in a cascade topology. The control design process needs to be carried out at the subsystem-level with no direct knowledge of the dynamics of other subsystems in the interconnection. We present a distributed approach to solve this problem, where subsystem-level controllers are locally designed in a sequence starting at one end of the cascade using only the dynamics of the particular subsystem, coupling with the immediately preceding subsystem and limited information from the preceding subsystem in the cascade to ensure passivity of the interconnected system up to that point. We demonstrate that this design framework also allows for new subsystems to be compositionally added to the interconnection without requiring redesign of the pre-existing controllers.Comment: Accepted to appear in the proceedings of the American Control Conference (ACC) 201

Interpolatory Methods for Generic BizJet Gust Load Alleviation Function

The paper's main contribution concerns the use of interpolatory methods to solve end to end industrial control problems involving complex linear dynamical systems. More in details, contributions show how the rational data and function interpolation framework is a pivotal tool (i) to construct (frequency-limited) reduced order dynamical models appropriate for model-based control design and (ii) to accurately discretise controllers in view of on-board computer-limited implementation. These contributions are illustrated along the paper through the design of an active feedback gust load alleviation function, applied on an industrial generic business jet aircraft use-case. The closed-loop validation and performances evaluation are assessed through the use of an industrial dedicated simulator and considering certification objectives. Although application is centred on aircraft applications, the method is not restrictive and can be extended to any linear dynamical systems.Comment: 23 pages, 9 figures, submitted to journa

Strong iISS: combination of iISS and ISS with respect to small inputs

International audienceThis paper studies the notion of Strong iISS, which imposes both integral input-to-state stability (iISS) and input-to-state stability (ISS) with respect to small inputs. This combination characterizes the robustness property, exhibited by many practical systems, that the state remains bounded as long as the magnitude of exogenous inputs is reasonably small but may diverge for stronger disturbances. We provide three Lyapunov-type sufficient conditions for Strong iISS. One is based on iISS Lyapunov functions admitting a radially non- vanishing (class K) dissipation rate. However we show that it is not a necessary condition for Strong iISS. Two less conservative conditions are then provided, which are used to demonstrate that asymptotically stable bilinear systems are Strongly iISS. Finally, we discuss cascade and feedback interconnections of Strong iISS systems

Stability and Performance Verification of Optimization-based Controllers

This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the $\mathcal{L}_2$ gain. The method applies to a wide range of practical control problems: For instance, a dynamical controller (e.g., a PID) plus input saturation, model predictive control with state estimation, inexact model and soft constraints, or a general optimization-based controller where the underlying problem is solved with a fixed number of iterations of a first-order method are all amenable to the proposed approach. The approach is based on the observation that the control input generated by an optimization-based controller satisfies the associated Karush-Kuhn-Tucker (KKT) conditions which, provided all data is polynomial, are a system of polynomial equalities and inequalities. The closed-loop properties can then be analyzed using sum-of-squares (SOS) programming